Metrics for Falkner and Boettcher, Equation (22+)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze4.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB 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)

sample892.0ms (16.7%)

Memory

676.0MiB live, 676.0MiB allocated

Samples

578.0ms	8 256×	0	valid
1.0ms	15×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 439.0ms

ival-mult: 211.0ms (48% of total)

ival-sub: 73.0ms (16.6% of total)

ival-sqrt: 53.0ms (12.1% of total)

ival-div: 49.0ms (11.2% of total)

ival-pi: 30.0ms (6.8% of total)

exact: 15.0ms (3.4% of total)

ival-true: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain281.0ms (5.3%)

Memory

189.3MiB live, 189.3MiB 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

56.0ms

512×

valid

Compiler

Compiled 449 to 180 computations (59.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 17.0ms (48.4% of total)

ival-sub: 6.0ms (17.1% of total)

ival-div: 4.0ms (11.4% of total)

ival-sqrt: 4.0ms (11.4% of total)

ival-pi: 2.0ms (5.7% of total)

exact: 2.0ms (5.7% of total)

ival-true: 1.0ms (2.8% of total)

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

preprocess175.0ms (3.3%)

Memory

72.3MiB live, 72.3MiB allocated

Algorithm

1×	egg-herbie

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 (/.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 v v #s(literal -1 binary64)))

Symmetry

(abs v)

Compiler

Compiled 20 to 16 computations (20% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

98.5%

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

Compiler

Compiled 20 to 16 computations (20% saved)

simplify115.0ms (2.2%)

Memory

51.3MiB live, 51.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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 (-.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)))

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

localize41.0ms (0.8%)

Memory

26.9MiB live, 26.9MiB 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	0.0078125	(.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	0.16701127930532603	(.f64 #s(literal 6 binary64) (.f64 v v))
accuracy	0.98828125	(/.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

28.0ms

256×

valid

Compiler

Compiled 172 to 34 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 8.0ms (44.1% of total)

ival-sub: 4.0ms (22% of total)

ival-div: 2.0ms (11% of total)

ival-sqrt: 2.0ms (11% of total)

ival-pi: 1.0ms (5.5% of total)

exact: 1.0ms (5.5% of total)

ival-assert: 1.0ms (5.5% of total)

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

series13.0ms (0.2%)

Memory

7.5MiB live, 7.5MiB allocated

Counts

6 → 60

Calls

Call 1

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

Outputs
#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>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))) (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))) (* (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)))))))))) (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 (* 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>) () ())) ())
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#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 #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 (* 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
4.0ms	v	@	inf	((* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 3 (PI)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* 6 (* v v)))
4.0ms	v	@	0	((* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 3 (PI)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* 6 (* v v)))
2.0ms	v	@	-inf	((* (* 3 (PI)) (- 1 (* v v))) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* 3 (PI)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* 6 (* v v)))

Time

Variable

Point

Expression

4.0ms

inf

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

4.0ms

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

2.0ms

-inf

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

simplify204.0ms (3.8%)

Memory

108.9MiB live, 108.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	200	1386
1	620	1206
2	2540	1131
3	7419	1131
0	8053	1091

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 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))))))))))
(* 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))))))))))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (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)))))
(* -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)))))))
(* -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))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (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)))))
(* -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))))))))
(* 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)))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))

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

rewrite164.0ms (3.1%)

Memory

91.0MiB live, 91.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	62
0	26	62
1	101	60
2	626	60
3	5773	60
0	8441	54

Stop Event

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

Counts

6 → 479

Calls

Call 1

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

Outputs
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eval82.0ms (1.5%)

Memory: 85.4MiB live, 85.4MiB allocated
Compiler: Compiled 14 851 to 1 864 computations (87.4% saved)

prune16.0ms (0.3%)

Memory

27.7MiB live, 27.7MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	535	4	539
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	536	4	540

Accuracy

100.0%

Counts

540 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶	97.7%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
▶	99.2%	(/.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)))))
▶	97.7%	#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 57 to 50 computations (12.3% saved)

simplify118.0ms (2.2%)

Memory

67.6MiB live, 67.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	271
0	73	266
1	124	262
2	211	262
3	451	262
4	1072	262
5	1690	262
6	3040	262
7	5847	262
8	7719	262
0	8228	255

Stop Event

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

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

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

localize98.0ms (1.8%)

Memory

76.3MiB live, 76.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(PI.f64)
accuracy	0.00390625	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0.0078125	(.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	0.98828125	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
accuracy	0.0078125	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))
accuracy	0.16701127930532603	(.f64 #s(literal 6 binary64) (.f64 v v))
accuracy	0.49086072552414817	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
accuracy	0.98828125	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
accuracy	0	(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #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 (fma.f64 v v #s(literal 1 binary64)) (PI.f64))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0	(PI.f64)
accuracy	0.5119396302420114	#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))

Samples

67.0ms

256×

valid

Compiler

Compiled 490 to 72 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 19.0ms (41% of total)

ival-sqrt: 7.0ms (15.1% of total)

ival-div: 6.0ms (13% of total)

ival-add: 4.0ms (8.6% of total)

const: 4.0ms (8.6% of total)

ival-sub: 3.0ms (6.5% of total)

ival-pi: 1.0ms (2.2% of total)

exact: 1.0ms (2.2% of total)

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

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

series19.0ms (0.4%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

20 → 168

Calls

Call 1

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

Outputs
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#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 (+ (* 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 #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 (+ (* 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 #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 (+ (* 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 #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 (* (PI) (sqrt 2)) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2))))) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))))) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3)))))))))))) (taylor 0 v) (#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 (PI) (taylor 0 v) (#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 (+ (PI) (* (pow v 2) (PI))) (taylor 0 v) (#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 (+ (PI) (* (pow v 2) (PI))) (taylor 0 v) (#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 (+ (PI) (* (pow v 2) (PI))) (taylor 0 v) (#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 1 (taylor 0 v) (#s(alt (fma.f64 v v #s(literal 1 binary64)) (patch (fma.f64 v v #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow v 2)) (taylor 0 v) (#s(alt (fma.f64 v v #s(literal 1 binary64)) (patch (fma.f64 v v #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow v 2)) (taylor 0 v) (#s(alt (fma.f64 v v #s(literal 1 binary64)) (patch (fma.f64 v v #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow v 2)) (taylor 0 v) (#s(alt (fma.f64 v v #s(literal 1 binary64)) (patch (fma.f64 v v #s(literal 1 binary64)) #<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 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))) (patch (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))) #<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 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))) (patch (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))) (patch (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))) (patch (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* 3 (PI)) (taylor 0 v) (#s(alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (patch #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (taylor 0 v) (#s(alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (patch #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (taylor 0 v) (#s(alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (patch #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI))) (taylor 0 v) (#s(alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (patch #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))) #<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 (* 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 (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 (+ (* 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 (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 (+ (* 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)))))))) (taylor 0 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 (+ (* 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)))))))))) (taylor 0 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 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#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>) () ())) ())
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#s(alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI)))) (taylor -inf v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))) #<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 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))) #<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 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))) #<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 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))) #<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>) () ())) ())
#s(alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI)))) (taylor -inf 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 (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 (* -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 #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 (* -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 #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 (* -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 #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>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	v	@	0	((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (/ (sqrt 1/2) (PI)) 4/3) (/ (sqrt 1/2) (PI)) (sqrt 1/2) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (+ (* v v) 1) (PI) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* (* 3 (PI)) (- 1 (* v v))) (* (PI) 3) (* (* 3 (PI)) (- 1 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* 3 (PI)) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (sqrt (+ (* -6 (* v v)) 2)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* 6 (* v v)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))))
4.0ms	v	@	inf	((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (/ (sqrt 1/2) (PI)) 4/3) (/ (sqrt 1/2) (PI)) (sqrt 1/2) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (+ (* v v) 1) (PI) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* (* 3 (PI)) (- 1 (* v v))) (* (PI) 3) (* (* 3 (PI)) (- 1 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* 3 (PI)) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (sqrt (+ (* -6 (* v v)) 2)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* 6 (* v v)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))))
2.0ms	v	@	-inf	((/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* (/ (sqrt 1/2) (PI)) 4/3) (/ (sqrt 1/2) (PI)) (sqrt 1/2) (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (* (+ (* v v) 1) (PI)) (+ (* v v) 1) (PI) (- 2 (* 6 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))) (* (* 3 (PI)) (- 1 (* v v))) (* (PI) 3) (* (* 3 (PI)) (- 1 (* v v))) (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))) (* 3 (PI)) (/ 4/3 (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2)))) (sqrt (+ (* -6 (* v v)) 2)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (* 6 (* v v)) (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))))

Time

Variable

Point

Expression

4.0ms

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

4.0ms

inf

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

2.0ms

-inf

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

simplify181.0ms (3.4%)

Memory

118.0MiB live, 118.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	344	4718
1	1122	4039
2	4621	3821
0	8616	3676

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

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

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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(* (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)
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 (*.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 3 binary64)) (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 (neg.f64 (pow.f64 v #s(literal 3 binary64))) (fma.f64 (/.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))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (neg.f64 (pow.f64 v #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (PI.f64) (.f64 (+.f64 (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (pow.f64 v #s(literal 4 binary64))) (/.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))))
(* -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))))))))
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(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(*.f64 (/.f64 #s(literal -4/3 binary64) (pow.f64 v #s(literal 3 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (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 (/.f64 (+.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)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (pow.f64 v #s(literal 3 binary64))) #s(literal -4/3 binary64))
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(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))
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(* -1 (* v (sqrt -6)))
(*.f64 (neg.f64 v) (sqrt.f64 #s(literal -6 binary64)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -6 binary64)) v (/.f64 (/.f64 v (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (neg.f64 v) (fma.f64 #s(literal 1/12 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 v #s(literal 4 binary64))) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 (neg.f64 v) (fma.f64 #s(literal 1/12 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 v #s(literal 4 binary64))) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (pow.f64 v #s(literal 6 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 v #s(literal 3 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (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 (-.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))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) #s(literal -4/3 binary64) (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))) v) (/.f64 #s(literal 4/3 binary64) v) (/.f64 (fma.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))) #s(literal 4/3 binary64) (/.f64 #s(literal 1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 4 binary64))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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 1/144 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))) (pow.f64 v #s(literal 4 binary64))) (/.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)))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* 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 (/.f64 #s(literal 4/3 binary64) (pow.f64 v #s(literal 3 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (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 (-.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))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) #s(literal -4/3 binary64) (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))) v) (/.f64 #s(literal 4/3 binary64) v) (/.f64 (fma.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))) #s(literal 4/3 binary64) (/.f64 #s(literal 1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 4 binary64))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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 1/144 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))) (pow.f64 v #s(literal 4 binary64))) (/.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)))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))

rewrite175.0ms (3.3%)

Memory

103.0MiB live, 103.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	209
0	73	205
1	234	201
2	1220	201
0	8691	201

Stop Event

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

Counts

20 → 1 150

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

Outputs
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eval218.0ms (4.1%)

Memory: 203.8MiB live, 203.8MiB allocated
Compiler: Compiled 35 801 to 5 040 computations (85.9% saved)

prune42.0ms (0.8%)

Memory

64.0MiB live, 64.0MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1 489	6	1 495
Fresh	0	0	0
Picked	3	1	4
Done	0	0	0
Total	1 492	7	1 499

Accuracy

100.0%

Counts

1 499 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
▶	97.7%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))))
	98.5%	(/.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)))))
▶	100.0%	(/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶	99.2%	(/.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)))))
▶	99.2%	(/.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))))
✓	97.7%	#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 173 to 154 computations (11% saved)

simplify115.0ms (2.2%)

Memory

63.5MiB live, 63.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	341
0	66	341
1	108	341
2	162	341
3	305	341
4	691	341
5	1180	341
6	1497	341
7	2782	341
8	4098	341
9	5998	341
0	8121	329

Stop Event

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

Calls

Call 1

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

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

localize93.0ms (1.7%)

Memory

93.6MiB live, 93.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(PI.f64)
accuracy	0.0078125	(/.f64 #s(literal 4 binary64) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64))))
accuracy	0.01171875	(/.f64 (/.f64 #s(literal 4 binary64) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
accuracy	0.49086072552414817	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))
accuracy	0	(PI.f64)
accuracy	0.0078125	(.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64))))
accuracy	0.49086072552414817	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))
accuracy	0.98828125	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))))
accuracy	0	(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #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	0.49734568677928104	#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	0.4739095502247489	#s(approx (* (* (+ (* v v) 1) (PI)) (sqrt (+ (* -6 (* v v)) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
accuracy	0	(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
accuracy	0	(PI.f64)
accuracy	0.00390625	(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64))
accuracy	0.0078125	(.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))

Samples

63.0ms

256×

valid

Compiler

Compiled 556 to 63 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 17.0ms (41.4% of total)

ival-div: 8.0ms (19.5% of total)

ival-sqrt: 5.0ms (12.2% of total)

ival-add: 4.0ms (9.7% of total)

const: 4.0ms (9.7% of total)

ival-pi: 1.0ms (2.4% of total)

ival-sub: 1.0ms (2.4% of total)

exact: 1.0ms (2.4% of total)

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

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

series17.0ms (0.3%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

22 → 216

Calls

Call 1

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

Outputs
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (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))))) (* 4/3 (/ (sqrt 1/2) (PI)))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #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 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #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 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (PI) (sqrt 2)) (taylor 0 v) (#s(alt (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (patch (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (patch (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))) (taylor 0 v) (#s(alt (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (patch (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* 3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))))))))) (taylor 0 v) (#s(alt (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (patch (.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (PI) (taylor 0 v) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (PI) (* -1 (* (pow v 2) (PI)))) (taylor 0 v) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (PI) (* -1 (* (pow v 2) (PI)))) (taylor 0 v) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (PI) (* -1 (* (pow v 2) (PI)))) (taylor 0 v) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 v v)) (patch (-.f64 #s(literal 1 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 v v)) (patch (-.f64 #s(literal 1 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 v v)) (patch (-.f64 #s(literal 1 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 v v)) (patch (-.f64 #s(literal 1 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#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 (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI)))) (taylor 0 v) (#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 (+ (* 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))))))))) (taylor 0 v) (#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 (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))))) (taylor 0 v) (#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 (* (PI) (sqrt 2)) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2))))) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))))) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3)))))))))))) (taylor 0 v) (#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 (* (PI) (sqrt 2)) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2))))) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))))) (taylor 0 v) (#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 (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3)))))))))))) (taylor 0 v) (#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 (PI) (taylor 0 v) (#s(alt #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) (patch #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (PI) (* (pow v 2) (PI))) (taylor 0 v) (#s(alt #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) (patch #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (PI) (* (pow v 2) (PI))) (taylor 0 v) (#s(alt #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) (patch #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (PI) (* (pow v 2) (PI))) (taylor 0 v) (#s(alt #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) (patch #s(approx (* (+ (* v v) 1) (PI)) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2)))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 3 (* (PI) (sqrt 2))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))) #<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 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))))))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2)))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))) (taylor -inf v) (#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 (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI)))) (taylor -inf v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64))))) #<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 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64))))) #<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 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64))))) #<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 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx ( (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64))))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

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

2.0ms

-inf

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

simplify193.0ms (3.6%)

Memory

110.4MiB live, 110.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	404	6215
1	1329	5346
2	5550	5105
0	8246	4935

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

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 (+.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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) #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 (+.f64 (/.f64 #s(literal 27/16 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 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 #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 (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 #s(literal 4/3 binary64) (fma.f64 (fma.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) (+.f64 (/.f64 #s(literal 27/16 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 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 #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)))
(* (PI) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))
(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)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))))))
(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)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* 3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(fma.f64 (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) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(PI)
(PI.f64)
(+ (PI) (* -1 (* (pow v 2) (PI))))
(-.f64 (PI.f64) (.f64 (.f64 v v) (PI.f64)))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(-.f64 (PI.f64) (.f64 (.f64 v v) (PI.f64)))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(-.f64 (PI.f64) (.f64 (.f64 v v) (PI.f64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* 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))))
(.f64 (fma.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) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) #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)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(.f64 #s(literal 4/3 binary64) (fma.f64 (fma.f64 (-.f64 (+.f64 (/.f64 #s(literal 27/16 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.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) (-.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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(fma.f64 (.f64 #s(literal 4/3 binary64) (fma.f64 (fma.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 135/32 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 3/4 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -27/16 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 (/.f64 #s(literal 27/16 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.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) (-.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)))
(* (PI) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(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)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(fma.f64 (fma.f64 (PI.f64) (+.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -21/4 binary64)) v) v)) (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(fma.f64 (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 -21/4 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) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(* (PI) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(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)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(fma.f64 (fma.f64 (PI.f64) (+.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -21/4 binary64)) v) v)) (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(fma.f64 (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 -21/4 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) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(PI)
(PI.f64)
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (*.f64 v v) (PI.f64) (PI.f64))
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (*.f64 v v) (PI.f64) (PI.f64))
(+ (PI) (* (pow v 2) (PI)))
(fma.f64 (*.f64 v v) (PI.f64) (PI.f64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64)))) #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 #s(literal -9/4 binary64) (.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 v (/.f64 v (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) #s(literal -27/2 binary64) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 v v) (sqrt.f64 #s(literal 2 binary64)))
(* 3 (* (PI) (sqrt 2)))
(.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(.f64 #s(literal 3 binary64) (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))))
(+ (* 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)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64)))) #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
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(/.f64 (.f64 #s(literal 4/3 binary64) (+.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.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)))) (pow.f64 v #s(literal 4 binary64)))) (+.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal -5/2592 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 #s(literal 1/36 binary64) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))) (/.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))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 v #s(literal 3 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (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 (-.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))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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))) (pow.f64 v #s(literal 4 binary64))) (/.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))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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 1/144 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))) (pow.f64 v #s(literal 4 binary64))) (/.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)))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))

rewrite167.0ms (3.1%)

Memory

106.0MiB live, 106.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	259
0	66	259
1	214	259
2	1040	259
0	8382	254

Stop Event

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

Counts

22 → 1 106

Calls

Call 1

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

Outputs
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eval251.0ms (4.7%)

Memory: 271.1MiB live, 271.1MiB allocated
Compiler: Compiled 43 360 to 5 038 computations (88.4% saved)

prune51.0ms (1%)

Memory

97.9MiB live, 97.9MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	1 864	2	1 866
Fresh	1	0	1
Picked	1	4	5
Done	0	1	1
Total	1 866	7	1 873

Accuracy

100.0%

Counts

1 873 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (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))))))
✓	97.7%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))))
▶	100.0%	(/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)))
✓	99.2%	(/.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)))))
✓	99.2%	(/.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))))
✓	97.7%	#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 90 to 81 computations (10% saved)

simplify120.0ms (2.3%)

Memory

92.3MiB live, 92.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	181
0	45	181
1	85	181
2	149	181
3	297	178
4	697	178
5	1107	178
6	1420	178
7	2655	178
8	3998	178
9	5922	178
10	7862	178
0	8174	177

Stop Event

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

Calls

Call 1

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

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

localize71.0ms (1.3%)

Memory

26.7MiB live, 26.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
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	0.0078125	(.f64 (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)))))
accuracy	0.0078125	(.f64 (PI.f64) (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 3 binary64)))
accuracy	0.98828125	(/.f64 #s(literal 4 binary64) (.f64 (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))))))
accuracy	0	(*.f64 v v)
accuracy	0	(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
accuracy	0	(PI.f64)
accuracy	0.00390625	(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Samples

50.0ms

256×

valid

Compiler

Compiled 321 to 52 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 16.0ms (45.6% of total)

ival-add: 4.0ms (11.4% of total)

ival-sqrt: 4.0ms (11.4% of total)

const: 4.0ms (11.4% of total)

ival-div: 3.0ms (8.5% of total)

ival-pi: 1.0ms (2.8% of total)

ival-sub: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

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

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

series12.0ms (0.2%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

12 → 132

Calls

Call 1

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

Outputs
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) #<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 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) #<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 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) #<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 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) (patch (/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (* (PI) (sqrt 2)) (taylor 0 v) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))) (taylor 0 v) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* 3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))))))))) (taylor 0 v) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2)))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 3 (* (PI) (sqrt 2))) (taylor 0 v) (#s(alt (.f64 (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))))) (patch (.f64 (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))))) #<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 (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))))) (patch (.f64 (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))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))) (taylor 0 v) (#s(alt (.f64 (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))))) (patch (.f64 (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))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))))))) (taylor 0 v) (#s(alt (.f64 (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))))) (patch (.f64 (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))))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2)))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2)))))) (taylor 0 v) (#s(alt (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 v) (#s(alt (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -6 (pow v 2))) (taylor 0 v) (#s(alt (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -6 (pow v 2))) (taylor 0 v) (#s(alt (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -6 (pow v 2))) (taylor 0 v) (#s(alt (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor 0 v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor 0 v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor 0 v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor 0 v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sqrt 1/2) (PI))) (taylor 0 v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 (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)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (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)))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor -inf v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor -inf v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor -inf v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (pow v 2) (taylor -inf v) (#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI)))) (taylor -inf v) (#s(alt (/.f64 #s(literal 4 binary64) (.f64 (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)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (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)))))) #<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 #s(literal 4 binary64) (.f64 (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)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (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)))))) #<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 #s(literal 4 binary64) (.f64 (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)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (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)))))) #<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 #s(literal 4 binary64) (.f64 (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)))))) (patch (/.f64 #s(literal 4 binary64) (.f64 (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)))))) #<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 (* -3 (* (pow v 2) (PI))) (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 (* (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>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

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

1.0ms

-inf

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

simplify167.0ms (3.1%)

Memory

46.9MiB live, 46.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	330	3420
1	1028	3002
2	4120	2847
0	8044	2750

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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

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 (+.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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) #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 (/.f64 (.f64 v v) (PI.f64)) (/.f64 #s(literal 27/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.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 (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 #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 v v) (PI.f64)) (/.f64 #s(literal 27/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.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)))
(* (PI) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))
(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)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))))))
(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)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* -1 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* 3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(fma.f64 (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) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))
(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)))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(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)))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 27/2 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) (.f64 v v) (-.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)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 #s(literal -3 binary64) v) (/.f64 v (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 #s(literal -9/4 binary64) (.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -27/2 binary64) v) (/.f64 v (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 v v) (sqrt.f64 #s(literal 2 binary64)))
(* 3 (* (PI) (sqrt 2)))
(.f64 #s(literal 3 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(.f64 #s(literal 3 binary64) (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))))
(+ (* 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)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 #s(literal -3 binary64) v) (/.f64 v (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 #s(literal -9/4 binary64) (.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -27/2 binary64) v) (/.f64 v (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 v v) (sqrt.f64 #s(literal 2 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))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(* 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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(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) #s(literal -4/3 binary64) (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))) v) (/.f64 #s(literal 4/3 binary64) v) (/.f64 (fma.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))) #s(literal 4/3 binary64) (/.f64 #s(literal 1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 4 binary64))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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 1/144 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))) (pow.f64 v #s(literal 4 binary64))) (/.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)))))) (neg.f64 (pow.f64 v #s(literal 3 binary64))))
(* -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 (/.f64 #s(literal 3 binary64) 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 (/.f64 #s(literal 3 binary64) 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 (/.f64 #s(literal 3 binary64) v) v) #s(literal -3 binary64))) 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 (/.f64 #s(literal 3 binary64) 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 (/.f64 #s(literal 3 binary64) 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 (/.f64 #s(literal 3 binary64) v) v) #s(literal -3 binary64))) v) v)

rewrite169.0ms (3.2%)

Memory

71.2MiB live, 71.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	149
0	45	149
1	171	149
2	952	149
0	8239	149

Stop Event

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

Counts

12 → 765

Calls

Call 1

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

Outputs
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eval147.0ms (2.8%)

Memory: 147.2MiB live, 147.2MiB allocated
Compiler: Compiled 27 278 to 3 603 computations (86.8% saved)

prune30.0ms (0.6%)

Memory

45.4MiB live, 45.4MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	1 011	0	1 011
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	1 011	7	1 018

Accuracy

100.0%

Counts

1 018 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
✓	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (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))))))
✓	97.7%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))))
✓	100.0%	(/.f64 #s(literal 4/3 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (PI.f64)))
✓	99.2%	(/.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)))))
✓	99.2%	(/.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))))
✓	97.7%	#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 286 to 144 computations (49.7% saved)

regimes17.0ms (0.3%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
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 42 to 33 computations (21.4% saved)

regimes12.0ms (0.2%)

Memory

6.4MiB live, 6.4MiB 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 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (.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 #s(literal 4 binary64) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal 3 binary64) (PI.f64)))) (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))

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

Calls

4 calls:

3.0ms	v
3.0ms	(*.f64 v v)
3.0ms	(.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)))))
3.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Results

Accuracy	Segments	Branch
99.2%	1	`v`
99.2%	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))))))`
99.2%	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)))))`
99.2%	1	`(*.f64 v v)`

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes11.0ms (0.2%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

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

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:

3.0ms	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
99.2%	1	`v`
99.2%	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))))))`
99.2%	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)))))`
99.2%	1	`(*.f64 v v)`

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes7.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB 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
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)))))
2.0ms	(*.f64 v 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))))))

Results

Accuracy	Segments	Branch
99.2%	1	`v`
99.2%	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))))))`
99.2%	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)))))`
99.2%	1	`(*.f64 v v)`

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes7.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB 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:

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
97.7%	1	`v`
97.7%	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))))))`
97.7%	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)))))`
97.7%	1	`(*.f64 v v)`

Compiler

Compiled 42 to 33 computations (21.4% saved)

simplify30.0ms (0.6%)

Memory

33.1MiB live, 33.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	109
1	64	109
2	71	109
3	75	109
4	77	109

Stop Event

1×

saturated

Calls

Call 1

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

soundness752.0ms (14.1%)

Memory

288.0MiB live, 288.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	200	1386
1	620	1206
2	2540	1131
3	7419	1131
0	8053	1091
0	16	62
0	26	62
1	101	60
2	626	60
3	5773	60
0	8441	54
0	45	209
0	73	205
1	234	201
2	1220	201
0	8691	201
0	41	259
0	66	259
1	214	259
2	1040	259
0	8382	254
0	344	4718
1	1122	4039
2	4621	3821
0	8616	3676

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

Compiler

Compiled 199 to 135 computations (32.2% saved)

preprocess53.0ms (1%)

Memory: 57.5MiB live, 57.5MiB allocated
Remove: (abs v)
Compiler: Compiled 222 to 150 computations (32.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze4.0ms (0.1%)

sample892.0ms (16.7%)

explain281.0ms (5.3%)

preprocess175.0ms (3.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify115.0ms (2.2%)

localize41.0ms (0.8%)

series13.0ms (0.2%)

simplify204.0ms (3.8%)

rewrite164.0ms (3.1%)

eval82.0ms (1.5%)

prune16.0ms (0.3%)

simplify118.0ms (2.2%)

localize98.0ms (1.8%)

series19.0ms (0.4%)

simplify181.0ms (3.4%)

rewrite175.0ms (3.3%)

eval218.0ms (4.1%)

prune42.0ms (0.8%)

simplify115.0ms (2.2%)

localize93.0ms (1.7%)

series17.0ms (0.3%)

simplify193.0ms (3.6%)

rewrite167.0ms (3.1%)

eval251.0ms (4.7%)

prune51.0ms (1%)

simplify120.0ms (2.3%)

localize71.0ms (1.3%)

series12.0ms (0.2%)

simplify167.0ms (3.1%)

rewrite169.0ms (3.2%)

eval147.0ms (2.8%)

prune30.0ms (0.6%)

regimes17.0ms (0.3%)

regimes12.0ms (0.2%)

regimes11.0ms (0.2%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

simplify30.0ms (0.6%)

soundness752.0ms (14.1%)

preprocess53.0ms (1%)

end0.0ms (0%)

Profiling