Metrics for Falkner and Boettcher, Equation (22+)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze4.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample1.1s (13.2%)

Memory

-2.4MiB live, 1 975.0MiB allocated

Samples

794.0ms	8 256×	0	valid
1.0ms	12×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 618.0ms

ival-mult: 281.0ms (45.5% of total)

ival-sub: 115.0ms (18.6% of total)

ival-pi: 74.0ms (12% of total)

ival-sqrt: 64.0ms (10.4% of total)

ival-div: 59.0ms (9.6% of total)

exact: 16.0ms (2.6% of total)

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

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

Bogosity

explain671.0ms (8%)

Memory

4.3MiB live, 324.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 3 binary64)`
-	-	`(*.f64 v v)`
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 4 binary64)`
-	-	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
-	-	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
-	-	`(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))`
-	-	`(*.f64 #s(literal 3 binary64) (PI.f64))`
-	-	`#s(literal 6 binary64)`
-	-	`v`
-	-	`#s(literal 2 binary64)`
-	-	`(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))`
-	-	`(.f64 #s(literal 6 binary64) (.f64 v v))`
-	-	`(-.f64 #s(literal 1 binary64) (*.f64 v v))`
-	-	`(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))`
-	-	`(PI.f64)`

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

188.0ms

512×

valid

Compiler

Compiled 195 to 52 computations (73.3% saved)

Precisions

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

ival-mult: 14.0ms (38.5% of total)

ival-div: 10.0ms (27.5% of total)

ival-sub: 5.0ms (13.7% of total)

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

ival-pi: 2.0ms (5.5% of total)

exact: 1.0ms (2.7% of total)

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

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

preprocess318.0ms (3.8%)

Memory

12.4MiB live, 167.4MiB allocated

Algorithm

1×	egg-herbie

Rules

4 898×	`lower-fma.f64`
4 898×	`lower-fma.f32`
2 702×	`lower-*.f32`
2 692×	`lower-*.f64`
1 796×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	59	37
2	176	36
3	654	36
4	2038	36
5	4182	36
6	6384	36
7	7270	36
0	16	20
0	26	20
1	51	18
2	118	18
3	318	18
4	896	18
5	1509	18
6	2857	18
7	5680	18
8	7756	18
0	8271	16

Stop Event

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

Calls

Call 1

Inputs

(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))

Outputs

(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))

(/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))

Symmetry

(abs v)

Compiler

Compiled 21 to 16 computations (23.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Status

Accuracy

Program

▶

98.5%

(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify224.0ms (2.7%)

Memory

-15.9MiB live, 104.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
cost-diff	128	(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
cost-diff	128	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
cost-diff	320	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Rules

4 898×	`lower-fma.f64`
4 898×	`lower-fma.f32`
2 702×	`lower-*.f32`
2 692×	`lower-*.f64`
1 796×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	85
0	26	85
1	51	83
2	118	83
3	318	83
4	896	83
5	1509	83
6	2857	83
7	5680	83
8	7756	83
0	8271	76

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
#s(literal 6 binary64)

Outputs
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
(.f64 (.f64 v v) #s(literal 6 binary64))
#s(literal 6 binary64)

localize38.0ms (0.4%)

Memory

33.0MiB live, 33.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
accuracy	0.0234375	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
accuracy	0.162441259768442	(.f64 #s(literal 6 binary64) (.f64 v v))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Samples

23.0ms

256×

valid

Compiler

Compiled 87 to 18 computations (79.3% saved)

Precisions

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

ival-mult: 7.0ms (49.8% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

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

series39.0ms (0.5%)

Memory

-30.7MiB live, 7.7MiB allocated

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))>
#<alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))>
#<alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))>
#<alt (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))>
#<alt (.f64 #s(literal 6 binary64) (.f64 v v))>
#<alt (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))>

Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>

Calls

18 calls:

Time	Variable		Point	Expression
30.0ms	v	@	0	(* (* 3 (PI)) (- 1 (* v v)))
2.0ms	v	@	inf	(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
2.0ms	v	@	0	(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
1.0ms	v	@	0	(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))
1.0ms	v	@	inf	(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))

simplify344.0ms (4.1%)

Memory

43.2MiB live, 347.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 354×	`lower-fma.f64`
15 354×	`lower-fma.f32`
6 176×	`lower-+.f64`
6 176×	`lower-+.f32`
5 400×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	241	1610
1	747	1426
2	2954	1351
0	8247	1301

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))

Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(.f64 #s(literal 4/3 binary64) (fma.f64 (fma.f64 v (/.f64 (.f64 v #s(literal 27/16 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(fma.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 (.f64 v v) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 27/8 binary64) (PI.f64)) (/.f64 #s(literal 135/16 binary64) (PI.f64)))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (/.f64 #s(literal 9/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (PI.f64) (.f64 v (.f64 v v))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal 4/3 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/27 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (.f64 v v))) (.f64 v (.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (.f64 v (.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v))) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64))) (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (.f64 v (*.f64 v v)))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (PI.f64) (.f64 v (.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal 4/3 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/27 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (.f64 v v))) (neg.f64 (.f64 v (.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (neg.f64 (.f64 v (.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v))) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64))) (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (neg.f64 (.f64 v (*.f64 v v))))
(* 3 (PI))
(*.f64 (PI.f64) #s(literal 3 binary64))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(* -3 (* (pow v 2) (PI)))
(.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* -3 (* (pow v 2) (PI)))
(.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* -6 (pow v 2))
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* 3 (* (PI) (sqrt 2)))
(.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(.f64 #s(literal 3 binary64) (fma.f64 (.f64 v v) (.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(.f64 #s(literal 3 binary64) (fma.f64 (fma.f64 (.f64 v v) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/4 binary64)) (.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 v v) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(fma.f64 (.f64 v v) (.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 (.f64 v v) (fma.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 9/4 binary64) (/.f64 (.f64 (PI.f64) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/4 binary64))) (.f64 v v)))) (.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v (.f64 v v)) (.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 3 binary64) (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v (.f64 v v)) (.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 3 binary64)))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64))))) (neg.f64 (.f64 v (.f64 v v))))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 #s(literal -27/2 binary64) (/.f64 (*.f64 v v) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))))
(* -1 (* v (sqrt -6)))
(neg.f64 (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(neg.f64 (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 v (neg.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))))

rewrite444.0ms (5.3%)

Memory

-6.9MiB live, 394.2MiB allocated

Rules

4 770×	`lower-*.f32`
4 760×	`lower-*.f64`
4 634×	`lower-fma.f64`
4 634×	`lower-fma.f32`
2 134×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	67
0	26	67
1	101	65
2	626	65
3	5771	65
0	8439	58

Stop Event

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

Counts

6 → 487

Calls

Call 1

Inputs
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 #s(literal 6 binary64) (.f64 v v))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))) #s(literal 3/4 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
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(.f64 (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64))) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (.f64 (cbrt.f64 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))) #s(literal 3 binary64))
(.f64 (neg.f64 (.f64 (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))) #s(literal -3 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))) (.f64 #s(literal 3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (neg.f64 (.f64 (PI.f64) #s(literal -3 binary64))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))) (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)) (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64)))) (PI.f64))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 #s(literal 3 binary64) (PI.f64)))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 3 binary64) (cbrt.f64 (PI.f64))))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (sqrt.f64 (PI.f64))) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (fma.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))) (/.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (.f64 v (*.f64 v #s(literal 6 binary64))))
(.f64 v (.f64 v #s(literal 6 binary64)))
(.f64 (.f64 v v) #s(literal 6 binary64))
(.f64 #s(literal 6 binary64) (.f64 v v))
(.f64 (.f64 v (*.f64 v #s(literal 6 binary64))) #s(literal 1 binary64))
(.f64 (.f64 v #s(literal 6 binary64)) v)
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 (log.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (*.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) (-.f64 (.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -8 binary64) (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -4 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (*.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64)))) #s(literal -1 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (pow.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (pow.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))

eval143.0ms (1.7%)

Memory: 4.7MiB live, 161.9MiB allocated
Compiler: Compiled 16 895 to 1 901 computations (88.7% saved)

prune136.0ms (1.6%)

Memory

-6.1MiB live, 153.6MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	551	8	559
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	552	8	560

Accuracy

100.0%

Counts

560 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
	46.3%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
	97.4%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
▶	98.8%	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
▶	97.3%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
▶	97.7%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))

Compiler

Compiled 322 to 224 computations (30.4% saved)

simplify214.0ms (2.6%)

Memory

-45.4MiB live, 189.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
cost-diff	0	(fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
cost-diff	0	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
cost-diff	640	(.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
cost-diff	0	(*.f64 #s(literal 3 binary64) (PI.f64))
cost-diff	0	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
cost-diff	128	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
cost-diff	320	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
cost-diff	0	(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
cost-diff	0	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
cost-diff	0	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
cost-diff	0	(.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
cost-diff	128	(.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))
cost-diff	320	(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
cost-diff	1984	(fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))

Rules

5 892×	`lower-fma.f32`
5 882×	`lower-fma.f64`
3 700×	`lower-*.f32`
3 668×	`lower-*.f64`
2 490×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	426
0	93	444
1	183	429
2	412	393
3	1259	391
4	2359	390
5	4108	386
6	6444	386
0	8104	376

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
#s(literal 4 binary64)
(fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(PI.f64)
(.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (*.f64 v v))))
(.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))
(neg.f64 (*.f64 v v))
(*.f64 v v)
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 4/3 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
#s(literal 4/3 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(PI.f64)
(fma.f64 v v #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
#s(literal 4/3 binary64)
(fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
v
(/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(*.f64 v #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(fma.f64 v v #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))

Outputs
(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal -4/3 binary64) (.f64 (fma.f64 v v #s(literal -1 binary64)) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) (PI.f64))))
#s(literal 4 binary64)
(fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))
(.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(PI.f64)
(.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64))))
(.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (*.f64 v v))))
(.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))
(.f64 (.f64 v v) #s(literal -3 binary64))
(neg.f64 (*.f64 v v))
(*.f64 v v)
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 4/3 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (fma.f64 v (*.f64 v (PI.f64)) (PI.f64))))
#s(literal 4/3 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (fma.f64 v (*.f64 v (PI.f64)) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(fma.f64 v (*.f64 v (PI.f64)) (PI.f64))
(PI.f64)
(fma.f64 v v #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal -4/3 binary64) (.f64 (fma.f64 v v #s(literal -1 binary64)) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) (PI.f64))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 v v) #s(literal 4/3 binary64) #s(literal 4/3 binary64)) (/.f64 (.f64 v v) (sqrt.f64 #s(literal 1/2 binary64)))) (PI.f64)))
(.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 v v) #s(literal 4/3 binary64) #s(literal 4/3 binary64)) (/.f64 (.f64 v v) (sqrt.f64 #s(literal 1/2 binary64)))) (PI.f64))
#s(literal 4/3 binary64)
(fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
v
(/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 v #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(fma.f64 v v #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))

localize219.0ms (2.6%)

Memory

20.7MiB live, 221.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
accuracy	0.30697250976844204	(/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
accuracy	0.5063258307454339	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
accuracy	1.0	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
accuracy	0.0078125	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0.0078125	(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
accuracy	0.0234375	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
accuracy	0.0078125	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
accuracy	0.0078125	(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
accuracy	0.0078125	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
accuracy	0.01171875	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0	(PI.f64)
accuracy	0.7467967762008296	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
accuracy	1.0	(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
accuracy	0.22169877930532605	(.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
accuracy	0.98046875	(.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
accuracy	0.98828125	(fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))

Samples

105.0ms

256×

valid

Compiler

Compiled 427 to 54 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-mult: 30.0ms (37.1% of total)

ival-add: 26.0ms (32.1% of total)

ival-div: 10.0ms (12.4% of total)

ival-sqrt: 7.0ms (8.7% of total)

const: 4.0ms (4.9% of total)

ival-sub: 2.0ms (2.5% of total)

ival-pi: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

series32.0ms (0.4%)

Memory

-19.8MiB live, 60.0MiB allocated

Counts

26 → 240

Calls

Call 1

Inputs
#<alt (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))>
#<alt (/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))>
#<alt (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))>
#<alt (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))>
#<alt #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))>
#<alt (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))>
#<alt (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))>
#<alt (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))>
#<alt (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))>
#<alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))>
#<alt (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal 3 binary64) (PI.f64))>
#<alt (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))>
#<alt #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))>
#<alt (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))>
#<alt (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))>
#<alt (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))>
#<alt (PI.f64)>
#<alt (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))>
#<alt (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))>
#<alt (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))>
#<alt (*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))>

Outputs
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (+ (* -3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (+ (* -3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* 9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (PI) (pow (sqrt 2) 5))) (* 27/2 (/ (PI) (pow (sqrt 2) 3))))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))))))>
#<alt (/ 4/3 (* (PI) (sqrt 2)))>
#<alt (+ (* -4/9 (/ (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))) (* (pow (PI) 2) (pow (sqrt 2) 2)))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))>
#<alt (+ (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2))))))) (* 4/9 (/ (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))>
#<alt (+ (* (pow v 2) (- (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -1/3 (/ (* (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* (PI) (sqrt 2)))) (+ (* -4/27 (/ (* (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -81/2 (/ (PI) (pow (sqrt 2) 5))) (* 27/2 (/ (PI) (pow (sqrt 2) 3)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))))) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2))))))) (* 4/9 (/ (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))>
#<alt (/ -4/3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (/ (- (* -4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6))))) (pow v 3))>
#<alt (/ (- (* -1 (/ (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (pow v 4))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))) (pow v 3))>
#<alt (/ (- (* -1 (/ (+ (* 4/27 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6))))) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (+ (* 1/3 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (* (PI) (sqrt -6)))) (* 4/9 (/ (+ (* -3/2 (/ (PI) (pow (sqrt -6) 3))) (* -3/2 (/ (PI) (pow (sqrt -6) 5)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (pow v 6))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow v 4) (* (pow (PI) 3) (pow (sqrt -6) 3))))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (+ (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow v 4) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))))) (pow v 3))>
#<alt (/ 4/3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (/ (- (* -4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6))))) (pow v 3)))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (pow v 4))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))) (pow v 3)))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* 4/27 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6))))) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (+ (* 1/3 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (* (PI) (sqrt -6)))) (* 4/9 (/ (+ (* -3/2 (/ (PI) (pow (sqrt -6) 3))) (* -3/2 (/ (PI) (pow (sqrt -6) 5)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (pow v 6))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow v 4) (* (pow (PI) 3) (pow (sqrt -6) 3))))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (+ (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow v 4) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))))) (pow v 3)))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* 3 (sqrt 2))>
#<alt (+ (* -9 (/ (pow v 2) (sqrt 2))) (* 3 (sqrt 2)))>
#<alt (+ (* 3 (sqrt 2)) (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 9 (/ 1 (sqrt 2))))))>
#<alt (+ (* 3 (sqrt 2)) (* (pow v 2) (- (* (pow v 2) (- (* -81/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 27/2 (/ 1 (pow (sqrt 2) 3))))) (* 9 (/ 1 (sqrt 2))))))>
#<alt (* 3 (* v (sqrt -6)))>
#<alt (* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -3 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))>
#<alt (* (PI) (sqrt 2))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))>
#<alt (* (pow v 3) (* (PI) (sqrt -6)))>
#<alt (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))>
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#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (/ (sqrt 1/2) (PI))>
#<alt (+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))>
#<alt (+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))>
#<alt (+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))>
#<alt (/ (* (pow v 2) (sqrt 1/2)) (PI))>
#<alt (* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))>
#<alt (* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))>
#<alt (* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))>
#<alt (/ (* (pow v 2) (sqrt 1/2)) (PI))>
#<alt (* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))>
#<alt (* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))>
#<alt (* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))>

Calls

60 calls:

Time	Variable		Point	Expression
3.0ms	v	@	inf	(/ (* v 3/4) (* (sqrt 1/2) (PI)))
3.0ms	v	@	-inf	(+ (* (* 3 (sqrt (+ (* v (* v -6)) 2))) (PI)) (* (* (PI) (* 3 (neg (* v v)))) (sqrt (+ (* v (* v -6)) 2))))
2.0ms	v	@	inf	(sqrt (+ (* (* v v) -6) 2))
2.0ms	v	@	0	(+ (* (* 3 (sqrt (+ (* v (* v -6)) 2))) (PI)) (* (* (PI) (* 3 (neg (* v v)))) (sqrt (+ (* v (* v -6)) 2))))
2.0ms	v	@	inf	(/ 4 (+ (* (* 3 (sqrt (+ (* v (* v -6)) 2))) (PI)) (* (* (PI) (* 3 (neg (* v v)))) (sqrt (+ (* v (* v -6)) 2)))))

simplify334.0ms (4%)

Memory

17.5MiB live, 522.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 918×	`lower-fma.f64`
11 918×	`lower-fma.f32`
7 022×	`lower-*.f64`
7 022×	`lower-*.f32`
4 248×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	580	7293
1	1956	6479
0	8352	6211

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (+ (* -3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (+ (* -3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* 9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (PI) (pow (sqrt 2) 5))) (* 27/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))))))
(/ 4/3 (* (PI) (sqrt 2)))
(+ (* -4/9 (/ (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))) (* (pow (PI) 2) (pow (sqrt 2) 2)))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))
(+ (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2))))))) (* 4/9 (/ (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))
(+ (* (pow v 2) (- (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -1/3 (/ (* (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* (PI) (sqrt 2)))) (+ (* -4/27 (/ (* (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -81/2 (/ (PI) (pow (sqrt 2) 5))) (* 27/2 (/ (PI) (pow (sqrt 2) 3)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))))) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2))))))) (* 4/9 (/ (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))
(/ -4/3 (* (pow v 3) (* (PI) (sqrt -6))))
(/ (- (* -4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6))))) (pow v 3))
(/ (- (* -1 (/ (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (pow v 4))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))) (pow v 3))
(/ (- (* -1 (/ (+ (* 4/27 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6))))) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (+ (* 1/3 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (* (PI) (sqrt -6)))) (* 4/9 (/ (+ (* -3/2 (/ (PI) (pow (sqrt -6) 3))) (* -3/2 (/ (PI) (pow (sqrt -6) 5)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (pow v 6))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow v 4) (* (pow (PI) 3) (pow (sqrt -6) 3))))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (+ (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow v 4) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))))) (pow v 3))
(/ 4/3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (/ (- (* -4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6))))) (pow v 3)))
(* -1 (/ (- (* -1 (/ (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (pow v 4))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))) (pow v 3)))
(* -1 (/ (- (* -1 (/ (+ (* 4/27 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6))))) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (+ (* 1/3 (/ (* (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow (PI) 3) (pow (sqrt -6) 3)))) (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (* (PI) (sqrt -6)))) (* 4/9 (/ (+ (* -3/2 (/ (PI) (pow (sqrt -6) 3))) (* -3/2 (/ (PI) (pow (sqrt -6) 5)))) (* (pow (PI) 2) (pow (sqrt -6) 2)))))) (pow v 6))) (+ (* 4/27 (/ (pow (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) 2) (* (pow v 4) (* (pow (PI) 3) (pow (sqrt -6) 3))))) (+ (* 4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (+ (* 4/9 (/ (+ (* 3/2 (/ (PI) (pow (sqrt -6) 3))) (* 3 (/ (PI) (sqrt -6)))) (* (pow v 4) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6)))))))) (pow v 3)))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* 3 (sqrt 2))
(+ (* -9 (/ (pow v 2) (sqrt 2))) (* 3 (sqrt 2)))
(+ (* 3 (sqrt 2)) (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 9 (/ 1 (sqrt 2))))))
(+ (* 3 (sqrt 2)) (* (pow v 2) (- (* (pow v 2) (- (* -81/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 27/2 (/ 1 (pow (sqrt 2) 3))))) (* 9 (/ 1 (sqrt 2))))))
(* 3 (* v (sqrt -6)))
(* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6))))))
(* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -3 (* v (sqrt -6)))
(* -1 (* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))
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(* (PI) (sqrt 2))
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(* (pow v 3) (* (PI) (sqrt -6)))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
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(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
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(sqrt 2)
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(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
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2
(+ 2 (* -6 (pow v 2)))
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(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
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(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
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(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
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(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (PI))
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(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
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(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
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(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
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(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))
(* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* 4/3 (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* 4/3 (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* 4/3 (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))
(* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* 4/3 (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* 4/3 (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* 4/3 (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
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(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
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(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(/ (sqrt 1/2) (PI))
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(* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))
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(* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI))))))
(* 3/4 (/ v (* (PI) (sqrt 1/2))))
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(* 3/4 (/ v (* (PI) (sqrt 1/2))))
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(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* -3 (/ (PI) (* (pow v 2) (sqrt -6))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))))
(PI)
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(/ (sqrt 1/2) (PI))
(+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))
(+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))
(+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))
(/ (* (pow v 2) (sqrt 1/2)) (PI))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(/ (* (pow v 2) (sqrt 1/2)) (PI))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))

Outputs
(* 3 (* (PI) (sqrt 2)))
(.f64 #s(literal 3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))))
(.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (-.f64 (/.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (+ (* -3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))))))))
(fma.f64 #s(literal 3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 v v) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 v v) (fma.f64 #s(literal -27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (+ (* -3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* 9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (PI) (pow (sqrt 2) 5))) (* 27/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 #s(literal -27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 v v) (fma.f64 #s(literal 27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -81/2 binary64) (PI.f64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) (/.f64 (.f64 #s(literal 9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v v) (.f64 v (.f64 #s(literal -3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))
(.f64 v (.f64 (.f64 v v) (fma.f64 #s(literal 3 binary64) (/.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (/.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v v)) (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (pow.f64 v #s(literal 4 binary64))))) (/.f64 (.f64 #s(literal 3/2 binary64) (PI.f64)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64))))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2))))))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 (PI.f64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (fma.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (/.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v v)) (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (pow.f64 v #s(literal 4 binary64))))) (/.f64 (.f64 #s(literal 3/2 binary64) (PI.f64)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64)))))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v (.f64 v v)) (.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))) (neg.f64 (.f64 v (.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(.f64 (.f64 v (.f64 v v)) (neg.f64 (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (/.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v v)) (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (pow.f64 v #s(literal 4 binary64))))) (/.f64 (.f64 #s(literal 3/2 binary64) (PI.f64)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64)))))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (/ (PI) (* (pow v 4) (sqrt -6)))) (* 3 (/ (* (PI) (sqrt -6)) (pow v 2)))))))))))
(.f64 (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 (PI.f64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (fma.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (/.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v v)) (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (pow.f64 v #s(literal 4 binary64))))) (/.f64 (.f64 #s(literal 3/2 binary64) (PI.f64)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64)))))))) (neg.f64 (.f64 v (*.f64 v v))))
(/ 4/3 (* (PI) (sqrt 2)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* -4/9 (/ (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))) (* (pow (PI) 2) (pow (sqrt 2) 2)))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))
(fma.f64 #s(literal -2/9 binary64) (/.f64 (.f64 (.f64 v v) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 4/3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2))))))) (* 4/9 (/ (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))
(fma.f64 (.f64 v v) (neg.f64 (fma.f64 (.f64 v v) (fma.f64 #s(literal 2/9 binary64) (/.f64 (fma.f64 #s(literal -27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (PI.f64))) (/.f64 (.f64 (.f64 #s(literal -4/27 binary64) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))))) (.f64 #s(literal 2/9 binary64) (/.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (PI.f64)))))) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* (pow v 2) (- (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -1/3 (/ (* (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* (PI) (sqrt 2)))) (+ (* -4/27 (/ (* (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2))))) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -81/2 (/ (PI) (pow (sqrt 2) 5))) (* 27/2 (/ (PI) (pow (sqrt 2) 3)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))))) (+ (* -4/27 (/ (pow (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) 2) (* (pow (PI) 3) (pow (sqrt 2) 3)))) (* 4/9 (/ (+ (* -27/2 (/ (PI) (pow (sqrt 2) 3))) (* 9 (/ (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2))))))) (* 4/9 (/ (+ (* -9 (/ (PI) (sqrt 2))) (* -3 (* (PI) (sqrt 2)))) (* (pow (PI) 2) (pow (sqrt 2) 2)))))) (* 4/3 (/ 1 (* (PI) (sqrt 2)))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (neg.f64 (fma.f64 (.f64 v v) (fma.f64 #s(literal -1/3 binary64) (/.f64 (.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 2/9 binary64) (/.f64 (fma.f64 #s(literal -27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (PI.f64))) (/.f64 (.f64 (.f64 #s(literal -4/27 binary64) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))))) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(literal -27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))))) #s(literal -4/27 binary64)) (.f64 #s(literal 2/9 binary64) (/.f64 (fma.f64 #s(literal 27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -81/2 binary64) (PI.f64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) (.f64 (PI.f64) (PI.f64)))))) (fma.f64 #s(literal 2/9 binary64) (/.f64 (fma.f64 #s(literal -27/4 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (PI.f64))) (/.f64 (.f64 (.f64 #s(literal -4/27 binary64) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))))))) (neg.f64 (.f64 #s(literal 2/9 binary64) (/.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -9 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (PI.f64)))))) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(/ -4/3 (* (pow v 3) (* (PI) (sqrt -6))))
(/.f64 #s(literal -4/3 binary64) (.f64 (.f64 v v) (.f64 v (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))))
(/ (- (* -4/9 (/ (+ (* -3 (/ (PI) (sqrt -6))) (* 3 (* (PI) (sqrt -6)))) (* (pow v 2) (* (pow (PI) 2) (pow (sqrt -6) 2))))) (* 4/3 (/ 1 (* (PI) (sqrt -6))))) (pow v 3))
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(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* -3 (/ (PI) (* (pow v 2) (sqrt -6))))))
(.f64 (.f64 (.f64 v (.f64 v v)) #s(literal -3 binary64)) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 (.f64 #s(literal 3/2 binary64) (PI.f64)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64)))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 #s(literal 3/2 binary64) (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64))))) (/.f64 (.f64 #s(literal -3/2 binary64) (PI.f64)) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v (.f64 v v)) (.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(neg.f64 (.f64 (.f64 (.f64 v (.f64 v v)) #s(literal -3 binary64)) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(.f64 (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 (.f64 #s(literal 3/2 binary64) (PI.f64)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64)))))) (neg.f64 (.f64 v (.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* -3 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))))
(.f64 (fma.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 #s(literal 3/2 binary64) (/.f64 (PI.f64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64))))) (/.f64 (.f64 #s(literal -3/2 binary64) (PI.f64)) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))) (neg.f64 (.f64 v (*.f64 v v))))
(PI)
(PI.f64)
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (PI.f64) (*.f64 v v) (PI.f64))
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (PI.f64) (*.f64 v v) (PI.f64))
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (PI.f64) (*.f64 v v) (PI.f64))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 #s(literal -9/4 binary64) (/.f64 (.f64 v v) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (-.f64 (/.f64 (.f64 #s(literal -27/2 binary64) (.f64 v v)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (/.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64))))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64)))))))))
(* -1 (* v (sqrt -6)))
(neg.f64 (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (/.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64))))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 #s(literal -6 binary64) (pow.f64 v #s(literal 4 binary64)))))))) (neg.f64 v))
(/ (sqrt 1/2) (PI))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
(+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))
(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))
(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(+ (/ (sqrt 1/2) (PI)) (/ (* (pow v 2) (sqrt 1/2)) (PI)))
(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/ (* (pow v 2) (sqrt 1/2)) (PI))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) v) v) (PI.f64))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (PI.f64) (.f64 v v)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (PI.f64) (.f64 v v)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (PI.f64) (.f64 v v)))))
(/ (* (pow v 2) (sqrt 1/2)) (PI))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) v) v) (PI.f64))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (PI.f64) (.f64 v v)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (PI.f64) (.f64 v v)))))
(* (pow v 2) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))
(.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (PI.f64) (.f64 v v)))))

rewrite375.0ms (4.5%)

Memory

18.7MiB live, 527.7MiB allocated

Rules

5 152×	`lower-*.f32`
5 120×	`lower-*.f64`
4 034×	`lower-/.f32`
4 022×	`lower-/.f64`
3 936×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	334
0	93	332
1	328	320
2	2137	320
0	8507	318

Stop Event

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

Counts

26 → 1 251

Calls

Call 1

Inputs
(fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))
(.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(*.f64 #s(literal 3 binary64) (PI.f64))
(.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(PI.f64)
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))

Outputs
(+.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64))))
(+.f64 (.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (.f64 v v)))))
(-.f64 (/.f64 (.f64 #s(literal 9 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))) (.f64 (PI.f64) (-.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(literal -3 binary64) (.f64 v v)))))) (/.f64 (.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (.f64 v v))))) (.f64 (PI.f64) (-.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(literal -3 binary64) (*.f64 v v)))))))
(fma.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (*.f64 v v)))))
(fma.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (.f64 v v))) (.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64))))
(fma.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(literal 3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (*.f64 v v)))))
(fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (*.f64 v v)))))
(fma.f64 (PI.f64) (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (*.f64 v v)))))
(fma.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(literal -3 binary64) (.f64 v v))) (.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64))))
(fma.f64 (.f64 #s(literal -3 binary64) (.f64 v v)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)) (.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64))))
(fma.f64 (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64))))
(fma.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64))))
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(/.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 v v #s(literal 1 binary64))) (PI.f64))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (*.f64 v v)) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (*.f64 v v)) (PI.f64)))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (*.f64 v v)) (neg.f64 (PI.f64))))
(/.f64 (.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 v v #s(literal -1 binary64)) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) (PI.f64)))
(/.f64 (.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (fma.f64 v v #s(literal -1 binary64)) (neg.f64 (PI.f64))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (*.f64 v v))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (.f64 v v) #s(literal -1 binary64))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 v v #s(literal -1 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64))) (.f64 (PI.f64) (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (*.f64 v v))))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 v v) (.f64 v v) #s(literal -1 binary64))) (.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64))) (.f64 (neg.f64 (PI.f64)) (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (*.f64 v v))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (.f64 v v) (.f64 v v) #s(literal -1 binary64))) (.f64 (neg.f64 (PI.f64)) (fma.f64 v v #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 v v #s(literal 1 binary64)))) (neg.f64 (PI.f64)))
(/.f64 (*.f64 (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (*.f64 (fma.f64 v v #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 (PI.f64)))
(/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64))) (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (.f64 v v)))
(/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (fma.f64 (.f64 v v) (*.f64 v v) #s(literal -1 binary64))) (fma.f64 v v #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (-.f64 (fma.f64 (.f64 v v) (.f64 v v) #s(literal 1 binary64)) (.f64 v v)))
(/.f64 (.f64 (fma.f64 (.f64 v v) (*.f64 v v) #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (fma.f64 v v #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 1 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (neg.f64 (PI.f64)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 v v #s(literal 1 binary64))) #s(literal 1 binary64)) (PI.f64))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 v v #s(literal 1 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 v v #s(literal 1 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (PI.f64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 v v #s(literal 1 binary64)))) #s(literal -1 binary64))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (fma.f64 v v #s(literal 1 binary64))))
(*.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (fma.f64 v v #s(literal 1 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 v v #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(*.f64 (/.f64 (fma.f64 v v #s(literal 1 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 (fma.f64 v v #s(literal 1 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))))

eval315.0ms (3.8%)

Memory: 12.1MiB live, 641.2MiB allocated
Compiler: Compiled 71 926 to 6 566 computations (90.9% saved)

prune386.0ms (4.6%)

Memory

-19.6MiB live, 648.2MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1 933	4	1 937
Fresh	2	1	3
Picked	4	1	5
Done	0	0	0
Total	1 939	6	1 945

Accuracy

100.0%

Counts

1 945 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
▶	46.3%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶	98.9%	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
▶	98.8%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
✓	97.3%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Compiler

Compiled 182 to 137 computations (24.7% saved)

simplify195.0ms (2.3%)

Memory

-10.8MiB live, 228.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
cost-diff	0	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
cost-diff	128	(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
cost-diff	1152	(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))
cost-diff	128	(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64)))
cost-diff	192	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
cost-diff	0	(.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
cost-diff	0	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))
cost-diff	0	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
cost-diff	0	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
cost-diff	0	(PI.f64)
cost-diff	0	(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
cost-diff	0	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))

Rules

4 188×	`lower-fma.f32`
4 180×	`lower-fma.f64`
3 956×	`lower-*.f32`
3 930×	`lower-*.f64`
2 116×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	464
0	95	442
1	190	442
2	393	440
3	997	440
4	1479	431
5	2530	431
6	6230	431
0	8139	425

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
#s(literal 4/3 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))
(PI.f64)
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(literal 4/3 binary64)
#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))
(.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(PI.f64)
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))
v
(*.f64 v #s(literal -3 binary64))
#s(literal -3 binary64)
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
(*.f64 v v)
#s(literal -6 binary64)
#s(literal 2 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
#s(literal 4 binary64)
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64)))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(fma.f64 v (neg.f64 v) #s(literal 1 binary64))
(neg.f64 v)
#s(literal 1 binary64)
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(*.f64 v v)
v
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(PI.f64)
(+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))
#s(literal -3 binary64)
(/.f64 #s(literal 3 binary64) (*.f64 v v))
#s(literal 3 binary64)
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
#s(literal 6 binary64)

Outputs
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
#s(literal 4/3 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))
(PI.f64)
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(literal 4/3 binary64)
#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))
(.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(PI.f64)
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))
v
(*.f64 v #s(literal -3 binary64))
#s(literal -3 binary64)
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(*.f64 v v)
#s(literal -6 binary64)
#s(literal 2 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (*.f64 v (neg.f64 (PI.f64))) (PI.f64))))
#s(literal 4 binary64)
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64)))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(fma.f64 v (neg.f64 v) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(neg.f64 v)
#s(literal 1 binary64)
(*.f64 #s(literal 3 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 3 binary64))
#s(literal 3 binary64)
(PI.f64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(*.f64 v v)
v
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(PI.f64)
(+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))
#s(literal -3 binary64)
(/.f64 #s(literal 3 binary64) (*.f64 v v))
#s(literal 3 binary64)
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
(.f64 v (.f64 v #s(literal 6 binary64)))
#s(literal 6 binary64)

localize161.0ms (1.9%)

Memory

18.1MiB live, 336.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.15234375	(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
accuracy	0.162441259768442	(.f64 #s(literal 6 binary64) (.f64 v v))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
accuracy	33.068283325917726	(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
accuracy	0.0078125	(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64)))
accuracy	0.0078125	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
accuracy	0.01171875	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
accuracy	0.0078125	(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
accuracy	0.01171875	(.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
accuracy	0.0234375	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(PI.f64)
accuracy	0.01171875	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.6861968162606648	#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0078125	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
accuracy	0.0078125	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
accuracy	0.01171875	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
accuracy	0.7207538580506946	#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))

Samples

93.0ms

256×

valid

Compiler

Compiled 402 to 50 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-mult: 31.0ms (48.3% of total)

ival-sqrt: 8.0ms (12.5% of total)

ival-div: 7.0ms (10.9% of total)

ival-add: 7.0ms (10.9% of total)

const: 5.0ms (7.8% of total)

ival-sub: 2.0ms (3.1% of total)

ival-pi: 1.0ms (1.6% of total)

exact: 1.0ms (1.6% of total)

ival-neg: 1.0ms (1.6% of total)

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

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

series14.0ms (0.2%)

Memory

-17.9MiB live, 20.4MiB allocated

Counts

24 → 252

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))>
#<alt (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))>
#<alt (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))>
#<alt (/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (PI.f64)>
#<alt (/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))>
#<alt (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))>
#<alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))>
#<alt (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))>
#<alt (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64)))>
#<alt (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))>
#<alt (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))>
#<alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))>
#<alt (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))>
#<alt #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))>
#<alt (.f64 #s(literal 6 binary64) (.f64 v v))>
#<alt (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))>

Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))>
#<alt (* (PI) (sqrt 2))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))>
#<alt (* (pow v 3) (* (PI) (sqrt -6)))>
#<alt (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))>
#<alt (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))>
#<alt (* -1 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
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#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (sqrt -6))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt (PI)>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 3 (/ (PI) (pow v 2)))>
#<alt (/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))>
#<alt (/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))>
#<alt (/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))>
#<alt (* -3 (PI))>
#<alt (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))>
#<alt (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))>
#<alt (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))>
#<alt (* -3 (PI))>
#<alt (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))>
#<alt (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))>
#<alt (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))>

Calls

63 calls:

Time	Variable		Point	Expression
3.0ms	v	@	0	(* (sqrt (+ (* v (* v -6)) 2)) (+ (* v (neg v)) 1))
1.0ms	v	@	inf	(* (sqrt (+ (* v (* v -6)) 2)) (+ (* v (neg v)) 1))
0.0ms	v	@	inf	(* (* v v) (* (PI) (+ -3 (/ 3 (* v v)))))
0.0ms	v	@	0	(* (* v v) (* (PI) (+ -3 (/ 3 (* v v)))))
0.0ms	v	@	inf	(* (PI) (+ (* v (* v -3)) 3))

simplify313.0ms (3.7%)

Memory

23.1MiB live, 527.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 780×	`lower-fma.f64`
9 780×	`lower-fma.f32`
6 394×	`lower-*.f64`
6 394×	`lower-*.f32`
3 682×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	390	7151
1	1251	6217
2	5079	5861
0	8694	5672

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))
(* (PI) (sqrt 2))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(* (pow v 3) (* (PI) (sqrt -6)))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))
(* (PI) (sqrt 2))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(* (pow v 3) (* (PI) (sqrt -6)))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(sqrt 2)
(+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(* -1 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (sqrt -6))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6))))))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(PI)
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 3 (/ (PI) (pow v 2)))
(/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))
(/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))
(/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))
(* -3 (PI))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(* -3 (PI))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))

Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(.f64 #s(literal 4/3 binary64) (fma.f64 v (.f64 v (-.f64 (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(.f64 #s(literal 4/3 binary64) (fma.f64 (-.f64 (fma.f64 (.f64 v v) (+.f64 (/.f64 #s(literal 27/16 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal -3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 v (.f64 v (fma.f64 #s(literal 4/3 binary64) (fma.f64 (+.f64 (fma.f64 (.f64 v v) (+.f64 (+.f64 (/.f64 #s(literal -27/16 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 #s(literal 135/32 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (-.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 27/16 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))) (/.f64 #s(literal -3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (neg.f64 (PI.f64)))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (PI.f64) (.f64 v (.f64 v v))))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/.f64 (.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (-.f64 (/.f64 #s(literal -1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)))) (.f64 v (*.f64 v v)))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))
(/.f64 (.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 #s(literal -1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))) (.f64 (.f64 v v) (.f64 v v)))))) (.f64 v (.f64 v v)))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))
(/.f64 (.f64 #s(literal 4/3 binary64) (+.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 #s(literal -1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))) (.f64 (.f64 v v) (.f64 v v))))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal -5/2592 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (-.f64 (/.f64 #s(literal -1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))) (.f64 v (*.f64 v v)))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) (.f64 (PI.f64) (.f64 v (.f64 v v))))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(/.f64 (.f64 #s(literal -4/3 binary64) (+.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (-.f64 (/.f64 #s(literal -1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)))) (.f64 v (*.f64 v v)))
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(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 (.f64 v v) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) (/.f64 #s(literal -27/2 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(.f64 v (fma.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (fma.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))))
(* -1 (* v (sqrt -6)))
(neg.f64 (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(neg.f64 (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (fma.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))) (neg.f64 v))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 3 (/ (PI) (pow v 2)))
(.f64 (PI.f64) (/.f64 #s(literal 3 binary64) (.f64 v v)))
(/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))
(/.f64 (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))) (*.f64 v v))
(/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))
(/.f64 (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))) (*.f64 v v))
(/ (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (pow v 2))
(/.f64 (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))) (*.f64 v v))
(* -3 (PI))
(*.f64 (PI.f64) #s(literal -3 binary64))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(* -3 (PI))
(*.f64 (PI.f64) #s(literal -3 binary64))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))

rewrite273.0ms (3.3%)

Memory

16.7MiB live, 498.2MiB allocated

Rules

4 390×	`lower-fma.f32`
4 382×	`lower-fma.f64`
4 164×	`lower-/.f32`
4 152×	`lower-/.f64`
3 864×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	343
0	95	340
1	343	340
2	2097	340
0	8286	323

Stop Event

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

Counts

24 → 699

Calls

Call 1

Inputs
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(PI.f64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))
(.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64)))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(.f64 #s(literal 6 binary64) (.f64 v v))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (neg.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 4/3 binary64) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))))
(/.f64 #s(literal -4/3 binary64) (neg.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))))
(/.f64 #s(literal -4/3 binary64) (neg.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))
(/.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))) (neg.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))) (neg.f64 (neg.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))))
(/.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))) (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(pow.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))))
(.f64 #s(literal -4/3 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal 4/3 binary64))
(.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 4/3 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
(.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 v v) #s(literal -12 binary64))))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) #s(literal 6 binary64)) (fma.f64 (.f64 v v) #s(literal 6 binary64) #s(literal 2 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal 6 binary64) #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (*.f64 v v))) #s(literal 36 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 v v) #s(literal 6 binary64)) (fma.f64 (.f64 v v) #s(literal 6 binary64) #s(literal 2 binary64)) #s(literal 4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (-.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal 6 binary64) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 v v) #s(literal -12 binary64)))))))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (-.f64 #s(literal 9 binary64) (/.f64 #s(literal 9 binary64) (.f64 v (.f64 v (*.f64 v v))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 9 binary64) (/.f64 (-.f64 (/.f64 #s(literal -9 binary64) (.f64 v v)) #s(literal 9 binary64)) (neg.f64 (.f64 v v)))) (.f64 (+.f64 #s(literal -27 binary64) (/.f64 #s(literal 27 binary64) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))))) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (-.f64 #s(literal 9 binary64) (/.f64 #s(literal 9 binary64) (.f64 v (.f64 v (*.f64 v v))))) (PI.f64))))
(/.f64 (fma.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -27 binary64) (/.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -27 binary64)) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (.f64 (PI.f64) #s(literal -3 binary64)) (-.f64 (.f64 (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))) (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64)))) (.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (/.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal 1/3 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (.f64 (PI.f64) #s(literal -3 binary64))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))) (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))))) (-.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (/.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal 1/3 binary64)))))
(/.f64 (.f64 (PI.f64) (+.f64 #s(literal -27 binary64) (/.f64 #s(literal 27 binary64) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))))) (+.f64 #s(literal 9 binary64) (/.f64 (-.f64 (/.f64 #s(literal -9 binary64) (.f64 v v)) #s(literal 9 binary64)) (neg.f64 (.f64 v v)))))
(/.f64 (.f64 (PI.f64) (-.f64 #s(literal 9 binary64) (/.f64 #s(literal 9 binary64) (.f64 v (.f64 v (.f64 v v)))))) (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v))))
(/.f64 (.f64 (+.f64 #s(literal -27 binary64) (/.f64 #s(literal 27 binary64) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))))) (PI.f64)) (+.f64 #s(literal 9 binary64) (/.f64 (-.f64 (/.f64 #s(literal -9 binary64) (.f64 v v)) #s(literal 9 binary64)) (neg.f64 (.f64 v v)))))
(/.f64 (.f64 (-.f64 #s(literal 9 binary64) (/.f64 #s(literal 9 binary64) (.f64 v (.f64 v (.f64 v v))))) (PI.f64)) (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v))))
(/.f64 (neg.f64 (fma.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -27 binary64) (/.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -27 binary64)) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))))) (neg.f64 (fma.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (.f64 (PI.f64) #s(literal -3 binary64)) (-.f64 (.f64 (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))) (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64)))) (.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (/.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal 1/3 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (.f64 (PI.f64) #s(literal -3 binary64))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))) (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64)))))) (neg.f64 (-.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (/.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal 1/3 binary64))))))
(/.f64 (neg.f64 (.f64 (PI.f64) (+.f64 #s(literal -27 binary64) (/.f64 #s(literal 27 binary64) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))))))) (neg.f64 (+.f64 #s(literal 9 binary64) (/.f64 (-.f64 (/.f64 #s(literal -9 binary64) (.f64 v v)) #s(literal 9 binary64)) (neg.f64 (.f64 v v))))))
(/.f64 (neg.f64 (.f64 (PI.f64) (-.f64 #s(literal 9 binary64) (/.f64 #s(literal 9 binary64) (.f64 v (.f64 v (.f64 v v))))))) (neg.f64 (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -27 binary64) (/.f64 #s(literal 27 binary64) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))))) (PI.f64))) (neg.f64 (+.f64 #s(literal 9 binary64) (/.f64 (-.f64 (/.f64 #s(literal -9 binary64) (.f64 v v)) #s(literal 9 binary64)) (neg.f64 (.f64 v v))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 9 binary64) (/.f64 #s(literal 9 binary64) (.f64 v (.f64 v (.f64 v v))))) (PI.f64))) (neg.f64 (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(/.f64 (fma.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (/.f64 #s(literal 27 binary64) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -27 binary64))) (fma.f64 (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))) (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))) (-.f64 (.f64 (.f64 (PI.f64) #s(literal -3 binary64)) (.f64 (PI.f64) #s(literal -3 binary64))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 v v) #s(literal 1/3 binary64))) (*.f64 (PI.f64) #s(literal -3 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))))
(.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (PI.f64))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(.f64 (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v))) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

eval205.0ms (2.4%)

Memory: -14.2MiB live, 456.0MiB allocated
Compiler: Compiled 37 098 to 3 820 computations (89.7% saved)

prune153.0ms (1.8%)

Memory

4.4MiB live, 415.6MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	1 219	2	1 221
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	1 220	7	1 227

Accuracy

100.0%

Counts

1 227 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
▶	46.3%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
✓	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	98.9%	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
✓	98.8%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
▶	97.4%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
✓	97.3%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Compiler

Compiled 109 to 84 computations (22.9% saved)

simplify260.0ms (3.1%)

Memory

0.5MiB live, 390.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))))
cost-diff	0	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
cost-diff	1152	(.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))
cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
cost-diff	0	(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64))
cost-diff	320	(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))

Rules

11 890×	`lower-fma.f32`
11 888×	`lower-fma.f64`
4 930×	`lower-*.f32`
4 916×	`lower-*.f64`
1 758×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	231
0	48	227
1	88	225
2	156	225
3	344	225
4	805	225
5	1421	213
6	2149	213
7	4219	213
8	6259	213
0	8473	202

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
#s(literal 1 binary64)
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))
(PI.f64)
#s(literal 3/4 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
#s(literal 4 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))
(.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))
(+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))
#s(literal -3 binary64)
(/.f64 #s(literal 3 binary64) (*.f64 v v))
#s(literal 3 binary64)
(*.f64 v v)
(.f64 (PI.f64) (.f64 v v))
(PI.f64)

Outputs
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
#s(literal 1 binary64)
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))
(PI.f64)
#s(literal 3/4 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))))
#s(literal 4 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64))))
(.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))
(.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))
#s(literal -3 binary64)
(/.f64 #s(literal 3 binary64) (*.f64 v v))
#s(literal 3 binary64)
(*.f64 v v)
(.f64 (PI.f64) (.f64 v v))
(PI.f64)

localize87.0ms (1%)

Memory

-4.3MiB live, 197.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(/.f64 #s(literal 3 binary64) (*.f64 v v))
accuracy	0.1484375	(.f64 (PI.f64) (.f64 v v))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
accuracy	33.037033325917726	(.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))
accuracy	0.0078125	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
accuracy	0.0078125	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
accuracy	0.7207538580506946	#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))
accuracy	0.98046875	(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))

Samples

45.0ms

256×

valid

Compiler

Compiled 192 to 30 computations (84.4% saved)

Precisions

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

ival-mult: 16.0ms (52.2% of total)

ival-div: 5.0ms (16.3% of total)

ival-add: 4.0ms (13.1% of total)

ival-sqrt: 4.0ms (13.1% of total)

ival-pi: 1.0ms (3.3% of total)

ival-sub: 1.0ms (3.3% of total)

exact: 1.0ms (3.3% of total)

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

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

series6.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))>
#<alt (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64))>
#<alt (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))>
#<alt (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))>
#<alt (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))))>
#<alt #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))>
#<alt (.f64 (PI.f64) (.f64 v v))>
#<alt (/.f64 #s(literal 3 binary64) (*.f64 v v))>

Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3/4 (* (PI) (sqrt 2)))>
#<alt (+ (* 3/4 (* (PI) (sqrt 2))) (* 3/4 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2))))))>
#<alt (+ (* 3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3/4 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))) (* 3/4 (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3/4 (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))) (* (pow v 2) (+ (* 3/4 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3/4 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))))))>
#<alt (* 3/4 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* 1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2)))))))>
#<alt (* -3/4 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2)))))))>
#<alt (* -1 (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* 1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2))))))))>
#<alt (* (PI) (sqrt 2))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))>
#<alt (* (pow v 3) (* (PI) (sqrt -6)))>
#<alt (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))>
#<alt (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))>
#<alt (* -1 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt (PI)>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>
#<alt (/ 3 (pow v 2))>

Calls

30 calls:

Time	Variable		Point	Expression
0.0ms	v	@	inf	(* (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) 3/4)
0.0ms	v	@	0	(* (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) 3/4)
0.0ms	v	@	0	(/ 3 (* v v))
0.0ms	v	@	inf	(* (PI) (* v v))
0.0ms	v	@	0	(* (PI) (* v v))

simplify320.0ms (3.8%)

Memory

-5.1MiB live, 468.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 108×	`lower-fma.f64`
11 108×	`lower-fma.f32`
6 276×	`lower-*.f64`
6 276×	`lower-*.f32`
3 634×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	375	3191
1	1250	2813
2	5335	2631
0	8028	2535

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))
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(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
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(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))
(* 3/4 (* (PI) (sqrt 2)))
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(+ (* 3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3/4 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))) (* 3/4 (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))))
(+ (* 3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3/4 (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))) (* (pow v 2) (+ (* 3/4 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3/4 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))))))
(* 3/4 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2))))))
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(* -3/4 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2))))))
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(* -1 (* (pow v 3) (+ (* 3/4 (* (PI) (sqrt -6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* 1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 3/4 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))) (* 3/4 (/ (+ (* (PI) (sqrt -6)) (/ (PI) (sqrt -6))) (pow v 2))))))))
(* (PI) (sqrt 2))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(* (pow v 3) (* (PI) (sqrt -6)))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(PI)
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))
(/ 3 (pow v 2))

Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(.f64 #s(literal 4/3 binary64) (fma.f64 (.f64 v v) (-.f64 (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(.f64 #s(literal 4/3 binary64) (fma.f64 (-.f64 (fma.f64 (.f64 v v) (+.f64 (/.f64 #s(literal 27/16 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal -3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
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(fma.f64 (PI.f64) (.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 v v) (.f64 #s(literal 3 binary64) (fma.f64 (fma.f64 (.f64 v v) (fma.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 9/4 binary64) (/.f64 (.f64 (PI.f64) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/4 binary64))) (.f64 v v) (*.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v v) (.f64 v (.f64 #s(literal -3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (.f64 #s(literal 3 binary64) (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (*.f64 v v))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (.f64 #s(literal -3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (+.f64 (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 1/12 binary64))) (pow.f64 v #s(literal 6 binary64))))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v (.f64 v v)) (.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 3 binary64)))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (.f64 #s(literal 3 binary64) (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (.f64 v v))) (neg.f64 (.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(.f64 (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (+.f64 (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 1/12 binary64))) (pow.f64 v #s(literal 6 binary64))))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (.f64 v (.f64 v v))))
(PI)
(PI.f64)
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (PI.f64) (*.f64 v v) (PI.f64))
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (PI.f64) (*.f64 v v) (PI.f64))
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (PI.f64) (*.f64 v v) (PI.f64))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 v (.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 v (.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 v (.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 v (.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 v (.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(.f64 v (.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(* (pow v 2) (PI))
(.f64 (PI.f64) (.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/ 3 (pow v 2))
(/.f64 #s(literal 3 binary64) (*.f64 v v))

rewrite296.0ms (3.5%)

Memory

10.5MiB live, 486.7MiB allocated

Rules

8 120×	`lower-fma.f32`
8 118×	`lower-fma.f64`
6 116×	`lower-*.f32`
6 102×	`lower-*.f64`
2 918×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	160
0	48	160
1	173	158
2	1085	158
0	8369	151

Stop Event

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

Counts

10 → 333

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v)))))
#s(approx (* (PI) (+ (* v v) 1)) (PI.f64))
(.f64 (PI.f64) (.f64 v v))
(/.f64 #s(literal 3 binary64) (*.f64 v v))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))))
(neg.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))))
(neg.f64 (.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))))) #s(literal 1 binary64)))
(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal -3/4 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal -3/4 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal 3/4 binary64))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(/.f64 (/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal -3/4 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal -3/4 binary64)))
(/.f64 #s(literal -4/3 binary64) (neg.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))))
(pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))))
(.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))))))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal 4/3 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))))
(.f64 #s(literal 4/3 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)))) #s(literal -4/3 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)) (.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 3/4 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64))) (pow.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(approx ( (PI) (+ (* v v) 1)) (PI.f64)) #s(literal -3/4 binary64))))
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(.f64 (.f64 (sqrt.f64 (PI.f64)) v) (*.f64 (sqrt.f64 (PI.f64)) v))
(.f64 (.f64 v (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) v))
(.f64 (.f64 v (sqrt.f64 (PI.f64))) (*.f64 v (sqrt.f64 (PI.f64))))
(.f64 (.f64 v (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 v (*.f64 v (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) v) (sqrt.f64 (PI.f64))) v)
(.f64 (.f64 (*.f64 v v) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (.f64 v (sqrt.f64 (PI.f64)))) (.f64 v (sqrt.f64 (PI.f64))))
(.f64 (.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) v))
(.f64 (.f64 (*.f64 v (sqrt.f64 (PI.f64))) v) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (.f64 v (.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (.f64 v (.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(.f64 (.f64 (.f64 v (.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (.f64 v (.f64 v (sqrt.f64 (PI.f64)))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (.f64 v (.f64 v (sqrt.f64 (PI.f64)))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (.f64 v (.f64 v (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 v v) #s(literal 1/3 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -3 binary64) (*.f64 v v)))
(neg.f64 (/.f64 #s(literal -3 binary64) (*.f64 v v)))
(neg.f64 (.f64 (/.f64 #s(literal -3 binary64) (.f64 v v)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal 1/3 binary64)))
(/.f64 #s(literal -3 binary64) (*.f64 v (neg.f64 v)))
(/.f64 #s(literal 3 binary64) (*.f64 v v))
(/.f64 #s(literal -1 binary64) (.f64 (.f64 v v) #s(literal -1/3 binary64)))
(/.f64 (/.f64 #s(literal 3 binary64) v) v)
(/.f64 (/.f64 #s(literal 3 binary64) v) (neg.f64 (neg.f64 v)))
(/.f64 (/.f64 #s(literal -3 binary64) v) (neg.f64 v))
(pow.f64 (.f64 (.f64 v v) #s(literal 1/3 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))
(.f64 #s(literal -3 binary64) (/.f64 #s(literal -1 binary64) (.f64 v v)))
(.f64 #s(literal -3 binary64) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 v v)) #s(literal 1 binary64)))
(.f64 #s(literal 3 binary64) (/.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 (/.f64 #s(literal 3 binary64) (.f64 v v)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -3 binary64) (.f64 v v)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 v v)) #s(literal 3 binary64))
(*.f64 (/.f64 #s(literal 3 binary64) v) (/.f64 #s(literal 1 binary64) v))
(.f64 (/.f64 #s(literal 3 binary64) v) (.f64 (/.f64 #s(literal 1 binary64) v) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -3 binary64) v) (/.f64 #s(literal 1 binary64) (neg.f64 v)))
(*.f64 (/.f64 #s(literal 1 binary64) v) (/.f64 #s(literal 3 binary64) v))
(.f64 (pow.f64 (.f64 (.f64 v v) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 v v) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)))

eval62.0ms (0.7%)

Memory: 11.9MiB live, 161.1MiB allocated
Compiler: Compiled 14 320 to 1 743 computations (87.8% saved)

prune99.0ms (1.2%)

Memory

12.7MiB live, 173.7MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	488	1	489
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	488	8	496

Accuracy

100.0%

Counts

496 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))
✓	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
✓	46.3%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
✓	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	98.9%	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
✓	98.8%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
✓	97.4%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
✓	97.3%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Compiler

Compiled 407 to 182 computations (55.3% saved)

regimes41.0ms (0.5%)

Memory

-34.7MiB live, 68.0MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))

Outputs

(/.f64 #s(literal 4 binary64) (fma.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (*.f64 (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (neg.f64 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))

Calls

4 calls:

27.0ms	(*.f64 v v)
5.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
5.0ms	v
4.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))

Results

Accuracy	Segments	Branch
100.0%	1	`v`
100.0%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
100.0%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
100.0%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes18.0ms (0.2%)

Memory

10.5MiB live, 48.6MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx ( (PI) (+ (* v v) 1)) (PI.f64))) #s(literal 3/4 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (.f64 #s(approx (* (PI) (+ (* v v) 1)) (PI.f64)) #s(literal 3/4 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v (neg.f64 v) #s(literal 1 binary64))) (.f64 #s(literal 3 binary64) (PI.f64))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v))) (.f64 (PI.f64) (.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))

Outputs
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))

Calls

4 calls:

5.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
4.0ms	v
4.0ms	(*.f64 v v)
4.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Results

Accuracy	Segments	Branch
98.9%	1	`v`
98.9%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
98.9%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
98.9%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes7.0ms (0.1%)

Memory

-21.8MiB live, 16.6MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))

Outputs
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))

Calls

4 calls:

2.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
1.0ms	v
1.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
1.0ms	(*.f64 v v)

Results

Accuracy	Segments	Branch
98.8%	1	`v`
98.8%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
98.8%	1	`(*.f64 v v)`
98.8%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes5.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Outputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Calls

4 calls:

1.0ms	v
1.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
1.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
1.0ms	(*.f64 v v)

Results

Accuracy	Segments	Branch
97.3%	1	`v`
97.3%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
97.3%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
97.3%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

simplify12.0ms (0.1%)

Memory

-20.2MiB live, 20.3MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`
16×	`+-commutative_binary64`
16×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	98
1	68	98
2	82	98
3	105	98
4	120	98
5	128	98
6	132	98
7	133	98

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Outputs
(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (neg.f64 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 4 binary64) (fma.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (*.f64 v (neg.f64 v)))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (PI) (+ (* v v) 1)) (PI.f64))))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

soundness421.0ms (5%)

Memory

17.3MiB live, 445.0MiB allocated

Rules

15 354×	`lower-fma.f64`
15 354×	`lower-fma.f32`
11 918×	`lower-fma.f64`
11 918×	`lower-fma.f32`
7 022×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	580	7293
1	1956	6479
0	8352	6211
0	16	67
0	26	67
1	101	65
2	626	65
3	5771	65
0	8439	58
0	241	1610
1	747	1426
2	2954	1351
0	8247	1301

Stop Event

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

Compiler

Compiled 103 to 67 computations (35% saved)

preprocess91.0ms (1.1%)

Memory: -9.4MiB live, 202.5MiB allocated
Remove: (abs v)
Compiler: Compiled 274 to 154 computations (43.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze4.0ms (0%)

sample1.1s (13.2%)

explain671.0ms (8%)

preprocess318.0ms (3.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify224.0ms (2.7%)

localize38.0ms (0.4%)

series39.0ms (0.5%)

simplify344.0ms (4.1%)

rewrite444.0ms (5.3%)

eval143.0ms (1.7%)

prune136.0ms (1.6%)

simplify214.0ms (2.6%)

localize219.0ms (2.6%)

series32.0ms (0.4%)

simplify334.0ms (4%)

rewrite375.0ms (4.5%)

eval315.0ms (3.8%)

prune386.0ms (4.6%)

simplify195.0ms (2.3%)

localize161.0ms (1.9%)

series14.0ms (0.2%)

simplify313.0ms (3.7%)

rewrite273.0ms (3.3%)

eval205.0ms (2.4%)

prune153.0ms (1.8%)

simplify260.0ms (3.1%)

localize87.0ms (1%)

series6.0ms (0.1%)

simplify320.0ms (3.8%)

rewrite296.0ms (3.5%)

eval62.0ms (0.7%)

prune99.0ms (1.2%)

regimes41.0ms (0.5%)

regimes18.0ms (0.2%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

simplify12.0ms (0.1%)

soundness421.0ms (5%)

preprocess91.0ms (1.1%)

end0.0ms (0%)

Profiling