Metrics for Falkner and Boettcher, Appendix B, 2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze5.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample1.2s (19.6%)

Memory

5.0MiB live, 1 840.5MiB allocated

Samples

838.0ms	8 256×	0	valid
1.0ms	13×	0	invalid

Precisions

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

ival-mult: 269.0ms (43.6% of total)

ival-sqrt: 173.0ms (28% of total)

ival-sub: 89.0ms (14.4% of total)

ival-div: 61.0ms (9.9% of total)

exact: 15.0ms (2.4% of total)

ival-true: 7.0ms (1.1% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain232.0ms (3.8%)

Memory

-23.4MiB live, 305.3MiB allocated

FPErrors

Click to see full error table

Overpredictions	Example	Example	Subexpression
0	-	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))`
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)))))`
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)))`
0	-	-	`(*.f64 v v)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`#s(literal 3 binary64)`
0	-	-	`(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))`
0	-	-	`(sqrt.f64 #s(literal 2 binary64))`
0	-	-	`(-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))`
0	-	-	`#s(literal 4 binary64)`
1	(-1.2431788259739382e-162)	-	`(.f64 #s(literal 3 binary64) (.f64 v v))`
0	-	-	`v`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(-.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

75.0ms

512×

valid

Compiler

Compiled 165 to 46 computations (72.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sqrt: 27.0ms (54.8% of total)

ival-mult: 12.0ms (24.4% of total)

ival-sub: 5.0ms (10.2% of total)

ival-div: 4.0ms (8.1% of total)

ival-true: 1.0ms (2% of total)

exact: 1.0ms (2% of total)

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

preprocess256.0ms (4.2%)

Memory

27.1MiB live, 183.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	53	38
2	168	38
3	591	38
4	1654	38
5	2972	38
6	4007	38
7	4338	38
8	4392	38
9	4452	38
10	4548	38
11	5258	38
12	6044	38
13	7156	38
14	7502	38
0	14	19
0	23	19
1	45	19
2	97	19
3	230	19
4	651	19
5	1485	19
6	2032	19
7	3628	19
8	4929	19
9	6447	19
10	7423	19
0	8047	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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

simplify176.0ms (2.9%)

Memory

8.3MiB live, 164.9MiB 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	97	71
3	230	71
4	651	71
5	1485	71
6	2032	71
7	3628	71
8	4929	71
9	6447	71
10	7423	71
0	8047	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))

localize37.0ms (0.6%)

Memory

10.8MiB live, 86.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))
accuracy	0.01171875	(.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	0.2265625	(.f64 #s(literal 3 binary64) (.f64 v v))

Samples

25.0ms

256×

valid

Compiler

Compiled 73 to 16 computations (78.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 7.0ms (43.9% of total)

ival-sqrt: 4.0ms (25.1% of total)

ival-sub: 3.0ms (18.8% of total)

ival-div: 2.0ms (12.5% of total)

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

exact: 0.0ms (0% of total)

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

series33.0ms (0.5%)

Memory

-46.7MiB live, 25.6MiB allocated

Counts

6 → 60

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

Calls

3 calls:

Time	Variable		Point	Expression
26.0ms	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 (- 1 (* 3 (* v v)))))
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 (- 1 (* 3 (* v v)))))
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 (- 1 (* 3 (* v v)))))

Time

Variable

Point

Expression

26.0ms

((/ (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 (- 1 (* 3 (* v v)))))

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 (- 1 (* 3 (* v v)))))

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 (- 1 (* 3 (* v v)))))

simplify221.0ms (3.6%)

Memory

-2.3MiB live, 306.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	174	1058
1	537	1029
2	2032	972
3	5887	963
0	8255	908

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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

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))))))
(fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (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 (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)) (fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (.f64 (sqrt.f64 #s(literal 2 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)))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 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 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 (fma.f64 #s(literal -9/32 binary64) (.f64 v v) #s(literal -3/8 binary64)) (sqrt.f64 #s(literal 2 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 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 v #s(literal 4 binary64)) (.f64 (fma.f64 #s(literal -27/64 binary64) (.f64 v v) #s(literal -9/32 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
1
#s(literal 1 binary64)
(+ 1 (* -3/2 (pow v 2)))
(fma.f64 #s(literal -3/2 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))
(fma.f64 (fma.f64 #s(literal -9/8 binary64) (.f64 v v) #s(literal -3/2 binary64)) (.f64 v v) #s(literal 1 binary64))
(+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -27/16 binary64) (.f64 v v) #s(literal -9/8 binary64)) (.f64 v v) #s(literal -3/2 binary64)) (*.f64 v v) #s(literal 1 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 (+.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))) (/.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 (.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64)))) #s(literal 1/4 binary64) (.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)))
(* -3 (pow v 2))
(.f64 #s(literal -3 binary64) (.f64 v v))
(* (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))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 binary64))
(* 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 (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 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) v) (/.f64 (sqrt.f64 #s(literal 2 binary64)) v) (fma.f64 (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 v #s(literal 4 binary64))) (.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 #s(literal 1/96 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 v #s(literal 4 binary64))) (sqrt.f64 #s(literal -3 binary64))) (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 (/.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)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* v (sqrt -3))
(*.f64 (sqrt.f64 #s(literal -3 binary64)) v)
(* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) v) #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -3 binary64)) v))
(* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3)))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) v) #s(literal 1 binary64) (*.f64 (-.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (pow.f64 v #s(literal 4 binary64)))) v))
(* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))
(*.f64 (-.f64 (+.f64 (+.f64 (/.f64 (/.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))) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) v) v)) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (pow.f64 v #s(literal 4 binary64)))) v)
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) (pow.f64 v #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 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 (fma.f64 (/.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 (*.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))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (fma.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) (.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))) (+ (* 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 (+.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))) (/.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 (.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64)))) #s(literal -1/4 binary64) (.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)))
(* -3 (pow v 2))
(.f64 #s(literal -3 binary64) (.f64 v v))
(* (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))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 (*.f64 #s(literal -3 binary64) v) v #s(literal 1 binary64))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 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 1/8 binary64) v) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) #s(literal -1 binary64) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 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 (fma.f64 #s(literal -1/96 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 v #s(literal 4 binary64))) (sqrt.f64 #s(literal -3 binary64))) (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) v) (.f64 (sqrt.f64 #s(literal -3 binary64)) v)) #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))) v)
(* -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 (fma.f64 #s(literal -1/64 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (pow.f64 v #s(literal 6 binary64))) (fma.f64 #s(literal -1/96 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 v #s(literal 4 binary64))) (sqrt.f64 #s(literal -3 binary64))) (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) v) (.f64 (sqrt.f64 #s(literal -3 binary64)) v)) #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* 3 (pow v 2))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(* -1 (* v (sqrt -3)))
(*.f64 (neg.f64 v) (sqrt.f64 #s(literal -3 binary64)))
(* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) v)) #s(literal -1 binary64) (.f64 (neg.f64 v) (sqrt.f64 #s(literal -3 binary64))))
(* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) v)) #s(literal -1 binary64) (.f64 (-.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (pow.f64 v #s(literal 4 binary64)))) (neg.f64 v)))
(* -1 (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (pow.f64 v #s(literal 4 binary64))) (+.f64 (+.f64 (/.f64 (/.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))) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) v) v))) v)

rewrite172.0ms (2.8%)

Memory

15.9MiB live, 286.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
0	23	56
1	80	54
2	492	54
3	4847	54
0	8499	49

Stop Event

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

Counts

6 → 429

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 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))

Outputs
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eval133.0ms (2.2%)

Memory: -17.3MiB live, 203.8MiB allocated
Compiler: Compiled 12 736 to 1 715 computations (86.5% saved)

prune14.0ms (0.2%)

Memory

2.2MiB live, 40.2MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	483	6	489
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	484	6	490

Accuracy

100.0%

Counts

490 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	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)))
▶	99.9%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
▶	99.5%	(.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)))
	97.9%	(.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (fma.f64 v v #s(literal 1 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))))
▶	100.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (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 160 to 128 computations (20% saved)

simplify179.0ms (2.9%)

Memory

-10.6MiB live, 143.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v)
cost-diff	0	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
cost-diff	960	(fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
cost-diff	0	(fma.f64 #s(literal -3/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 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))))) (*.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 (.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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	302
0	58	296
1	102	296
2	218	288
3	518	288
4	1382	288
5	2150	288
6	3279	288
7	4139	288
8	5507	288
9	6789	288
0	8055	279

Stop Event

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

Calls

Call 1

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

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

localize84.0ms (1.4%)

Memory

27.4MiB live, 151.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.01171875	(fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
accuracy	0.02064610241743066	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
accuracy	0.19140625	(.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.01171875	(.f64 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.01171875	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0.03283258384037635	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (.f64 (fma.f64 #s(literal -3/8 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 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	0.33279263978299634	#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	0.34689829444350995	#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	(.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	0.00390625	(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)))

Samples

62.0ms

256×

valid

Compiler

Compiled 264 to 34 computations (87.1% saved)

Precisions

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

ival-mult: 28.0ms (65.8% of total)

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

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

ival-sub: 3.0ms (7% of total)

ival-div: 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)

series32.0ms (0.5%)

Memory

-4.0MiB live, 34.5MiB allocated

Counts

18 → 180

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
19.0ms	v	@	inf	((* (+ (* -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)) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (+ (* -3/8 (* v v)) 1/4) (sqrt 2)) (+ (* -3/8 (* v v)) 1/4) (+ (* (* (* -5/8 (sqrt 2)) v) v) (* (sqrt 2) 1/4)) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (* -5/8 (sqrt 2)) v) (* -5/8 (sqrt 2)) (* v v))
2.0ms	v	@	0	((* (+ (* -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)) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (+ (* -3/8 (* v v)) 1/4) (sqrt 2)) (+ (* -3/8 (* v v)) 1/4) (+ (* (* (* -5/8 (sqrt 2)) v) v) (* (sqrt 2) 1/4)) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (* -5/8 (sqrt 2)) v) (* -5/8 (sqrt 2)) (* v v))
2.0ms	v	@	-inf	((* (+ (* -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)) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (sqrt 2) 1/4) (sqrt 2) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (+ (* -3/8 (* v v)) 1/4) (sqrt 2)) (+ (* -3/8 (* v v)) 1/4) (+ (* (* (* -5/8 (sqrt 2)) v) v) (* (sqrt 2) 1/4)) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (* -5/8 (sqrt 2)) v) (* -5/8 (sqrt 2)) (* v v))

Time

Variable

Point

Expression

19.0ms

inf

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

2.0ms

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

2.0ms

-inf

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

simplify260.0ms (4.3%)

Memory

-19.3MiB live, 296.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	185	3894
1	583	3683
2	2247	3444
3	5927	3417
0	8040	3224

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

rewrite195.0ms (3.2%)

Memory

34.1MiB live, 301.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	241
0	58	235
1	177	229
2	1174	215
0	9355	200

Stop Event

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

Counts

18 → 748

Calls

Call 1

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

Outputs
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eval234.0ms (3.8%)

Memory: -15.3MiB live, 458.1MiB allocated
Compiler: Compiled 25 123 to 2 624 computations (89.6% saved)

prune23.0ms (0.4%)

Memory

35.3MiB live, 74.4MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 099	3	1 102
Fresh	1	0	1
Picked	3	2	5
Done	0	0	0
Total	1 103	5	1 108

Accuracy

100.0%

Counts

1 108 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
▶	98.4%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (/.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v))) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 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))) (fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
▶	99.9%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -5/8 binary64) 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 82 to 53 computations (35.4% saved)

simplify178.0ms (2.9%)

Memory

5.2MiB live, 196.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
cost-diff	0	(*.f64 v v)
cost-diff	0	(fma.f64 #s(literal -1/4 binary64) (*.f64 v v) #s(literal 1/4 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
cost-diff	0	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (/.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v))) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 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 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v))) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
cost-diff	128	(-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (*.f64 v v))) #s(literal 1/8 binary64))
cost-diff	1088	(-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
cost-diff	0	(fma.f64 (*.f64 #s(literal -5/8 binary64) 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 (.f64 #s(literal -5/8 binary64) 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 (.f64 #s(literal -5/8 binary64) v) v #s(literal 1/4 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	308
0	62	308
1	129	286
2	310	246
3	969	236
4	2917	236
5	4813	236
0	8119	224

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

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

localize130.0ms (2.1%)

Memory

-11.4MiB live, 186.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
accuracy	0	(*.f64 v v)
accuracy	0.00390625	(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
accuracy	0.01171875	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
accuracy	0.12175751953688405	(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (*.f64 v v)))
accuracy	0.3046875	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (*.f64 v v))
accuracy	0.98046875	(/.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v))) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 v v)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
accuracy	1.0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64))
accuracy	0	(*.f64 #s(literal -5/8 binary64) v)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.01171875	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -5/8 binary64) v) v #s(literal 1/4 binary64)))
accuracy	0.02064610241743066	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -5/8 binary64) v) v #s(literal 1/4 binary64))))

Samples

108.0ms

256×

valid

Compiler

Compiled 239 to 39 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-sqrt: 21.0ms (32.4% of total)

ival-mult: 20.0ms (30.9% of total)

ival-add: 13.0ms (20.1% of total)

ival-sub: 5.0ms (7.7% of total)

ival-div: 4.0ms (6.2% of total)

exact: 1.0ms (1.5% of total)

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

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

series39.0ms (0.6%)

Memory

-0.0MiB live, 46.7MiB allocated

Counts

18 → 192

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

Calls

3 calls:

Time

Variable

Point

Expression

21.0ms

-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) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4)) (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (+ (* -1/4 (* v v)) 1/4) (sqrt (+ (* -6 (* v v)) 2))) (+ (* -1/4 (* v v)) 1/4) (* v v) (sqrt (+ (* -6 (* v v)) 2)) (* -5/8 v) (* (sqrt 2) -3/8) (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (* (* (sqrt 2) -3/8) (* v v)) (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) (+ (* -6 (* v v)) 2))

4.0ms

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) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4)) (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (+ (* -1/4 (* v v)) 1/4) (sqrt (+ (* -6 (* v v)) 2))) (+ (* -1/4 (* v v)) 1/4) (* v v) (sqrt (+ (* -6 (* v v)) 2)) (* -5/8 v) (* (sqrt 2) -3/8) (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (* (* (sqrt 2) -3/8) (* v v)) (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) (+ (* -6 (* v v)) 2))

4.0ms

((* (* (/ (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) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4)) (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (+ (* -1/4 (* v v)) 1/4) (sqrt (+ (* -6 (* v v)) 2))) (+ (* -1/4 (* v v)) 1/4) (* v v) (sqrt (+ (* -6 (* v v)) 2)) (* -5/8 v) (* (sqrt 2) -3/8) (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (* (* (sqrt 2) -3/8) (* v v)) (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) (+ (* -6 (* v v)) 2))

simplify214.0ms (3.5%)

Memory

6.9MiB live, 264.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	320	3146
1	945	2926
2	3306	2779
0	8209	2654

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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

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 (.f64 v v) #s(literal -9/16 binary64) #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 (sqrt 2))
(*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 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)))
(- (* -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)))
(- (* -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)))
-1/8
#s(literal -1/8 binary64)
(- (* 9/64 (* (pow v 4) (pow (sqrt 2) 2))) 1/8)
(fma.f64 #s(literal 9/32 binary64) (pow.f64 v #s(literal 4 binary64)) #s(literal -1/8 binary64))
(- (* 9/64 (* (pow v 4) (pow (sqrt 2) 2))) 1/8)
(fma.f64 #s(literal 9/32 binary64) (pow.f64 v #s(literal 4 binary64)) #s(literal -1/8 binary64))
(- (* 9/64 (* (pow v 4) (pow (sqrt 2) 2))) 1/8)
(fma.f64 #s(literal 9/32 binary64) (pow.f64 v #s(literal 4 binary64)) #s(literal -1/8 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 (.f64 v v) #s(literal -9/16 binary64) #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 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -27/64 binary64) (.f64 v v) #s(literal -9/32 binary64))) (pow.f64 v #s(literal 4 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))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 2 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 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 9/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 v v) (fma.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
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(neg.f64 (fma.f64 (sqrt.f64 #s(literal -6 binary64)) v (/.f64 v (.f64 (.f64 (sqrt.f64 #s(literal -6 binary64)) v) v))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (neg.f64 v) (fma.f64 #s(literal 1/12 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (pow.f64 v #s(literal 4 binary64))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 (neg.f64 v) (fma.f64 #s(literal 1/12 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (pow.f64 v #s(literal 4 binary64))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (pow.f64 v #s(literal 6 binary64))) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 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)
(* -3/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 (*.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v)
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal -3/8 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 v v)))) (.f64 v v))
(* (pow v 2) (- (+ (* -3/8 (sqrt 2)) (* 1/3 (/ 1 (* (pow v 4) (sqrt 2))))) (+ (* -1/4 (/ (sqrt 2) (pow v 2))) (* 1/6 (/ (sqrt 2) (pow v 4))))))
(.f64 (-.f64 (fma.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 v #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (.f64 v v))))) (.f64 v v))
(* (pow v 2) (- (+ (* -2/3 (/ (- (* 1/3 (/ 1 (sqrt 2))) (* 1/6 (sqrt 2))) (pow v 6))) (+ (* -3/8 (sqrt 2)) (* 1/3 (/ 1 (* (pow v 4) (sqrt 2)))))) (+ (* -1/4 (/ (sqrt 2) (pow v 2))) (* 1/6 (/ (sqrt 2) (pow v 4))))))
(.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 v #s(literal 6 binary64))) #s(literal -2/3 binary64) (-.f64 (fma.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 v #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 v #s(literal 4 binary64))) (/.f64 #s(literal -1/4 binary64) (.f64 v v)))))) (.f64 v v))
(* -3/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 (*.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v)
(* -3/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 (*.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v)
(* -3/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 (*.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v)
(* -3/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 (*.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v)
(* 9/64 (* (pow v 4) (pow (sqrt 2) 2)))
(*.f64 #s(literal 9/32 binary64) (pow.f64 v #s(literal 4 binary64)))
(* 9/64 (* (pow v 4) (pow (sqrt 2) 2)))
(*.f64 #s(literal 9/32 binary64) (pow.f64 v #s(literal 4 binary64)))
(* 9/64 (* (pow v 4) (pow (sqrt 2) 2)))
(*.f64 #s(literal 9/32 binary64) (pow.f64 v #s(literal 4 binary64)))
(* 9/64 (* (pow v 4) (pow (sqrt 2) 2)))
(*.f64 #s(literal 9/32 binary64) (pow.f64 v #s(literal 4 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)

rewrite225.0ms (3.7%)

Memory

-7.6MiB live, 288.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	279
0	62	244
1	232	229
2	1646	180
0	8282	173

Stop Event

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

Counts

18 → 609

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

Outputs
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eval212.0ms (3.5%)

Memory: -2.4MiB live, 395.8MiB allocated
Compiler: Compiled 34 764 to 3 521 computations (89.9% saved)

prune47.0ms (0.8%)

Memory

17.8MiB live, 57.0MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	997	1	998
Fresh	0	0	0
Picked	1	2	3
Done	0	2	2
Total	998	5	1 003

Accuracy

100.0%

Counts

1 003 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
▶	98.0%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) #s(approx (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	100.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
✓	99.9%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -5/8 binary64) 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 54 to 46 computations (14.8% saved)

simplify217.0ms (3.6%)

Memory

-29.7MiB live, 104.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	166
0	37	166
1	82	151
2	211	127
3	718	121
4	2423	121
5	4410	121
0	8499	113

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

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

localize58.0ms (1%)

Memory

-5.9MiB live, 68.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) #s(approx (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
accuracy	0.03283258384037635	#s(approx (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) #s(approx (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.33279263917623936	#s(approx (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
accuracy	1.0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))

Samples

37.0ms

256×

valid

Compiler

Compiled 85 to 28 computations (67.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 11.0ms (42.9% of total)

ival-sub: 5.0ms (19.5% of total)

ival-div: 5.0ms (19.5% of total)

ival-sqrt: 4.0ms (15.6% of total)

exact: 1.0ms (3.9% of total)

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

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

series4.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

4 → 36

Calls

Call 1

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

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

0.0ms

-inf

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

0.0ms

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

simplify315.0ms (5.2%)

Memory

-5.9MiB live, 268.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	181	1029
1	561	986
2	2113	925
3	5948	919
0	8256	859

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

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

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

rewrite193.0ms (3.2%)

Memory

17.5MiB live, 170.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	152
0	37	131
1	153	120
2	1106	81
0	8734	76

Stop Event

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

Counts

4 → 48

Calls

Call 1

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

Outputs
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eval39.0ms (0.6%)

Memory: -6.0MiB live, 33.1MiB allocated
Compiler: Compiled 2 055 to 369 computations (82% saved)

prune5.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	84	5	89

Accuracy

100.0%

Counts

89 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
✓	98.0%	(.f64 #s(approx ( (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) #s(approx (/ (- (* (* (* (sqrt 2) -3/8) (* v v)) (* (* (sqrt 2) -3/8) (* v v))) 1/8) (- (* (* (sqrt 2) -3/8) (* v v)) (* (sqrt 2) 1/4))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	100.0%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (fma.f64 (.f64 (.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))) v) v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
✓	99.9%	#s(approx (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -5/8 binary64) 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 229 to 111 computations (51.5% saved)

regimes12.0ms (0.2%)

Memory

-17.0MiB live, 22.3MiB allocated

Counts

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

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

Calls

3 calls:

4.0ms

3.0ms

(*.f64 v v)

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)

regimes6.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

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

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

Calls

3 calls:

2.0ms

(*.f64 v v)

2.0ms

(*.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
99.9%	1	`v`
99.9%	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)))`
99.9%	1	`(*.f64 v v)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes4.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 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)))

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:

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)))

1.0ms

(*.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)

simplify44.0ms (0.7%)

Memory

-21.9MiB live, 36.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	67
1	37	67

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

soundness617.0ms (10.1%)

Memory

-1.6MiB live, 430.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
0	23	56
1	80	54
2	492	54
3	4847	54
0	8499	49
0	38	241
0	58	235
1	177	229
2	1174	215
0	9355	200
0	174	1058
1	537	1029
2	2032	972
3	5887	963
0	8255	908
0	185	3894
1	583	3683
2	2247	3444
3	5927	3417
0	8040	3224

Stop Event

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

Compiler

Compiled 70 to 44 computations (37.1% saved)

preprocess65.0ms (1.1%)

Memory: 5.4MiB live, 119.6MiB allocated
Remove: (abs v)
Compiler: Compiled 180 to 124 computations (31.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze5.0ms (0.1%)

sample1.2s (19.6%)

explain232.0ms (3.8%)

preprocess256.0ms (4.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify176.0ms (2.9%)

localize37.0ms (0.6%)

series33.0ms (0.5%)

simplify221.0ms (3.6%)

rewrite172.0ms (2.8%)

eval133.0ms (2.2%)

prune14.0ms (0.2%)

simplify179.0ms (2.9%)

localize84.0ms (1.4%)

series32.0ms (0.5%)

simplify260.0ms (4.3%)

rewrite195.0ms (3.2%)

eval234.0ms (3.8%)

prune23.0ms (0.4%)

simplify178.0ms (2.9%)

localize130.0ms (2.1%)

series39.0ms (0.6%)

simplify214.0ms (3.5%)

rewrite225.0ms (3.7%)

eval212.0ms (3.5%)

prune47.0ms (0.8%)

simplify217.0ms (3.6%)

localize58.0ms (1%)

series4.0ms (0.1%)

simplify315.0ms (5.2%)

rewrite193.0ms (3.2%)

eval39.0ms (0.6%)

prune5.0ms (0.1%)

regimes12.0ms (0.2%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

simplify44.0ms (0.7%)

soundness617.0ms (10.1%)

preprocess65.0ms (1.1%)

end0.0ms (0%)

Profiling