Metrics for Falkner and Boettcher, Equation (22+)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze4.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB 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)

sample1.0s (15.4%)

Memory

39.7MiB live, 1 643.5MiB allocated

Samples

698.0ms	8 256×	0	valid
1.0ms	9×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 505.0ms

ival-mult: 240.0ms (47.5% of total)

ival-sub: 82.0ms (16.2% of total)

ival-sqrt: 61.0ms (12.1% of total)

ival-div: 58.0ms (11.5% of total)

ival-pi: 39.0ms (7.7% of total)

exact: 17.0ms (3.4% of total)

ival-true: 6.0ms (1.2% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain163.0ms (2.5%)

Memory

12.7MiB live, 246.8MiB 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

48.0ms

512×

valid

Compiler

Compiled 195 to 52 computations (73.3% saved)

Precisions

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

ival-mult: 14.0ms (45.4% of total)

ival-sub: 6.0ms (19.5% of total)

ival-sqrt: 4.0ms (13% of total)

ival-div: 3.0ms (9.7% of total)

ival-pi: 2.0ms (6.5% of total)

exact: 1.0ms (3.2% of total)

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

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

preprocess185.0ms (2.8%)

Memory

-17.1MiB live, 145.4MiB 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 (*.f64 (fma.f64 v v #s(literal -1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))

Symmetry

(abs v)

Compiler

Compiled 21 to 16 computations (23.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(/.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

▶

98.4%

(/.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)

simplify119.0ms (1.8%)

Memory

13.9MiB live, 91.5MiB 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 (.f64 (fma.f64 v v #s(literal -1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #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 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (.f64 (fma.f64 v v #s(literal -1 binary64)) (PI.f64)) #s(literal -3 binary64)))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 (fma.f64 v v #s(literal -1 binary64)) (PI.f64)) #s(literal -3 binary64))
(*.f64 #s(literal 3 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 3 binary64))
#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 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
#s(literal 6 binary64)

localize55.0ms (0.8%)

Memory

3.4MiB live, 41.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0.01953125	(.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	0.12957001953688402	(.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

45.0ms

256×

valid

Compiler

Compiled 87 to 18 computations (79.3% saved)

Precisions

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

ival-mult: 29.0ms (79.4% of total)

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

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

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

ival-pi: 1.0ms (2.7% of total)

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

exact: 0.0ms (0% of total)

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

series42.0ms (0.6%)

Memory

-24.6MiB live, 13.4MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#s(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)))))) (patch (/.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI)))) (taylor 0 v) (#s(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)))))) (patch (/.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)))))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor 0 v) (#s(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)))))) (patch (/.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)))))) #<representation binary64>) () ())) ())
#s(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)))))))))) (taylor 0 v) (#s(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)))))) (patch (/.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)))))) #<representation binary64>) () ())) ())
#s(alt (* 3 (PI)) (taylor 0 v) (#s(alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (taylor 0 v) (#s(alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (taylor 0 v) (#s(alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (taylor 0 v) (#s(alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 v) (#s(alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) (patch (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -6 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) (patch (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -6 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) (patch (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -6 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) (patch (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* 3 (* (PI) (sqrt 2))) (taylor 0 v) (#s(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))))) (patch (.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))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))) (taylor 0 v) (#s(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))))) (patch (.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))))) #<representation binary64>) () ())) ())
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#s(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))))))) (taylor -inf v) (#s(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))))) (patch (.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))))) #<representation binary64>) () ())) ())
#s(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)))))))) (taylor -inf v) (#s(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))))) (patch (.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))))) #<representation binary64>) () ())) ())
#s(alt (* 6 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 6 binary64) (.f64 v v)) (patch (.f64 #s(literal 6 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 6 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 6 binary64) (.f64 v v)) (patch (.f64 #s(literal 6 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 6 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 6 binary64) (.f64 v v)) (patch (.f64 #s(literal 6 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 6 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 6 binary64) (.f64 v v)) (patch (.f64 #s(literal 6 binary64) (.f64 v v)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
34.0ms	v	@	0	((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 6 (* v v)))
4.0ms	v	@	inf	((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 6 (* v v)))
1.0ms	v	@	-inf	((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 6 (* v v)))

Time

Variable

Point

Expression

34.0ms

((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 6 (* v v)))

4.0ms

inf

((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 6 (* v v)))

1.0ms

-inf

((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 6 (* v v)))

simplify202.0ms (3.1%)

Memory

10.0MiB live, 158.2MiB allocated

Algorithm

1×	egg-herbie

Rules

16 554×	`lower-fma.f64`
16 554×	`lower-fma.f32`
5 558×	`lower-+.f64`
5 558×	`lower-+.f32`
5 146×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	200	1386
1	620	1206
2	2547	1131
3	7429	1131
0	8063	1091

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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))))))))))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* 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))))))))))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 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 (/ (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))
(* -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)))))
(* -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 (* (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)))))))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 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 (* (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)))))
(* -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 (* (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))

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

rewrite261.0ms (4%)

Memory

-6.9MiB live, 192.7MiB 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	59
0	26	59
1	101	57
2	626	57
3	5771	57
0	8439	51

Stop Event

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

Counts

5 → 457

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))

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

eval142.0ms (2.2%)

Memory: 25.4MiB live, 137.3MiB allocated
Compiler: Compiled 15 567 to 1 744 computations (88.8% saved)

prune123.0ms (1.9%)

Memory

11.6MiB live, 137.2MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	509	8	517
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	510	8	518

Accuracy

100.0%

Counts

518 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(/.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)))))
	50.0%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 3 binary64) (.f64 v v)) #s(literal -3 binary64))) v) v)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
	98.4%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.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))))))
	97.3%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
▶	98.8%	(/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (fma.f64 v v #s(literal 1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
▶	100.0%	(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))) (fma.f64 v v #s(literal 1 binary64)))
▶	97.9%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)))
▶	97.2%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64)))

Compiler

Compiled 316 to 226 computations (28.5% saved)

simplify153.0ms (2.3%)

Memory

-20.4MiB live, 137.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 v v #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v))
cost-diff	0	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)))
cost-diff	320	(.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))
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	192	(/.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 v #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 v v #s(literal 1 binary64)) (PI.f64))
cost-diff	0	(.f64 (.f64 (fma.f64 v v #s(literal 1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
cost-diff	0	(/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (fma.f64 v v #s(literal 1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
cost-diff	0	(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64))
cost-diff	0	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64)))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 #s(literal 4/3 binary64) (PI.f64))
cost-diff	0	(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))) (fma.f64 v v #s(literal 1 binary64)))
cost-diff	384	(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))))

Rules

9 422×	`lower-fma.f32`
9 412×	`lower-fma.f64`
4 954×	`lower-*.f32`
4 926×	`lower-*.f64`
1 850×	`lower-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	415
0	89	413
1	172	397
2	394	389
3	1036	387
4	3079	386
5	4140	386
0	8002	378

Stop Event

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

Calls

Call 1

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

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

localize242.0ms (3.7%)

Memory

19.0MiB live, 102.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)
accuracy	0.1171875	(.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v)
accuracy	0.3834319258838696	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)))
accuracy	1.0	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
accuracy	0	(PI.f64)
accuracy	0.00390625	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0.01953125	(.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	(PI.f64)
accuracy	0.00390625	(/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (fma.f64 v v #s(literal 1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
accuracy	0.0078125	(.f64 (.f64 (fma.f64 v v #s(literal 1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
accuracy	0.015625	(*.f64 (fma.f64 v v #s(literal 1 binary64)) (PI.f64))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0	(PI.f64)
accuracy	0.8003622970451503	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64)))
accuracy	1.0	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
accuracy	0	(PI.f64)
accuracy	0.00390625	(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))))
accuracy	0.0625	(.f64 (.f64 v v) v)
accuracy	1.0	(/.f64 #s(literal 4/3 binary64) (PI.f64))

Samples

176.0ms

256×

valid

Compiler

Compiled 416 to 52 computations (87.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

const: 101.0ms (65.8% of total)

ival-mult: 26.0ms (16.9% of total)

ival-div: 10.0ms (6.5% of total)

ival-sqrt: 6.0ms (3.9% of total)

ival-add: 5.0ms (3.3% of total)

ival-sub: 2.0ms (1.3% of total)

ival-pi: 1.0ms (0.7% of total)

exact: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

series470.0ms (7.2%)

Memory

-12.2MiB live, 24.4MiB allocated

Counts

22 → 192

Calls

Call 1

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

Outputs
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2)))) (taylor 0 v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(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))))) (/ 1 (* (PI) (sqrt 1/2)))))) (taylor 0 v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (* (pow v 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)))))) (/ 1 (* (PI) (sqrt 1/2)))))) (taylor 0 v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (fma.f64 (.f64 (.f64 v v) v) (neg.f64 v) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(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)))))))) (taylor -inf v) (#s(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)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) (patch (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (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)))))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) (patch (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (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)))))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) (patch (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (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)))))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) (patch (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI)))) (taylor -inf v) (#s(alt #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) (patch #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(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))) (taylor -inf v) (#s(alt #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) (patch #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(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))) (taylor -inf v) (#s(alt #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) (patch #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(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))) (taylor -inf v) (#s(alt #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) (patch #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (.f64 (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (taylor -inf v) (#s(alt (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) (patch (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))) (taylor -inf v) (#s(alt (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) (patch (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))) (taylor -inf v) (#s(alt (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) (patch (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (+ (/ (sqrt 1/2) (PI)) (/ (sqrt 1/2) (* (pow v 2) (PI)))))) (taylor -inf v) (#s(alt (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) (patch (fma.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v)) #<representation binary64>) () ())) ())
#s(alt (pow v 3) (taylor -inf v) (#s(alt (.f64 (.f64 v v) v) (patch (.f64 (.f64 v v) v) #<representation binary64>) () ())) ())
#s(alt (pow v 3) (taylor -inf v) (#s(alt (.f64 (.f64 v v) v) (patch (.f64 (.f64 v v) v) #<representation binary64>) () ())) ())
#s(alt (pow v 3) (taylor -inf v) (#s(alt (.f64 (.f64 v v) v) (patch (.f64 (.f64 v v) v) #<representation binary64>) () ())) ())
#s(alt (pow v 3) (taylor -inf v) (#s(alt (.f64 (.f64 v v) v) (patch (.f64 (.f64 v v) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ v (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) (patch (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ v (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) (patch (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ v (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) (patch (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ v (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) (patch (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (pow v 2) (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) (patch (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (pow v 2) (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) (patch (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (pow v 2) (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) (patch (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (pow v 2) (* (PI) (sqrt 1/2)))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) (patch (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) v) v) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

450.0ms

((/ (/ 4/3 (PI)) (* (+ (* (* (* v v) v) (neg v)) 1) (sqrt (+ (* -6 (* v v)) 2)))) (* (/ (/ 4/3 (PI)) (* (+ (* (* (* v v) v) (neg v)) 1) (sqrt (+ (* -6 (* v v)) 2)))) (+ (* v v) 1)) (/ 4/3 (PI)) (PI) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (/ (sqrt 1/2) (PI)) 4/3) (/ (sqrt 1/2) (PI)) (sqrt 1/2) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (+ (* v v) 1) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))) (* (* 3 (PI)) (- 1 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* 3 (PI)) (* (+ (* (+ (* v v) 1) (/ (sqrt 1/2) (PI))) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v)) 4/3) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (+ (* (+ (* v v) 1) (/ (sqrt 1/2) (PI))) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v)) (* (* v v) v) (* (/ 3/4 (* (PI) (sqrt 1/2))) v) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v))

6.0ms

inf

((/ (/ 4/3 (PI)) (* (+ (* (* (* v v) v) (neg v)) 1) (sqrt (+ (* -6 (* v v)) 2)))) (* (/ (/ 4/3 (PI)) (* (+ (* (* (* v v) v) (neg v)) 1) (sqrt (+ (* -6 (* v v)) 2)))) (+ (* v v) 1)) (/ 4/3 (PI)) (PI) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (/ (sqrt 1/2) (PI)) 4/3) (/ (sqrt 1/2) (PI)) (sqrt 1/2) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (+ (* v v) 1) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))) (* (* 3 (PI)) (- 1 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* 3 (PI)) (* (+ (* (+ (* v v) 1) (/ (sqrt 1/2) (PI))) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v)) 4/3) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (+ (* (+ (* v v) 1) (/ (sqrt 1/2) (PI))) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v)) (* (* v v) v) (* (/ 3/4 (* (PI) (sqrt 1/2))) v) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v))

4.0ms

-inf

((/ (/ 4/3 (PI)) (* (+ (* (* (* v v) v) (neg v)) 1) (sqrt (+ (* -6 (* v v)) 2)))) (* (/ (/ 4/3 (PI)) (* (+ (* (* (* v v) v) (neg v)) 1) (sqrt (+ (* -6 (* v v)) 2)))) (+ (* v v) 1)) (/ 4/3 (PI)) (PI) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (/ (sqrt 1/2) (PI)) 4/3) (/ (sqrt 1/2) (PI)) (sqrt 1/2) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (+ (* v v) 1) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))) (* (* 3 (PI)) (- 1 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* 3 (PI)) (* (+ (* (+ (* v v) 1) (/ (sqrt 1/2) (PI))) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v)) 4/3) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (+ (* (+ (* v v) 1) (/ (sqrt 1/2) (PI))) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v)) (* (* v v) v) (* (/ 3/4 (* (PI) (sqrt 1/2))) v) (* (* (/ 3/4 (* (PI) (sqrt 1/2))) v) v))

simplify259.0ms (4%)

Memory

-40.0MiB live, 138.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 216×	`lower-fma.f64`
10 216×	`lower-fma.f32`
6 304×	`lower-*.f64`
6 304×	`lower-*.f32`
3 302×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	354	5630
1	1159	4725
2	4800	4528
0	8122	4368

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

rewrite395.0ms (6.1%)

Memory

-20.2MiB live, 286.9MiB allocated

Rules

5 176×	`lower-*.f32`
5 148×	`lower-*.f64`
4 150×	`lower-/.f32`
4 138×	`lower-/.f64`
3 622×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	283
0	89	275
1	318	265
2	2164	265
0	8404	265

Stop Event

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

Counts

22 → 1 274

Calls

Call 1

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

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

eval392.0ms (6%)

Memory: 11.9MiB live, 638.0MiB allocated
Compiler: Compiled 78 944 to 5 494 computations (93% saved)

prune307.0ms (4.7%)

Memory

35.4MiB live, 515.4MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1 766	5	1 771
Fresh	3	0	3
Picked	4	1	5
Done	0	0	0
Total	1 773	6	1 779

Accuracy

100.0%

Counts

1 779 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))
▶	100.0%	(/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))))))
▶	98.4%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶	98.8%	(/.f64 #s(literal 4/3 binary64) (.f64 #s(approx ( (+ (* v v) 1) (PI)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
▶	98.7%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))))
✓	97.2%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64)))

Compiler

Compiled 166 to 129 computations (22.3% saved)

simplify101.0ms (1.5%)

Memory

-5.6MiB live, 107.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (neg.f64 v) v #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))
cost-diff	128	(/.f64 #s(literal 4/3 binary64) (*.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)))
cost-diff	384	(/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))
cost-diff	0	(.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))
cost-diff	0	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))))
cost-diff	0	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #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 #s(literal -3 binary64) (.f64 v v) #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	#s(approx (* (+ (* v v) 1) (PI)) (PI.f64))
cost-diff	0	(.f64 #s(approx ( (+ (* v v) 1) (PI)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
cost-diff	0	(/.f64 #s(literal 4/3 binary64) (.f64 #s(approx ( (+ (* v v) 1) (PI)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))
cost-diff	0	#s(approx (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
cost-diff	0	(/.f64 #s(literal 4/3 binary64) #s(approx (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))))
cost-diff	0	(PI.f64)
cost-diff	0	(.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))
cost-diff	128	(.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
cost-diff	320	(/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))))))

Rules

3 504×	`lower-fma.f32`
3 496×	`lower-fma.f64`
2 730×	`lower-*.f32`
2 712×	`lower-*.f64`
2 022×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	382
0	77	384
1	138	384
2	247	375
3	586	375
4	1350	375
5	1951	375
6	3283	375
7	4855	375
8	6541	375
0	8149	367

Stop Event

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

Calls

Call 1

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

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

localize156.0ms (2.4%)

Memory

-19.6MiB live, 179.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 v)
accuracy	0	(PI.f64)
accuracy	0.015625	(/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))
accuracy	0.984375	(/.f64 #s(literal 4/3 binary64) (*.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)))
accuracy	0	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))))
accuracy	0.01171875	(.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))
accuracy	0.01953125	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #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 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
accuracy	0	(PI.f64)
accuracy	0.00390625	(/.f64 #s(literal 4/3 binary64) (.f64 #s(approx ( (+ (* v v) 1) (PI)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
accuracy	0.0078125	(.f64 #s(approx ( (+ (* v v) 1) (PI)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
accuracy	0.7730386071785871	#s(approx (* (+ (* v v) 1) (PI)) (PI.f64))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(PI.f64)
accuracy	0.00390625	(/.f64 #s(literal 4/3 binary64) #s(approx (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))))
accuracy	0.7349843651213593	#s(approx (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
accuracy	0.01171875	(.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))
accuracy	0.97265625	(.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))
accuracy	0.97265625	(.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
accuracy	0.9765625	(/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))))))

Samples

111.0ms

256×

valid

Compiler

Compiled 371 to 42 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-mult: 45.0ms (50.3% of total)

ival-pi: 17.0ms (19% of total)

ival-sqrt: 8.0ms (8.9% of total)

ival-div: 7.0ms (7.8% of total)

ival-add: 6.0ms (6.7% of total)

const: 3.0ms (3.4% of total)

ival-sub: 1.0ms (1.1% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

series21.0ms (0.3%)

Memory

21.5MiB live, 21.5MiB allocated

Counts

21 → 216

Calls

Call 1

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

Outputs
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI)))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(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)))))))))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt (* 3 (sqrt 2)) (taylor 0 v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) (patch (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (sqrt 2)) (* 3 (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))) (taylor 0 v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) (patch (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (sqrt 2)) (* (pow v 2) (+ (* 3 (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))))) (taylor 0 v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) (patch (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))) (taylor -inf v) (#s(alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) (patch #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))) (taylor -inf v) (#s(alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) (patch #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))) (taylor -inf v) (#s(alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) (patch #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -3 (* (pow v 2) (PI))) (taylor -inf v) (#s(alt (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) (patch (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))) (taylor -inf v) (#s(alt (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) (patch (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))) (taylor -inf v) (#s(alt (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) (patch (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2))))) (taylor -inf v) (#s(alt (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) (patch (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI)))) (taylor -inf v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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))) (taylor -inf v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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))) (taylor -inf v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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))) (taylor -inf v) (#s(alt (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ -4/3 (* (pow v 2) (PI))) (taylor -inf v) (#s(alt (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (taylor -inf v) (#s(alt (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2)) (taylor -inf v) (#s(alt (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2)) (taylor -inf v) (#s(alt (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 2) (PI))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2)))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2)))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2)))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow v 2)) (taylor -inf v) (#s(alt (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 1)) (taylor -inf v) (#s(alt (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 1)) (taylor -inf v) (#s(alt (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 1)) (taylor -inf v) (#s(alt (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 3) (sqrt -6)) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor -inf v) (#s(alt (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 v) (taylor -inf v) (#s(alt (neg.f64 v) (patch (neg.f64 v) #<representation binary64>) () ())) ())
#s(alt (* -1 v) (taylor -inf v) (#s(alt (neg.f64 v) (patch (neg.f64 v) #<representation binary64>) () ())) ())
#s(alt (* -1 v) (taylor -inf v) (#s(alt (neg.f64 v) (patch (neg.f64 v) #<representation binary64>) () ())) ())
#s(alt (* -1 v) (taylor -inf v) (#s(alt (neg.f64 v) (patch (neg.f64 v) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

((/ 4 (* (PI) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2)))))) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2)))) (* (PI) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2))))) (PI) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (sqrt 2) (PI)) (sqrt 2) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* (* 3 (PI)) (- 1 (* v v))) (* (PI) (+ (* -3 (* v v)) 3)) (/ (/ 4/3 (* (+ (* (neg v) v) 1) (PI))) (sqrt (+ (* -6 (* v v)) 2))) (/ 4/3 (* (+ (* (neg v) v) 1) (PI))) (* (+ (* (neg v) v) 1) (PI)) (+ (* (neg v) v) 1) (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2))) (neg v))

3.0ms

inf

((/ 4 (* (PI) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2)))))) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2)))) (* (PI) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2))))) (PI) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (sqrt 2) (PI)) (sqrt 2) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* (* 3 (PI)) (- 1 (* v v))) (* (PI) (+ (* -3 (* v v)) 3)) (/ (/ 4/3 (* (+ (* (neg v) v) 1) (PI))) (sqrt (+ (* -6 (* v v)) 2))) (/ 4/3 (* (+ (* (neg v) v) 1) (PI))) (* (+ (* (neg v) v) 1) (PI)) (+ (* (neg v) v) 1) (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2))) (neg v))

2.0ms

-inf

((/ 4 (* (PI) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2)))))) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2)))) (* (PI) (* 3 (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2))))) (PI) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (sqrt 2) (PI)) (sqrt 2) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* (* 3 (PI)) (- 1 (* v v))) (* (PI) (+ (* -3 (* v v)) 3)) (/ (/ 4/3 (* (+ (* (neg v) v) 1) (PI))) (sqrt (+ (* -6 (* v v)) 2))) (/ 4/3 (* (+ (* (neg v) v) 1) (PI))) (* (+ (* (neg v) v) 1) (PI)) (+ (* (neg v) v) 1) (* (+ (* (neg v) v) 1) (sqrt (+ (* -6 (* v v)) 2))) (neg v))

simplify208.0ms (3.2%)

Memory

5.7MiB live, 243.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 794×	`lower-fma.f64`
10 794×	`lower-fma.f32`
6 564×	`lower-*.f64`
6 564×	`lower-*.f32`
3 842×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	423	6519
1	1380	5589
2	5653	5353
0	8313	5187

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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))))))))))
(* 3 (sqrt 2))
(+ (* 3 (sqrt 2)) (* 3 (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))))
(+ (* 3 (sqrt 2)) (* (pow v 2) (+ (* 3 (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))))
(+ (* 3 (sqrt 2)) (* (pow v 2) (+ (* 3 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 3 (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 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))))))))))
(* 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)))))))))
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(* (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)))))
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)
(* 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 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (+ (* -3 (sqrt -6)) (* 3 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (sqrt -6)) (+ (* 3 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 3 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))
(* -1 (* (pow v 3) (+ (* -3 (sqrt -6)) (+ (* -3 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 3 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 3 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))))
(* 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 -1/6) (* (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)))
(* -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 -1/6) (* (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)))
(* -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))))))))))
(* (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))))
(* 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 (* (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 (* (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 -1/6) (* (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 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(* -1 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (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))))))
(* -1 v)
(* -1 v)
(* -1 v)
(* -1 v)

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

rewrite172.0ms (2.6%)

Memory

-0.0MiB live, 351.3MiB allocated

Rules

4 042×	`lower-/.f32`
4 030×	`lower-/.f64`
3 982×	`lower-*.f32`
3 964×	`lower-*.f64`
2 666×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	278
0	77	280
1	268	280
2	1562	276
0	8729	260

Stop Event

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

Counts

21 → 1 083

Calls

Call 1

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

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

eval288.0ms (4.4%)

Memory: -13.5MiB live, 545.1MiB allocated
Compiler: Compiled 44 778 to 4 514 computations (89.9% saved)

prune292.0ms (4.5%)

Memory

11.5MiB live, 484.4MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	1 591	0	1 591
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	1 591	6	1 597

Accuracy

100.0%

Counts

1 597 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (PI.f64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))))
✓	100.0%	(/.f64 #s(literal 4 binary64) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (.f64 (fma.f64 (neg.f64 v) v #s(literal 1 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))))))
✓	98.4%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	98.8%	(/.f64 #s(literal 4/3 binary64) (.f64 #s(approx ( (+ (* v v) 1) (PI)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
✓	98.7%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))))
✓	97.2%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64)))

Compiler

Compiled 332 to 143 computations (56.9% saved)

regimes18.0ms (0.3%)

Memory

10.1MiB live, 47.8MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

6.0ms	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))))))
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)

regimes12.0ms (0.2%)

Memory

-8.7MiB live, 29.7MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	v
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))))))
2.0ms	(*.f64 v v)
2.0ms	(.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
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 (.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)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes6.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

4 calls:

2.0ms	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 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)))))

Results

Accuracy	Segments	Branch
98.7%	1	`v`
98.7%	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))))))`
98.7%	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)))))`
98.7%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes5.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB 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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64)))

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

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
97.2%	1	`v`
97.2%	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))))))`
97.2%	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)))))`
97.2%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

simplify11.0ms (0.2%)

Memory

-25.3MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	88
1	58	88
2	60	88
3	61	88

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness589.0ms (9%)

Memory

-6.2MiB live, 599.7MiB allocated

Rules

16 554×	`lower-fma.f64`
16 554×	`lower-fma.f32`
10 216×	`lower-fma.f64`
10 216×	`lower-fma.f32`
6 304×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	283
0	89	275
1	318	265
2	2164	265
0	8404	265
0	200	1386
1	620	1206
2	2547	1131
3	7429	1131
0	8063	1091
0	16	59
0	26	59
1	101	57
2	626	57
3	5771	57
0	8439	51
0	354	5630
1	1159	4725
2	4800	4528
0	8122	4368

Stop Event

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

Compiler

Compiled 151 to 92 computations (39.1% saved)

preprocess127.0ms (1.9%)

Memory: -0.6MiB live, 115.4MiB allocated
Remove: (abs v)
Compiler: Compiled 214 to 148 computations (30.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze4.0ms (0.1%)

sample1.0s (15.4%)

explain163.0ms (2.5%)

preprocess185.0ms (2.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify119.0ms (1.8%)

localize55.0ms (0.8%)

series42.0ms (0.6%)

simplify202.0ms (3.1%)

rewrite261.0ms (4%)

eval142.0ms (2.2%)

prune123.0ms (1.9%)

simplify153.0ms (2.3%)

localize242.0ms (3.7%)

series470.0ms (7.2%)

simplify259.0ms (4%)

rewrite395.0ms (6.1%)

eval392.0ms (6%)

prune307.0ms (4.7%)

simplify101.0ms (1.5%)

localize156.0ms (2.4%)

series21.0ms (0.3%)

simplify208.0ms (3.2%)

rewrite172.0ms (2.6%)

eval288.0ms (4.4%)

prune292.0ms (4.5%)

regimes18.0ms (0.3%)

regimes12.0ms (0.2%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

simplify11.0ms (0.2%)

soundness589.0ms (9%)

preprocess127.0ms (1.9%)

end0.0ms (0%)

Profiling