Metrics for Falkner and Boettcher, Appendix B, 2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB 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 21 to 16 computations (23.8% saved)

sample1.4s (23%)

Memory

12.4MiB live, 1 884.1MiB allocated

Samples

1.0s	8 256×	0	valid
1.0ms	8×	0	invalid

Precisions

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

ival-mult: 357.0ms (45.8% of total)

ival-sqrt: 241.0ms (30.9% of total)

ival-sub: 83.0ms (10.6% of total)

ival-div: 73.0ms (9.4% of total)

exact: 16.0ms (2.1% of total)

ival-true: 7.0ms (0.9% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain164.0ms (2.7%)

Memory

-12.4MiB live, 272.1MiB allocated

FPErrors

Click to see full error table

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

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

59.0ms

512×

valid

Compiler

Compiled 236 to 60 computations (74.6% saved)

Precisions

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

ival-mult: 18.0ms (43.5% of total)

ival-div: 10.0ms (24.1% of total)

ival-sqrt: 7.0ms (16.9% of total)

ival-sub: 5.0ms (12.1% of total)

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

exact: 1.0ms (2.4% of total)

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

preprocess261.0ms (4.4%)

Memory

1.5MiB live, 150.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	53	38
2	180	38
3	602	38
4	1738	38
5	3320	38
6	4322	38
7	4653	38
8	4705	38
9	4765	38
10	4861	38
11	5567	38
12	6325	38
13	7420	38
14	7767	38
0	14	19
0	23	19
1	45	19
2	105	19
3	238	19
4	655	19
5	1473	19
6	2012	19
7	3618	19
8	4868	19
9	6382	19
10	7490	19
0	8062	17

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Symmetry

(abs v)

Compiler

Compiled 19 to 14 computations (26.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Status

Accuracy

Program

▶

100.0%

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify141.0ms (2.4%)

Memory

5.9MiB live, 91.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v)))))
cost-diff	128	(-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))
cost-diff	128	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
cost-diff	384	(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	71
0	23	71
1	45	71
2	105	71
3	238	71
4	655	71
5	1473	71
6	2012	71
7	3618	71
8	4868	71
9	6382	71
10	7490	71
0	8062	66

Stop Event

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

Calls

Call 1

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

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

localize41.0ms (0.7%)

Memory

-19.9MiB live, 53.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0078125	(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v)))))
accuracy	0.01171875	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0.171875	(.f64 #s(literal 3 binary64) (.f64 v v))

Samples

27.0ms

256×

valid

Compiler

Compiled 144 to 30 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 10.0ms (53.7% of total)

ival-sqrt: 4.0ms (21.5% of total)

ival-div: 2.0ms (10.7% of total)

ival-sub: 2.0ms (10.7% of total)

exact: 1.0ms (5.4% of total)

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

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

series8.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

6 → 48

Calls

Call 1

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

Outputs
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))) (taylor 0 v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))))))) (taylor 0 v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -3 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -3 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -3 (pow v 2))) (taylor 0 v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2))) (taylor 0 v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2))))))) (taylor 0 v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor 0 v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor 0 v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor 0 v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor 0 v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2)))) (taylor inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))) (taylor inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))) (taylor inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))) (taylor inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -3 (pow v 2)) (taylor inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 3)) (taylor inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 3)) (taylor inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 3)) (taylor inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* v (* (sqrt -3) (sqrt 2)))) (taylor inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))) (taylor inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))) (taylor inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))) (taylor inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))) (taylor -inf v) (#s(alt (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -3 (pow v 2)) (taylor -inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 3)) (taylor -inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 3)) (taylor -inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 3)) (taylor -inf v) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) (patch (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (* v (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))) (taylor -inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))) (taylor -inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))) (taylor -inf v) (#s(alt (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (patch (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())
#s(alt (* 3 (pow v 2)) (taylor -inf v) (#s(alt (.f64 #s(literal 3 binary64) (.f64 v v)) (patch (.f64 #s(literal 3 binary64) (.f64 v v)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	v	@	inf	((/ (sqrt 2) 4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (- 1 (* 3 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* 3 (* v v)) (sqrt 2))
2.0ms	v	@	0	((/ (sqrt 2) 4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (- 1 (* 3 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* 3 (* v v)) (sqrt 2))
1.0ms	v	@	-inf	((/ (sqrt 2) 4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (- 1 (* 3 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* 3 (* v v)) (sqrt 2))

Time

Variable

Point

Expression

3.0ms

inf

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

2.0ms

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

1.0ms

-inf

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

simplify233.0ms (3.9%)

Memory

-12.3MiB live, 267.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	139	862
1	431	833
2	1712	784
3	4876	723
0	8454	691

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
1
(+ 1 (* -3 (pow v 2)))
(+ 1 (* -3 (pow v 2)))
(+ 1 (* -3 (pow v 2)))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -3 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -3 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))

Outputs
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal -5/8 binary64))) (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -3 (pow v 2)))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
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(* 3 (pow v 2))
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(* 3 (pow v 2))
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(* 3 (pow v 2))
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(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
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(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
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(* (pow v 2) (- (/ 1 (pow v 2)) 3))
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(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) v) v)))) v)
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 v v))) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) v)
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
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(* 3 (pow v 2))
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(* 3 (pow v 2))
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(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
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(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
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(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
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(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(.f64 (neg.f64 v) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 v v))))))
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(.f64 #s(literal 3 binary64) (.f64 v v))
(* 3 (pow v 2))
(.f64 #s(literal 3 binary64) (.f64 v v))
(* 3 (pow v 2))
(.f64 #s(literal 3 binary64) (.f64 v v))
(* 3 (pow v 2))
(.f64 #s(literal 3 binary64) (.f64 v v))

rewrite135.0ms (2.3%)

Memory

31.5MiB live, 223.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	50
0	23	50
1	80	48
2	500	48
3	4875	48
0	8529	44

Stop Event

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

Counts

6 → 416

Calls

Call 1

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

Outputs
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#<batchref>
#<batchref>
#<batchref>

eval64.0ms (1.1%)

Memory: 4.7MiB live, 122.9MiB allocated
Compiler: Compiled 11 957 to 1 611 computations (86.5% saved)

prune11.0ms (0.2%)

Memory

-4.2MiB live, 33.3MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	458	6	464
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	459	6	465

Accuracy

100.0%

Counts

465 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
▶	100.0%	(.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
▶	100.0%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
▶	99.6%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
▶	100.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
▶	99.5%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))

Compiler

Compiled 170 to 134 computations (21.2% saved)

simplify123.0ms (2.1%)

Memory

10.4MiB live, 126.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
cost-diff	128	(.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
cost-diff	320	(.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))
cost-diff	0	(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
cost-diff	320	(.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
cost-diff	0	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
cost-diff	0	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
cost-diff	0	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))
cost-diff	0	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))))
cost-diff	0	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	332
0	62	326
1	121	326
2	324	322
3	785	320
4	1978	320
5	2726	320
6	4180	320
7	5655	320
8	7610	320
0	8045	311

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))
(*.f64 v v)
v
(fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64))
#s(literal -9/32 binary64)
#s(literal -3/8 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
#s(literal -5/2 binary64)
(*.f64 v v)
v
#s(literal 1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)))
(.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
#s(literal -3 binary64)
(*.f64 v v)
v
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))

Outputs
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (fma.f64 (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) (*.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (fma.f64 (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) (*.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))
(.f64 (fma.f64 (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) (*.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))
(fma.f64 (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) (.f64 v v) #s(literal 1/4 binary64))
(*.f64 v v)
v
(fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64))
#s(literal -9/32 binary64)
#s(literal -3/8 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(.f64 (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
#s(literal -5/2 binary64)
(*.f64 v v)
v
#s(literal 1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 #s(literal -1/4 binary64) (fma.f64 v v #s(literal -1 binary64))) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
#s(literal -3 binary64)
(*.f64 v v)
v
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))

localize259.0ms (4.3%)

Memory

-208.1MiB live, 260.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
accuracy	0	(*.f64 v v)
accuracy	0	(sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)))
accuracy	0.01171875	(.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0	(*.f64 v v)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0078125	(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.015625	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
accuracy	0	(*.f64 v v)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.01171875	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
accuracy	0.2820905580798483	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
accuracy	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.29360558067171516	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))))
accuracy	0.0078125	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))
accuracy	0.01171875	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))

Samples

231.0ms

256×

valid

Compiler

Compiled 532 to 66 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 26.0ms (60.8% of total)

ival-sqrt: 6.0ms (14% of total)

ival-add: 5.0ms (11.7% of total)

ival-div: 2.0ms (4.7% of total)

ival-sub: 2.0ms (4.7% of total)

exact: 1.0ms (2.3% of total)

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

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

series18.0ms (0.3%)

Memory

2.9MiB live, 41.9MiB allocated

Counts

17 → 180

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())

Outputs
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2))) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2)))))) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2))))))) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))))))) (taylor 0 v) (#s(alt (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2))) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2)))))) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2))))))) (taylor 0 v) (#s(alt #s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2))) (taylor 0 v) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2))) (taylor 0 v) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2))))) (taylor -inf v) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -5/2 (* (pow v 2) (sqrt 2))) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2)))) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2)))) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2)))) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -5/2 (pow v 2)) (taylor -inf v) (#s(alt (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 5/2)) (taylor -inf v) (#s(alt (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 5/2)) (taylor -inf v) (#s(alt (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (/ 1 (pow v 2)) 5/2)) (taylor -inf v) (#s(alt (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -6 (pow v 2)) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))) (taylor -inf v) (#s(alt (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))) (taylor -inf v) (#s(alt (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))) (taylor -inf v) (#s(alt (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (* v (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))) (taylor -inf v) (#s(alt (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))) (taylor -inf v) (#s(alt (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))) (taylor -inf v) (#s(alt (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))) (taylor -inf v) (#s(alt (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))) (taylor -inf v) (#s(alt (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))) (taylor -inf v) (#s(alt (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 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>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	v	@	inf	((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt 2) (+ (* (* v v) (+ (* -9/32 (* v v)) -3/8)) 1/4)) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) (+ (* -5/2 (* v v)) 1) (* (+ (* -3 (* v v)) 1) 2) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* v v))
2.0ms	v	@	0	((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt 2) (+ (* (* v v) (+ (* -9/32 (* v v)) -3/8)) 1/4)) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) (+ (* -5/2 (* v v)) 1) (* (+ (* -3 (* v v)) 1) 2) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* v v))
2.0ms	v	@	-inf	((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt 2) (+ (* (* v v) (+ (* -9/32 (* v v)) -3/8)) 1/4)) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) (+ (* -5/2 (* v v)) 1) (* (+ (* -3 (* v v)) 1) 2) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* v v))

Time

Variable

Point

Expression

3.0ms

inf

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt 2) (+ (* (* v v) (+ (* -9/32 (* v v)) -3/8)) 1/4)) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) (+ (* -5/2 (* v v)) 1) (* (+ (* -3 (* v v)) 1) 2) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* v v))

2.0ms

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt 2) (+ (* (* v v) (+ (* -9/32 (* v v)) -3/8)) 1/4)) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) (+ (* -5/2 (* v v)) 1) (* (+ (* -3 (* v v)) 1) 2) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* v v))

2.0ms

-inf

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt 2) (+ (* (* v v) (+ (* -9/32 (* v v)) -3/8)) 1/4)) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) 1/4) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (+ (* -5/2 (* v v)) 1) (sqrt 2)) (+ (* -5/2 (* v v)) 1) (* (+ (* -3 (* v v)) 1) 2) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* v v))

simplify214.0ms (3.6%)

Memory

38.7MiB live, 223.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	4041
1	622	3863
2	2375	3588
3	6252	3467
0	8068	3300

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(sqrt 2)
(+ (sqrt 2) (* -5/2 (* (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* -5/2 (* (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* -5/2 (* (pow v 2) (sqrt 2))))
1
(+ 1 (* -5/2 (pow v 2)))
(+ 1 (* -5/2 (pow v 2)))
(+ 1 (* -5/2 (pow v 2)))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(sqrt 2)
(+ (sqrt 2) (* -3/2 (* (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -9/8 (* (pow v 2) (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* (pow v 2) (+ (* -27/16 (* (pow v 2) (sqrt 2))) (* -9/8 (sqrt 2)))))))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -9/32 (* (pow v 4) (sqrt 2)))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (* -9/32 (sqrt 2))))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (+ (* -9/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (+ (* -9/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -5/2 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
(* -5/2 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* -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))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* v (* (sqrt -3) (sqrt 2)))
(* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))
(* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(* -9/32 (* (pow v 4) (sqrt 2)))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (* -9/32 (sqrt 2))))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (+ (* -9/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (+ (* -9/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -5/2 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
(* -5/2 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* -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))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(* -1 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)

Outputs
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64))) (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -27/64 binary64) (.f64 v v) #s(literal -9/32 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64))) (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64))) (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64))) (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -27/64 binary64) (.f64 v v) #s(literal -9/32 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -5/2 (* (pow v 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* -5/2 (* (pow v 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* -5/2 (* (pow v 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -5/2 (pow v 2)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -5/2 (pow v 2)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -5/2 (pow v 2)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 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))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64))) (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -27/64 binary64) (.f64 v v) #s(literal -9/32 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3/2 (* (pow v 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal -3/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -9/8 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/8 binary64) (.f64 v v) #s(literal -3/2 binary64))) (*.f64 v v) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* (pow v 2) (+ (* -27/16 (* (pow v 2) (sqrt 2))) (* -9/8 (sqrt 2)))))))
(fma.f64 (fma.f64 #s(literal -3/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -27/16 binary64) (.f64 v v) #s(literal -9/8 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)
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (/.f64 (/.f64 #s(literal 1/4 binary64) v) v))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) #s(literal 1/4 binary64))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (+.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))))) (pow.f64 v #s(literal 6 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64)))))) (pow.f64 v #s(literal 3 binary64)))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) v) (/.f64 (sqrt.f64 #s(literal 2 binary64)) v) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) v)
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 v v))) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) v)
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 v #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 v v))) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))) v)
(* -9/32 (* (pow v 4) (sqrt 2)))
(.f64 (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -9/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (* -9/32 (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 (/.f64 #s(literal -3/8 binary64) v) v) #s(literal -9/32 binary64))) (pow.f64 v #s(literal 4 binary64)))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (+ (* -9/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(.f64 (fma.f64 (/.f64 #s(literal -3/8 binary64) v) (/.f64 (sqrt.f64 #s(literal 2 binary64)) v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 v #s(literal 4 binary64))) #s(literal -9/32 binary64)))) (pow.f64 v #s(literal 4 binary64)))
(* (pow v 4) (+ (* -3/8 (/ (sqrt 2) (pow v 2))) (+ (* -9/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
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(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
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(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
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(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
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(* -5/2 (* (pow v 2) (sqrt 2)))
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(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
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(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
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(* (pow v 2) (+ (* -5/2 (sqrt 2)) (/ (sqrt 2) (pow v 2))))
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(* -5/2 (pow v 2))
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(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(* -6 (pow v 2))
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(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
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(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
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(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
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(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
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(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
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(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
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(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
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(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
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(* v (* (sqrt -3) (sqrt 2)))
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(* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))
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(* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
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(.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)
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v)))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(.f64 (neg.f64 (pow.f64 v #s(literal 3 binary64))) (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (+.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))))) (pow.f64 v #s(literal 6 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64)))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal -3 binary64)) v)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(fma.f64 (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (sqrt.f64 #s(literal -3 binary64))) #s(literal -1/8 binary64) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) v)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 v v))) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 v #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 v v))) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) v) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) v) (/.f64 (sqrt.f64 #s(literal 2 binary64)) v) (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 v v))) (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 v #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 v v))) (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #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)

rewrite136.0ms (2.3%)

Memory

3.5MiB live, 162.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	253
0	62	247
1	208	241
2	1449	241
0	8683	241

Stop Event

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

Counts

17 → 646

Calls

Call 1

Inputs
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))
(.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 v v)

Outputs
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eval214.0ms (3.6%)

Memory: -6.4MiB live, 237.1MiB allocated
Compiler: Compiled 24 110 to 2 743 computations (88.6% saved)

prune35.0ms (0.6%)

Memory

-24.4MiB live, 50.3MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	995	3	998
Fresh	1	0	1
Picked	3	2	5
Done	0	0	0
Total	999	5	1 004

Accuracy

100.0%

Counts

1 004 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	100.0%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
▶	98.4%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
▶	100.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
✓	99.5%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))

Compiler

Compiled 67 to 54 computations (19.4% saved)

simplify137.0ms (2.3%)

Memory

11.6MiB live, 129.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
cost-diff	0	(.f64 (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
cost-diff	128	(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
cost-diff	0	(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
cost-diff	0	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
cost-diff	320	(.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
cost-diff	704	(/.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64))
cost-diff	0	(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
cost-diff	0	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	228
0	59	226
1	112	222
2	244	210
3	514	210
4	1244	210
5	2020	210
6	3158	206
7	4045	206
8	5043	206
9	6013	206
10	7011	206
0	8047	201

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
#s(literal -5/8 binary64)
(*.f64 v v)
v
#s(literal 1/4 binary64)
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
#s(literal -5/2 binary64)
(*.f64 v v)
v
#s(literal 1 binary64)
#s(literal 4 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
#s(approx (* (+ (* -3 (* v v)) 1) 2) (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)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)

Outputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (fma.f64 (.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(.f64 (fma.f64 (.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(fma.f64 (*.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64))
#s(literal -5/8 binary64)
(*.f64 v v)
v
#s(literal 1/4 binary64)
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (/.f64 (fma.f64 (*.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 (*.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64))
(fma.f64 (*.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
#s(literal -5/2 binary64)
(*.f64 v v)
v
#s(literal 1 binary64)
#s(literal 4 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 (.f64 #s(literal -1/4 binary64) (fma.f64 v v #s(literal -1 binary64))) (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
#s(approx (* (+ (* -3 (* v v)) 1) 2) (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)
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)

localize94.0ms (1.6%)

Memory

-9.6MiB live, 145.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 v v)
accuracy	0	(sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
accuracy	0	#s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
accuracy	0.01171875	(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
accuracy	0	(*.f64 v v)
accuracy	0.0078125	(.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
accuracy	0.015625	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
accuracy	0	(*.f64 v v)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0078125	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
accuracy	0.015625	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))

Samples

67.0ms

256×

valid

Compiler

Compiled 337 to 65 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 20.0ms (38.1% of total)

ival-sqrt: 15.0ms (28.6% of total)

ival-div: 5.0ms (9.5% of total)

ival-add: 5.0ms (9.5% of total)

ival-pow: 4.0ms (7.6% of total)

ival-sub: 2.0ms (3.8% of total)

exact: 1.0ms (1.9% of total)

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

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

series12.0ms (0.2%)

Memory

21.8MiB live, 21.8MiB allocated

Counts

14 → 144

Calls

Call 1

Inputs
#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (patch (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (patch (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))) (patch (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (patch (.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 v v) (patch (.f64 v v) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))) (taylor -inf v) (#s(alt (.f64 (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))) (taylor -inf v) (#s(alt (.f64 (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (patch (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))) (taylor -inf v) (#s(alt (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))) (taylor -inf v) (#s(alt (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))) (taylor -inf v) (#s(alt (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -6 (pow v 2)) (taylor -inf v) (#s(alt #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6)) (taylor -inf v) (#s(alt #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (patch #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #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>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) (+ (* -5/8 (* v v)) 1/4)) (sqrt 2) (+ (* -5/8 (* v v)) 1/4) (/ (+ (* -5/2 (* v v)) 1) 4) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (+ (* -5/2 (* v v)) 1) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* (+ (* -3 (* v v)) 1) 2) (* v v) (/ 1 (pow 2 -1/2)))

2.0ms

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) (+ (* -5/8 (* v v)) 1/4)) (sqrt 2) (+ (* -5/8 (* v v)) 1/4) (/ (+ (* -5/2 (* v v)) 1) 4) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (+ (* -5/2 (* v v)) 1) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* (+ (* -3 (* v v)) 1) 2) (* v v) (/ 1 (pow 2 -1/2)))

1.0ms

-inf

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) (+ (* -5/8 (* v v)) 1/4)) (sqrt 2) (+ (* -5/8 (* v v)) 1/4) (/ (+ (* -5/2 (* v v)) 1) 4) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (+ (* -5/2 (* v v)) 1) (* (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (- 1 (* v v))) (* (sqrt (* (+ (* -3 (* v v)) 1) 2)) 1/4) (sqrt (* (+ (* -3 (* v v)) 1) 2)) (* (+ (* -3 (* v v)) 1) 2) (* v v) (/ 1 (pow 2 -1/2)))

simplify219.0ms (3.7%)

Memory

20.7MiB live, 292.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	200	2586
1	611	2484
2	2329	2331
3	6101	2261
0	8330	2153

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(/ 1/4 (sqrt 1/2))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
1
(+ 1 (* -5/2 (pow v 2)))
(+ 1 (* -5/2 (pow v 2)))
(+ 1 (* -5/2 (pow v 2)))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(sqrt 2)
(+ (sqrt 2) (* -3/2 (* (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -9/8 (* (pow v 2) (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* (pow v 2) (+ (* -27/16 (* (pow v 2) (sqrt 2))) (* -9/8 (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)
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -5/2 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* v (* (sqrt -3) (sqrt 2)))
(* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))
(* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 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))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -5/2 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(* -1 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 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))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)

Outputs
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(/ 1/4 (sqrt 1/2))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -5/2 (pow v 2)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -5/2 (pow v 2)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -5/2 (pow v 2)))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64))) (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(fma.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -27/64 binary64) (.f64 v v) #s(literal -9/32 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3/2 (* (pow v 2) (sqrt 2))))
(.f64 (fma.f64 #s(literal -3/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -9/8 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/8 binary64) (.f64 v v) #s(literal -3/2 binary64))) (*.f64 v v) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* (pow v 2) (+ (* -27/16 (* (pow v 2) (sqrt 2))) (* -9/8 (sqrt 2)))))))
(fma.f64 (fma.f64 #s(literal -3/2 binary64) (.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -27/16 binary64) (.f64 v v) #s(literal -9/8 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)
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) #s(literal 1/4 binary64))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (+.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))))) (pow.f64 v #s(literal 6 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64)))))) (pow.f64 v #s(literal 3 binary64)))
(* -5/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 (*.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v)
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(* -5/8 (pow v 2))
(.f64 #s(literal -5/8 binary64) (.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal 5/8 binary64)) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal 5/8 binary64)) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal 5/8 binary64)) v) v)
(* -5/8 (pow v 2))
(.f64 #s(literal -5/8 binary64) (.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal 5/8 binary64)) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal 5/8 binary64)) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal 5/8 binary64)) v) v)
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (+.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) #s(literal 1/4 binary64))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (+.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))))) (pow.f64 v #s(literal 6 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) (/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) #s(literal 11/24 binary64)) (pow.f64 v #s(literal 4 binary64)))))) (pow.f64 v #s(literal 3 binary64)))
(* -5/2 (pow v 2))
(.f64 #s(literal -5/2 binary64) (.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 5/2))
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(.f64 (.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal -3 binary64)) v)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1/8 binary64) v) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) v)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 v v))) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 v #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 v v))) (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (neg.f64 v) (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) v) (/.f64 (sqrt.f64 #s(literal 2 binary64)) v) (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 v v))) (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))))
(.f64 (neg.f64 v) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 v #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 v #s(literal 4 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 v v))) (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(* -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)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)

rewrite163.0ms (2.7%)

Memory

-10.5MiB live, 181.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	193
0	59	184
1	220	182
2	1565	180
0	8460	174

Stop Event

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

Counts

14 → 561

Calls

Call 1

Inputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(/.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64))
(.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
(fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
#s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(*.f64 v v)
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))

Outputs
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eval99.0ms (1.6%)

Memory: 10.5MiB live, 163.5MiB allocated
Compiler: Compiled 15 712 to 2 219 computations (85.9% saved)

prune16.0ms (0.3%)

Memory

6.4MiB live, 44.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	763	2	765
Fresh	0	0	0
Picked	1	2	3
Done	0	2	2
Total	764	6	770

Accuracy

100.0%

Counts

770 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	100.0%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	100.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
✓	99.5%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
▶	98.4%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
▶	98.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 72 to 59 computations (18.1% saved)

simplify175.0ms (2.9%)

Memory

-29.4MiB live, 105.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -5/8 binary64) v)
cost-diff	0	#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
cost-diff	1024	(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	173
0	40	173
1	78	165
2	161	165
3	323	165
4	790	165
5	1436	165
6	2389	157
7	4442	157
8	6302	157
0	8088	146

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1/4 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal -5/8 binary64) v)
#s(literal -5/8 binary64)
v
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1/4 binary64)

Outputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1/4 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (.f64 (fma.f64 (.f64 v v) #s(literal -5/2 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (.f64 (fma.f64 (.f64 v v) #s(literal -5/2 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (fma.f64 (.f64 v v) #s(literal -5/2 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal -5/8 binary64) v)
#s(literal -5/8 binary64)
v
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1/4 binary64)

localize83.0ms (1.4%)

Memory

3.8MiB live, 118.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.015625	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
accuracy	0.43359375	(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.015625	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	0.2936055807346357	#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	1.0	(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Samples

53.0ms

256×

valid

Compiler

Compiled 183 to 46 computations (74.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 18.0ms (42.1% of total)

ival-div: 8.0ms (18.7% of total)

ival-sqrt: 6.0ms (14% of total)

ival-pow: 4.0ms (9.4% of total)

ival-add: 2.0ms (4.7% of total)

ival-sub: 2.0ms (4.7% of total)

exact: 1.0ms (2.3% of total)

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

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

series10.0ms (0.2%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

9 → 84

Calls

Call 1

Inputs
#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (patch (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx ( (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -5/8 binary64) v) (patch (.f64 #s(literal -5/8 binary64) v) #<representation binary64>) () ())
#s(alt (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (patch (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ 1/4 (sqrt 1/2)) (taylor 0 v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2)))) (taylor 0 v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2)))) (taylor 0 v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2)))) (taylor 0 v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1/4 (sqrt 1/2)) (taylor 0 v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2)))) (taylor 0 v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2)))) (taylor 0 v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2)))) (taylor 0 v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (sqrt 2)) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))))))) (taylor 0 v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -5/8 (/ (pow v 2) (sqrt 1/2))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -5/8 (/ (pow v 2) (sqrt 1/2))) (taylor -inf v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2)))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))) (taylor -inf v) (#s(alt #s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (patch #s(approx ( (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -5/8 (/ (pow v 2) (sqrt 1/2))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx ( (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx ( (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx ( (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2))))) (taylor -inf v) (#s(alt #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx ( (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -5/8 v) (taylor -inf v) (#s(alt (.f64 #s(literal -5/8 binary64) v) (patch (.f64 #s(literal -5/8 binary64) v) #<representation binary64>) () ())) ())
#s(alt (* -5/8 v) (taylor -inf v) (#s(alt (.f64 #s(literal -5/8 binary64) v) (patch (.f64 #s(literal -5/8 binary64) v) #<representation binary64>) () ())) ())
#s(alt (* -5/8 v) (taylor -inf v) (#s(alt (.f64 #s(literal -5/8 binary64) v) (patch (.f64 #s(literal -5/8 binary64) v) #<representation binary64>) () ())) ())
#s(alt (* -5/8 v) (taylor -inf v) (#s(alt (.f64 #s(literal -5/8 binary64) v) (patch (.f64 #s(literal -5/8 binary64) v) #<representation binary64>) () ())) ())
#s(alt (/ v (sqrt 1/2)) (taylor -inf v) (#s(alt (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (patch (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ v (sqrt 1/2)) (taylor -inf v) (#s(alt (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (patch (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ v (sqrt 1/2)) (taylor -inf v) (#s(alt (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (patch (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ v (sqrt 1/2)) (taylor -inf v) (#s(alt (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (patch (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/ 1/4 (sqrt 1/2)) (sqrt 1/2) (+ (* (* -5/8 v) (/ v (sqrt 1/2))) (/ 1/4 (sqrt 1/2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (* -5/8 v) (/ v (sqrt 1/2)))

2.0ms

-inf

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/ 1/4 (sqrt 1/2)) (sqrt 1/2) (+ (* (* -5/8 v) (/ v (sqrt 1/2))) (/ 1/4 (sqrt 1/2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (* -5/8 v) (/ v (sqrt 1/2)))

2.0ms

((* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/ 1/4 (sqrt 1/2)) (sqrt 1/2) (+ (* (* -5/8 v) (/ v (sqrt 1/2))) (/ 1/4 (sqrt 1/2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (* -5/8 v) (/ v (sqrt 1/2)))

simplify216.0ms (3.6%)

Memory

-9.2MiB live, 219.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	1421
1	310	1381
2	1174	1305
3	4764	1265
4	7913	1265
0	8015	1212

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(/ 1/4 (sqrt 1/2))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(/ 1/4 (sqrt 1/2))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(/ 1/4 (sqrt 1/2))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))
(/ v (sqrt 1/2))

Outputs
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal -5/2 binary64) v) v #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64)))) #s(literal 1/4 binary64) (.f64 (.f64 (fma.f64 (.f64 #s(literal -5/2 binary64) v) v #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(/ 1/4 (sqrt 1/2))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/ 1/4 (sqrt 1/2))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* 1/4 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal -5/2 binary64) v) v #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64)))) #s(literal 1/4 binary64) (.f64 (.f64 (fma.f64 (.f64 #s(literal -5/2 binary64) v) v #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(/ 1/4 (sqrt 1/2))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -5/8 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(fma.f64 (*.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (/.f64 (/.f64 #s(literal 1/4 binary64) v) v))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v))) #s(literal 1/4 binary64))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))))) (pow.f64 v #s(literal 3 binary64)))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(.f64 (.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(.f64 (.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (/.f64 (/.f64 #s(literal 1/4 binary64) v) v))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v))) #s(literal 1/4 binary64))) (pow.f64 v #s(literal 3 binary64)))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))))) (pow.f64 v #s(literal 3 binary64)))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(.f64 (.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 v #s(literal 3 binary64)))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v)))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64))))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(.f64 (.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(.f64 (.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 v #s(literal 3 binary64)))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v)))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(.f64 (.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 11/24 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 v v))) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64))))))
(* -5/8 (/ (pow v 2) (sqrt 1/2)))
(.f64 (.f64 (/.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) v) v)
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 5/8 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) v) v) #s(literal 5/8 binary64))) (*.f64 v v))
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(* -5/8 v)
(*.f64 #s(literal -5/8 binary64) v)
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))
(/ v (sqrt 1/2))
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))

rewrite316.0ms (5.3%)

Memory

8.4MiB live, 204.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	161
0	40	149
1	172	147
2	1270	143
0	8492	137

Stop Event

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

Counts

9 → 188

Calls

Call 1

Inputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(*.f64 #s(literal -5/8 binary64) v)
(/.f64 v (sqrt.f64 #s(literal 1/2 binary64)))

Outputs
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eval99.0ms (1.6%)

Memory: -29.7MiB live, 120.0MiB allocated
Compiler: Compiled 6 195 to 1 107 computations (82.1% saved)

prune10.0ms (0.2%)

Memory

30.3MiB live, 30.3MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	319	6	325

Accuracy

100.0%

Counts

325 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	100.0%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	100.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
✓	99.5%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
✓	98.4%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
✓	98.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 237 to 128 computations (46% saved)

regimes13.0ms (0.2%)

Memory

0.9MiB live, 38.4MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 #s(literal -5/8 binary64) v) (/.f64 v (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (/.f64 (fma.f64 #s(literal -5/2 binary64) (.f64 v v) #s(literal 1 binary64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 #s(literal -3 binary64) (.f64 v v) #s(literal 1 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))

Outputs

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

Calls

3 calls:

5.0ms

(*.f64 v v)

4.0ms

3.0ms

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

Results

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

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes12.0ms (0.2%)

Memory

-25.9MiB live, 15.0MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (.f64 (fma.f64 #s(literal -5/2 binary64) (*.f64 v v) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64)))

Outputs
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))

Calls

3 calls:

8.0ms

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

2.0ms

(*.f64 v v)

Results

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

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes4.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Accuracy

Total -1.0b remaining (-335.3%)

Threshold costs -1b (-335.3%)

Counts

2 → 1

Calls

Call 1

Inputs

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

#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) #s(approx (* (/ (+ (* -5/2 (* v v)) 1) 4) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

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

Calls

3 calls:

2.0ms

1.0ms

(*.f64 v v)

1.0ms

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

Results

Accuracy	Segments	Branch
99.5%	1	`v`
99.5%	1	`(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))`
99.5%	1	`(*.f64 v v)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify118.0ms (2%)

Memory

-14.4MiB live, 62.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	78
1	69	78
2	152	78
3	313	78
4	781	78
5	1417	78
6	2878	78
7	5220	78
8	7806	78

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))

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

Outputs
(.f64 (.f64 (sqrt.f64 #s(approx (* (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(approx ( (+ (* -3 (* v v)) 1) 2) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))

soundness684.0ms (11.4%)

Memory

14.4MiB live, 418.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	4041
1	622	3863
2	2375	3588
3	6252	3467
0	8068	3300
0	14	50
0	23	50
1	80	48
2	500	48
3	4875	48
0	8529	44
0	139	862
1	431	833
2	1712	784
3	4876	723
0	8454	691

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

Compiler

Compiled 59 to 44 computations (25.4% saved)

preprocess64.0ms (1.1%)

Memory: 8.8MiB live, 47.8MiB allocated
Remove: (abs v)
Compiler: Compiled 196 to 138 computations (29.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze4.0ms (0.1%)

sample1.4s (23%)

explain164.0ms (2.7%)

preprocess261.0ms (4.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify141.0ms (2.4%)

localize41.0ms (0.7%)

series8.0ms (0.1%)

simplify233.0ms (3.9%)

rewrite135.0ms (2.3%)

eval64.0ms (1.1%)

prune11.0ms (0.2%)

simplify123.0ms (2.1%)

localize259.0ms (4.3%)

series18.0ms (0.3%)

simplify214.0ms (3.6%)

rewrite136.0ms (2.3%)

eval214.0ms (3.6%)

prune35.0ms (0.6%)

simplify137.0ms (2.3%)

localize94.0ms (1.6%)

series12.0ms (0.2%)

simplify219.0ms (3.7%)

rewrite163.0ms (2.7%)

eval99.0ms (1.6%)

prune16.0ms (0.3%)

simplify175.0ms (2.9%)

localize83.0ms (1.4%)

series10.0ms (0.2%)

simplify216.0ms (3.6%)

rewrite316.0ms (5.3%)

eval99.0ms (1.6%)

prune10.0ms (0.2%)

regimes13.0ms (0.2%)

regimes12.0ms (0.2%)

regimes4.0ms (0.1%)

simplify118.0ms (2%)

soundness684.0ms (11.4%)

preprocess64.0ms (1.1%)

end0.0ms (0%)

Profiling