Metrics for Octave 3.8, jcobi/4

analyze43.0ms (0.3%)

Memory

-18.3MiB live, 25.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	14%	86%	0%	0%	0%	0
0%	0%	14%	86%	0%	0%	0%	1
0%	0%	14%	86%	0%	0%	0%	2
25%	3.5%	10.5%	86%	0%	0%	0%	3
62.5%	8.8%	5.3%	86%	0%	0%	0%	4
75%	10.5%	3.5%	86%	0%	0%	0%	5
84.4%	11.8%	2.2%	86%	0%	0%	0%	6
92.2%	12.9%	1.1%	86%	0%	0%	0%	7
93.8%	13.2%	0.9%	86%	0%	0%	0%	8
95.7%	13.4%	0.6%	86%	0%	0%	0%	9
97.9%	13.7%	0.3%	86%	0%	0%	0%	10
98.4%	13.8%	0.2%	86%	0%	0%	0%	11
99%	13.9%	0.1%	86%	0%	0%	0%	12

Compiler

Compiled 65 to 24 computations (63.1% saved)

sample2.1s (14.5%)

Memory

-72.8MiB live, 2 425.3MiB allocated

Samples

1.7s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-mult: 742.0ms (54.7% of total)

ival-add: 236.0ms (17.4% of total)

ival-div: 224.0ms (16.5% of total)

ival-sub: 62.0ms (4.6% of total)

ival->: 60.0ms (4.4% of total)

ival-and: 16.0ms (1.2% of total)

exact: 14.0ms (1% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

preprocess563.0ms (3.8%)

Memory

23.7MiB live, 491.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12 580×	`lower-fma.f64`
12 580×	`lower-fma.f32`
4 108×	`lower-*.f32`
4 098×	`lower-*.f64`
3 894×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	508
1	377	482
2	2068	478
0	17	53
0	29	53
1	76	53
2	324	53
3	2002	53
4	6883	53
0	8193	47

Stop Event

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

Calls

Call 1

Inputs

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Outputs

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

(/.f64 (*.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))

Symmetry

(sort alpha beta)

explain440.0ms (3%)

Memory

-28.9MiB live, 366.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
214	0	-	-	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`
145	1	(2.319317377342773e+220 1.5812315003474158e+286 2.5680207359633066e+29)	-	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`i`
0	0	-	-	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`
0	0	-	-	`(*.f64 #s(literal 2 binary64) i)`
0	0	-	-	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`
0	0	-	-	`beta`
0	0	-	-	`(+.f64 alpha beta)`
0	0	-	-	`(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))`
0	0	-	-	`(+.f64 (+.f64 alpha beta) i)`
0	0	-	-	`alpha`
0	0	-	-	`(*.f64 beta alpha)`
0	0	-	-	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`
0	0	-	-	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`
0	0	-	-	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`
0	0	-	-	`#s(literal 2 binary64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`	o/o	162	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	146
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	214
↳	`(*.f64 beta alpha)`	overflow	18
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	284
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	162
`/.f64`	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`	o/o	126	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	146
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	214
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	284
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(*.f64 beta alpha)`	overflow	18
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	162
↳	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`	overflow	126
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))`	overflow	162
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	162
`/.f64`	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`	o/n	52	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	146
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	214
↳	`(*.f64 beta alpha)`	overflow	18
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	284
`/.f64`	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`	n/o	20	0
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))`	overflow	162
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	162

Confusion

	Predicted +	Predicted -
+	214	0
-	0	42

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	214	0	0
-	0	0	42

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	42
1	68
2	146

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

104.0ms

512×

valid

Compiler

Compiled 482 to 72 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-add: 40.0ms (63.5% of total)

ival-mult: 14.0ms (22.2% of total)

ival-div: 6.0ms (9.5% of total)

ival-sub: 2.0ms (3.2% of total)

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

exact: 1.0ms (1.6% of total)

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	16.9%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Status

Accuracy

Program

▶

16.9%

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Compiler

Compiled 56 to 17 computations (69.6% saved)

simplify711.0ms (4.8%)

Memory

-8.3MiB live, 503.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
✓	cost-diff	128	(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
✓	cost-diff	128	(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))
✓	cost-diff	384	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Rules

12 580×	`lower-fma.f64`
12 580×	`lower-fma.f32`
4 108×	`lower-*.f32`
4 098×	`lower-*.f64`
3 894×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	183
0	29	183
1	76	183
2	324	183
3	2002	183
4	6883	183
0	8193	166

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))
(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
(*.f64 i (+.f64 (+.f64 alpha beta) i))
i
(+.f64 (+.f64 alpha beta) i)
(+.f64 alpha beta)
alpha
beta
(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))
(*.f64 beta alpha)
(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
(*.f64 #s(literal 2 binary64) i)
#s(literal 2 binary64)
(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(/.f64 (.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))
(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))
(/.f64 (.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
(.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
(*.f64 i (+.f64 (+.f64 alpha beta) i))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
i
(+.f64 (+.f64 alpha beta) i)
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(*.f64 beta alpha)
(*.f64 alpha beta)
(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))
(*.f64 #s(literal 2 binary64) i)
(*.f64 i #s(literal 2 binary64))
#s(literal 2 binary64)
(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))
#s(literal 1 binary64)

localize77.0ms (0.5%)

Memory

-0.5MiB live, 78.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
✓	accuracy	99.9%	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
✓	accuracy	45.3%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
✓	accuracy	28.3%	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))

Samples

27.0ms

256×

valid

Compiler

Compiled 185 to 19 computations (89.7% saved)

Precisions

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

ival-mult: 7.0ms (43.5% of total)

ival-add: 5.0ms (31.1% of total)

ival-div: 3.0ms (18.7% of total)

ival-sub: 1.0ms (6.2% of total)

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

exact: 0.0ms (0% of total)

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

series88.0ms (0.6%)

Memory

7.0MiB live, 80.2MiB allocated

Counts

7 → 252

Calls

Call 1

Inputs
#<alt (/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))>
#<alt (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))>
#<alt (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))>
#<alt (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))>
#<alt (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))>
#<alt (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))>
#<alt (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))>

Outputs
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt 1/16>
#<alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))>
#<alt (- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))))))>
#<alt (- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3)))))))))>
#<alt 1/16>
#<alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))>
#<alt (+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i)))>
#<alt (+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i)))>
#<alt (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))>
#<alt (+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))>
#<alt (+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))>
#<alt (+ (* alpha (- (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 4 beta) (* 8 i)))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))))) (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))>
#<alt (/ (* i (+ beta i)) (pow alpha 2))>
#<alt (/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2))>
#<alt (/ (- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2))>
#<alt (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2)))>
#<alt (/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))>
#<alt (/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -4 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))>
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#<alt (* i (+ beta i))>
#<alt (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha))>
#<alt (- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2)))))>
#<alt (- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2)))))>
#<alt (* -1 (* i (+ (* -1 beta) (* -1 i))))>
#<alt (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)))>
#<alt (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)))>
#<alt (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i)))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) alpha))) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)))>
#<alt (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (+ (* beta (- (+ (* beta (- (+ (* beta (- (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (pow (+ alpha (* 2 i)) 2))))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (* i (+ alpha i))>
#<alt (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta))>
#<alt (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))>
#<alt (- (+ (* -1 (/ (+ (* (+ (* 2 alpha) (* 4 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))>
#<alt (* -1 (* i (+ (* -1 alpha) (* -1 i))))>
#<alt (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))>
#<alt (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))>
#<alt (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i)))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))>
#<alt (* alpha (* beta (* i (+ alpha beta))))>
#<alt (* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (pow (+ alpha beta) 2)))))>
#<alt (* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ (* 2 alpha) (* 2 beta))) (pow (+ alpha beta) 2))))))>
#<alt (* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ i (+ (* 2 alpha) (* 2 beta)))) (pow (+ alpha beta) 2))))))>
#<alt (pow i 4)>
#<alt (* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))>
#<alt (* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (/ (pow (+ alpha beta) 2) (pow i 2)))))))>
#<alt (* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (+ (/ (* alpha (* beta (+ alpha beta))) (pow i 3)) (/ (pow (+ alpha beta) 2) (pow i 2))))))))>
#<alt (pow i 4)>
#<alt (* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))>
#<alt (* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (+ (* -1 (/ (* alpha beta) i)) (* -1 (/ (pow (+ alpha beta) 2) i)))) i))))>
#<alt (* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (* -1 (/ (+ (* -1 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (/ (* alpha (* beta (+ alpha beta))) i)) i))) i))))>
#<alt (* (pow i 2) (pow (+ beta i) 2))>
#<alt (+ (* alpha (* i (+ (* i (+ beta i)) (pow (+ beta i) 2)))) (* (pow i 2) (pow (+ beta i) 2)))>
#<alt (+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))>
#<alt (+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))>
#<alt (* (pow alpha 2) (* i (+ beta i)))>
#<alt (* (pow alpha 2) (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)))>
#<alt (* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))>
#<alt (* -1 (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))))>
#<alt (* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) alpha))))>
#<alt (* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))>
#<alt (* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))>
#<alt (* (pow i 2) (pow (+ alpha i) 2))>
#<alt (+ (* beta (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2)))) (* (pow i 2) (pow (+ alpha i) 2)))>
#<alt (+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))>
#<alt (+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))>
#<alt (* (pow beta 2) (* i (+ alpha i)))>
#<alt (* (pow beta 2) (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)))>
#<alt (* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))>
#<alt (* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))>
#<alt (* -1 (* (pow beta 2) (* i (+ (* -1 alpha) (* -1 i)))))>
#<alt (* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) beta))))>
#<alt (* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))>
#<alt (* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))>
#<alt (pow (+ beta (* 2 i)) 2)>
#<alt (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))>
#<alt (pow (+ alpha (* 2 i)) 2)>
#<alt (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))>
#<alt (pow (+ alpha beta) 2)>
#<alt (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))>
#<alt (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))>
#<alt (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))>

Calls

63 calls:

Time	Variable		Point	Expression
20.0ms	alpha	@	0	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
17.0ms	alpha	@	inf	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
4.0ms	beta	@	0	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
4.0ms	i	@	inf	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
3.0ms	i	@	0	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))

rewrite511.0ms (3.5%)

Memory

4.0MiB live, 525.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 174×	`lower-fma.f64`
5 174×	`lower-fma.f32`
4 888×	`lower-/.f32`
4 884×	`lower-/.f64`
4 186×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	157
0	29	127
1	146	127
2	1503	127
0	8201	117

Stop Event

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

Counts

7 → 609

Calls

Call 1

Inputs
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))
(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (neg.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) #s(literal 1 binary64))))
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(*.f64 (exp.f64 (log.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (exp.f64 (log.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))

simplify644.0ms (4.4%)

Memory

-2.6MiB live, 817.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 164×	`lower-fma.f64`
9 164×	`lower-fma.f32`
5 962×	`lower-+.f64`
5 962×	`lower-+.f32`
4 964×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1089	12630
1	3841	11840
0	8260	10972

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 248

Calls

Call 1

Inputs
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(/ (* i (+ beta i)) (pow alpha 2))
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2)))
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
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(/ (* i (+ alpha i)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2))
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(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2))
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2)))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(* i (+ alpha i))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(* beta (+ alpha i))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* -1 (* beta (+ (* -1 alpha) (* -1 i))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* i (+ beta i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(* alpha (+ beta i))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* -1 (* alpha (+ (* -1 beta) (* -1 i))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* alpha beta)
(+ (* alpha beta) (* i (+ alpha beta)))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(+ beta (* 2 i))
(+ alpha (+ beta (* 2 i)))
(+ alpha (+ beta (* 2 i)))
(+ alpha (+ beta (* 2 i)))
alpha
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha))))
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha))))
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (/ beta alpha))))
alpha
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ (+ beta (* 2 i)) alpha)) 1)))
(+ alpha (* 2 i))
(+ alpha (+ beta (* 2 i)))
(+ alpha (+ beta (* 2 i)))
(+ alpha (+ beta (* 2 i)))
beta
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta))))
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta))))
(* beta (+ 1 (+ (* 2 (/ i beta)) (/ alpha beta))))
beta
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1)))
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1)))
(* -1 (* beta (- (* -1 (/ (+ alpha (* 2 i)) beta)) 1)))
(+ alpha beta)
(+ alpha (+ beta (* 2 i)))
(+ alpha (+ beta (* 2 i)))
(+ alpha (+ beta (* 2 i)))
(* 2 i)
(* i (+ 2 (+ (/ alpha i) (/ beta i))))
(* i (+ 2 (+ (/ alpha i) (/ beta i))))
(* i (+ 2 (+ (/ alpha i) (/ beta i))))
(* 2 i)
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2)))
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2)))
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 2)))
(- (pow (+ beta (* 2 i)) 2) 1)
(- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)
(pow alpha 2)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(- (pow (+ alpha (* 2 i)) 2) 1)
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(- (pow (+ alpha beta) 2) 1)
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(/ (* alpha (* beta i)) (+ alpha beta))
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))))
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))))
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))))
(* 1/4 (pow i 2))
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i))))
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2))))))
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3))))))))
(* 1/4 (pow i 2))
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i))))
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i))))
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)))
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)))
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (pow (+ beta (* 2 i)) 2))))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)))
(* i (+ beta i))
(- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha))
(- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2)))))
(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2)))))
(* -1 (* i (+ (* -1 beta) (* -1 i))))
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)))
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)))
(+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i)))))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) alpha))) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))))) (* -1 (* i (* (pow (+ beta (* 2 i)) 2) (+ (* -1 beta) (* -1 i))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* 2 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)))
(/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (pow (+ alpha (* 2 i)) 2))))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))
(* i (+ alpha i))
(- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta))
(- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))
(- (+ (* -1 (/ (+ (* (+ (* 2 alpha) (* 4 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))
(* -1 (* i (+ (* -1 alpha) (* -1 i))))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i)))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(* alpha (* beta (* i (+ alpha beta))))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (pow (+ alpha beta) 2)))))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ (* 2 alpha) (* 2 beta))) (pow (+ alpha beta) 2))))))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ i (+ (* 2 alpha) (* 2 beta)))) (pow (+ alpha beta) 2))))))
(pow i 4)
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (/ (pow (+ alpha beta) 2) (pow i 2)))))))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (+ (/ (* alpha (* beta (+ alpha beta))) (pow i 3)) (/ (pow (+ alpha beta) 2) (pow i 2))))))))
(pow i 4)
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (+ (* -1 (/ (* alpha beta) i)) (* -1 (/ (pow (+ alpha beta) 2) i)))) i))))
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (* -1 (/ (+ (* -1 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (/ (* alpha (* beta (+ alpha beta))) i)) i))) i))))
(* (pow i 2) (pow (+ beta i) 2))
(+ (* alpha (* i (+ (* i (+ beta i)) (pow (+ beta i) 2)))) (* (pow i 2) (pow (+ beta i) 2)))
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))
(* (pow alpha 2) (* i (+ beta i)))
(* (pow alpha 2) (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)))
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))
(* -1 (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) alpha))))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))
(* (pow i 2) (pow (+ alpha i) 2))
(+ (* beta (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2)))) (* (pow i 2) (pow (+ alpha i) 2)))
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))
(* (pow beta 2) (* i (+ alpha i)))
(* (pow beta 2) (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)))
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))
(* -1 (* (pow beta 2) (* i (+ (* -1 alpha) (* -1 i)))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) beta))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))
(pow (+ beta (* 2 i)) 2)
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(pow (+ alpha (* 2 i)) 2)
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(pow (+ alpha beta) 2)
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))

Outputs
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(.f64 (.f64 alpha alpha) (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))) (/.f64 #s(literal -1 binary64) (*.f64 alpha alpha))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))
(.f64 (.f64 alpha alpha) (+.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))) (/.f64 #s(literal -1 binary64) (*.f64 alpha alpha))))
(pow alpha 2)
(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) alpha)) alpha)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) alpha)) alpha)))
(- (pow (+ alpha (* 2 i)) 2) 1)
(fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)))
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)))
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta)))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta)))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta)))
(- (pow (+ alpha beta) 2) 1)
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1)
(fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (+.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i)) (/.f64 #s(literal -1 binary64) (*.f64 i i)))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (+.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i)) (/.f64 #s(literal -1 binary64) (*.f64 i i)))))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) i)) i)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (*.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) i)) i)))
(/ (* alpha (* beta i)) (+ alpha beta))
(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
(* i (+ (* i (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))))
(.f64 i (fma.f64 i (+.f64 (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (.f64 alpha beta) (+.f64 alpha beta))))
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))))
(.f64 i (fma.f64 alpha (/.f64 beta (+.f64 alpha beta)) (.f64 i (+.f64 (fma.f64 i (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (+.f64 alpha beta))))) (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64))) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha beta) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))))
(* i (+ (* i (- (+ 1 (+ (* i (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (+ (* 2 (/ beta (pow (+ alpha beta) 2))) (* i (- (/ 1 (pow (+ alpha beta) 2)) (+ (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (pow (+ alpha beta) 2))) (* 4 (/ (- (+ (* 2 (/ alpha (pow (+ alpha beta) 2))) (* 2 (/ beta (pow (+ alpha beta) 2)))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta))))) (+ alpha beta)))))))) (+ (* 4 (/ (* alpha beta) (pow (+ alpha beta) 3))) (* 4 (/ (- (+ 1 (/ (* alpha beta) (pow (+ alpha beta) 2))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2)))) (+ alpha beta)))))) (/ (* alpha beta) (pow (+ alpha beta) 2)))) (* 4 (/ (* alpha beta) (pow (+ alpha beta) 2))))) (/ (* alpha beta) (+ alpha beta))))
(.f64 i (fma.f64 i (+.f64 (fma.f64 i (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (fma.f64 i (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 #s(literal -4 binary64) (+.f64 (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (+.f64 alpha beta))))) (+.f64 alpha beta))))) (.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (+.f64 (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (+.f64 alpha beta)))))) (fma.f64 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1 binary64))) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (*.f64 alpha beta) (+.f64 alpha beta))))
(* 1/4 (pow i 2))
(.f64 (.f64 i i) #s(literal 1/4 binary64))
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2))))))
(.f64 (.f64 i i) (-.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta)) (.f64 i i))) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i)) (fma.f64 (+.f64 alpha beta) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (.f64 i i)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/4 binary64)) i)))))
(* (pow i 2) (- (+ 1/4 (+ (* 1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/4 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 3))) (+ (* 1/4 (/ (+ alpha beta) i)) (+ (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (pow i 2)) (/ (* (+ alpha beta) (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow (+ alpha beta) 2)) (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))))) (pow i 3))))))))
(.f64 (.f64 i i) (-.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 alpha (/.f64 (.f64 beta (+.f64 alpha beta)) (.f64 i (.f64 i i))) (+.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta)) (.f64 i i)))) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (.f64 i (.f64 i i))) (/.f64 (+.f64 alpha beta) i)) (fma.f64 (+.f64 alpha beta) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (.f64 i i)) (/.f64 (+.f64 (fma.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta)) #s(literal 1/4 binary64) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal -1/16 binary64))) (.f64 (+.f64 alpha beta) (.f64 #s(literal -1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (.f64 i (.f64 i i)))) (.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)))))))
(* 1/4 (pow i 2))
(.f64 (.f64 i i) #s(literal 1/4 binary64))
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i)))
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)) (* -1/16 (/ (pow (+ alpha beta) 2) i)))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (fma.f64 (/.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) i) #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i) (/.f64 (.f64 (+.f64 alpha beta) (.f64 #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) i))) i)))
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* (+ alpha beta) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta))))) (* -1/16 (pow (+ alpha beta) 2))))) i)) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 (+ alpha beta)))) i)))) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 #s(literal -1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 alpha (.f64 beta (+.f64 alpha beta)))) i) (+.f64 (fma.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) #s(literal 1/4 binary64) (.f64 (+.f64 alpha beta) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 1/16 binary64)))) (fma.f64 (-.f64 (neg.f64 alpha) beta) (/.f64 (+.f64 (fma.f64 (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) #s(literal 1/4 binary64) (.f64 (+.f64 alpha beta) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 1/16 binary64))) i) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) i)))) i)) i)))
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))
(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)))
(fma.f64 alpha (fma.f64 i (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (.f64 i (neg.f64 i)) (/.f64 (.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 4))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)))
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(* i (+ beta i))
(*.f64 i (+.f64 beta i))
(- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha))
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(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2)))))
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(* -1 (* i (+ (* -1 beta) (* -1 i))))
(*.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))
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(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))
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(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))
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(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta))
(fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) beta))))
(- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))
(-.f64 (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 beta beta))) (fma.f64 i (+.f64 (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) beta) (/.f64 (.f64 (+.f64 alpha i) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) (.f64 beta beta))) (/.f64 (.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))))))) (*.f64 beta beta))))
(- (+ (* -1 (/ (+ (* (+ (* 2 alpha) (* 4 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))
(-.f64 (-.f64 (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 beta beta))) (/.f64 (fma.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (-.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (fma.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))))) (.f64 (.f64 i (+.f64 alpha i)) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))))))) (.f64 beta (.f64 beta beta)))) (fma.f64 i (+.f64 (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) beta) (/.f64 (.f64 (+.f64 alpha i) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) (.f64 beta beta))) (/.f64 (.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))))))) (*.f64 beta beta))))
(* -1 (* i (+ (* -1 alpha) (* -1 i))))
(neg.f64 (*.f64 i (-.f64 (neg.f64 i) alpha)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))) beta)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (+.f64 (/.f64 (+.f64 (fma.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))))) (.f64 i (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))) (neg.f64 beta)) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (*.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) beta)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i)))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (+.f64 (fma.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))))) (.f64 i (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) beta) (-.f64 (fma.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))) beta) (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)))) (-.f64 (.f64 (.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) (.f64 i (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))))) (neg.f64 beta)) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (*.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) beta)))
(* alpha (* beta (* i (+ alpha beta))))
(.f64 (.f64 alpha beta) (*.f64 i (+.f64 alpha beta)))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (pow (+ alpha beta) 2)))))
(.f64 i (fma.f64 i (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta)) (.f64 alpha (.f64 beta (+.f64 alpha beta)))))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ (* 2 alpha) (* 2 beta))) (pow (+ alpha beta) 2))))))
(.f64 i (fma.f64 i (fma.f64 i (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) (.f64 alpha (*.f64 beta (+.f64 alpha beta)))))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ i (+ (* 2 alpha) (* 2 beta)))) (pow (+ alpha beta) 2))))))
(.f64 i (fma.f64 i (fma.f64 i (fma.f64 #s(literal 2 binary64) (+.f64 alpha beta) i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) (.f64 alpha (.f64 beta (+.f64 alpha beta)))))
(pow i 4)
(pow.f64 i #s(literal 4 binary64))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (/ (pow (+ alpha beta) 2) (pow i 2)))))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)) (fma.f64 alpha (/.f64 beta (.f64 i i)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i)))))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (+ (/ (* alpha (* beta (+ alpha beta))) (pow i 3)) (/ (pow (+ alpha beta) 2) (pow i 2))))))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)) (fma.f64 alpha (+.f64 (/.f64 beta (.f64 i i)) (/.f64 (.f64 beta (+.f64 alpha beta)) (.f64 i (.f64 i i)))) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)))))
(pow i 4)
(pow.f64 i #s(literal 4 binary64))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)))
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (+ (* -1 (/ (* alpha beta) i)) (* -1 (/ (pow (+ alpha beta) 2) i)))) i))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 alpha beta) (neg.f64 (fma.f64 alpha (/.f64 beta i) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)))) i)))
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (* -1 (/ (+ (* -1 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (/ (* alpha (* beta (+ alpha beta))) i)) i))) i))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) (+.f64 alpha beta)) (/.f64 (-.f64 (/.f64 (.f64 alpha (.f64 beta (+.f64 alpha beta))) i) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta)))) i)) i)))
(* (pow i 2) (pow (+ beta i) 2))
(.f64 (.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)))
(+ (* alpha (* i (+ (* i (+ beta i)) (pow (+ beta i) 2)))) (* (pow i 2) (pow (+ beta i) 2)))
(fma.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i)) (.f64 alpha (.f64 i (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))))
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))
(fma.f64 alpha (fma.f64 alpha (.f64 i (+.f64 beta i)) (.f64 i (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))) (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))))
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))
(fma.f64 alpha (fma.f64 alpha (.f64 i (+.f64 beta i)) (.f64 i (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))) (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))))
(* (pow alpha 2) (* i (+ beta i)))
(.f64 (.f64 i (+.f64 beta i)) (*.f64 alpha alpha))
(* (pow alpha 2) (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)))
(.f64 (.f64 alpha alpha) (.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha))))
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))
(.f64 (.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 alpha alpha)))))
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))
(.f64 (.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 alpha alpha)))))
(* -1 (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))))
(.f64 (.f64 alpha alpha) (*.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta)))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (.f64 i (+.f64 (-.f64 (neg.f64 i) beta) (/.f64 (.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) alpha)))))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) beta) (/.f64 (fma.f64 i (.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) (.f64 (.f64 i (neg.f64 i)) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) alpha))) alpha))))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) beta) (/.f64 (fma.f64 i (.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) (.f64 (.f64 i (neg.f64 i)) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) alpha))) alpha))))
(* (pow i 2) (pow (+ alpha i) 2))
(.f64 (.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i)))
(+ (* beta (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2)))) (* (pow i 2) (pow (+ alpha i) 2)))
(fma.f64 (.f64 beta i) (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i))))
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))
(fma.f64 beta (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 beta (.f64 i (+.f64 alpha i)))) (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))))
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))
(fma.f64 beta (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 beta (.f64 i (+.f64 alpha i)))) (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))))
(* (pow beta 2) (* i (+ alpha i)))
(.f64 (.f64 i (+.f64 alpha i)) (*.f64 beta beta))
(* (pow beta 2) (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)))
(.f64 (.f64 beta beta) (.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta))))
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))
(.f64 (.f64 beta beta) (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (*.f64 beta beta))))
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))
(.f64 (.f64 beta beta) (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (*.f64 beta beta))))
(* -1 (* (pow beta 2) (* i (+ (* -1 alpha) (* -1 i)))))
(.f64 (.f64 beta beta) (neg.f64 (*.f64 i (-.f64 (neg.f64 i) alpha))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) beta))))
(.f64 (.f64 beta beta) (neg.f64 (.f64 i (+.f64 (-.f64 (neg.f64 i) alpha) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) beta)))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))
(.f64 (.f64 beta beta) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (neg.f64 beta))) beta))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))
(.f64 (.f64 beta beta) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (neg.f64 beta))) beta))))
(pow (+ beta (* 2 i)) 2)
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(pow alpha 2)
(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))))
(pow alpha 2)
(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha)) alpha)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha)) alpha)))
(pow (+ alpha (* 2 i)) 2)
(*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (neg.f64 beta))) beta)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (neg.f64 beta))) beta)))
(pow (+ alpha beta) 2)
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))
(*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i))))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)) i)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)) i)))

eval212.0ms (1.4%)

Memory: 19.6MiB live, 520.2MiB allocated
Compiler: Compiled 119 800 to 4 604 computations (96.2% saved)

prune250.0ms (1.7%)

Memory

-3.5MiB live, 533.0MiB allocated

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1 376	20	1 396
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1 377	20	1 397

Accuracy

86.6%

Counts

1 397 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	14.4%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
	5.0%	(/.f64 (/.f64 (.f64 (.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (.f64 alpha alpha))))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
▶	5.3%	(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	39.3%	(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	32.8%	(/.f64 (.f64 (.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	14.7%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
	13.4%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	36.9%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	19.4%	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
▶	16.5%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
	6.0%	(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	18.6%	(.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))))
▶	39.3%	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
	15.2%	(.f64 (/.f64 (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) #s(literal -1 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)))
	44.3%	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))
	16.9%	(.f64 (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))
	39.2%	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))
	26.0%	(.f64 (/.f64 i (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
	15.2%	(.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))))
▶	68.2%	#s(literal 1/16 binary64)

Compiler

Compiled 1 658 to 618 computations (62.7% saved)

simplify322.0ms (2.2%)

Memory

28.0MiB live, 411.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 i (+.f64 alpha beta))
✓	cost-diff	0	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
✓	cost-diff	384	(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
✓	cost-diff	384	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
✓	cost-diff	0	(+.f64 alpha i)
✓	cost-diff	0	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
✓	cost-diff	320	(fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta))))
✓	cost-diff	1216	(-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta))
✓	cost-diff	0	(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) i)
✓	cost-diff	128	(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
✓	cost-diff	384	(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
✓	cost-diff	0	(*.f64 beta beta)
✓	cost-diff	0	(+.f64 alpha i)
✓	cost-diff	0	(*.f64 i (+.f64 alpha i))
✓	cost-diff	0	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))

Rules

7 122×	`lower-fma.f32`
7 112×	`lower-fma.f64`
4 164×	`lower-*.f32`
4 138×	`lower-*.f64`
3 108×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	460
0	79	449
1	194	433
2	557	425
3	2263	425
4	4907	416
5	7714	416
0	8165	407

Stop Event

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

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(*.f64 i (+.f64 alpha i))
i
(+.f64 alpha i)
alpha
(*.f64 beta beta)
beta
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
(.f64 alpha (.f64 beta i))
alpha
(*.f64 beta i)
beta
i
(+.f64 alpha beta)
(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
(*.f64 #s(literal 2 binary64) i)
#s(literal 2 binary64)
#s(literal 1 binary64)
(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
(fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta))))
i
(+.f64 alpha i)
alpha
(.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))
(-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta))
(/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)
(*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i))
(+.f64 (+.f64 alpha i) i)
beta
(/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)
(.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))
(fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))
#s(literal 4 binary64)
(*.f64 i #s(literal 8 binary64))
#s(literal 8 binary64)
(*.f64 beta beta)
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))
#s(literal 2 binary64)
#s(literal -1 binary64)
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))

Outputs
#s(literal 1/16 binary64)
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(*.f64 i (+.f64 alpha i))
(*.f64 i (+.f64 i alpha))
i
(+.f64 alpha i)
(+.f64 i alpha)
alpha
(*.f64 beta beta)
beta
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(/.f64 (.f64 i (.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i))) #s(literal -1 binary64))))
(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
(.f64 i (.f64 alpha (/.f64 beta (+.f64 alpha beta))))
(.f64 alpha (.f64 beta i))
(.f64 i (.f64 alpha beta))
alpha
(*.f64 beta i)
(*.f64 i beta)
beta
i
(+.f64 alpha beta)
(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
(fma.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i))) #s(literal -1 binary64))
(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
(*.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i))))
(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
(+.f64 alpha (+.f64 beta (+.f64 i i)))
(*.f64 #s(literal 2 binary64) i)
(+.f64 i i)
#s(literal 2 binary64)
#s(literal 1 binary64)
(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
(.f64 (fma.f64 (/.f64 (+.f64 i alpha) beta) (+.f64 (+.f64 i (+.f64 i alpha)) (fma.f64 i #s(literal -8 binary64) (.f64 alpha #s(literal -4 binary64)))) (+.f64 i alpha)) (/.f64 i (*.f64 beta beta)))
(fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta))))
(.f64 i (fma.f64 (/.f64 (+.f64 i alpha) beta) (+.f64 (+.f64 i (+.f64 i alpha)) (fma.f64 i #s(literal -8 binary64) (.f64 alpha #s(literal -4 binary64)))) (+.f64 i alpha)))
i
(+.f64 alpha i)
(+.f64 i alpha)
alpha
(.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))
(.f64 (/.f64 (.f64 i (+.f64 i alpha)) beta) (+.f64 (+.f64 i (+.f64 i alpha)) (fma.f64 i #s(literal -8 binary64) (*.f64 alpha #s(literal -4 binary64)))))
(-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta))
(.f64 (/.f64 (+.f64 i alpha) beta) (+.f64 (+.f64 i (+.f64 i alpha)) (fma.f64 i #s(literal -8 binary64) (.f64 alpha #s(literal -4 binary64)))))
(/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)
(*.f64 (+.f64 i alpha) (/.f64 (+.f64 i (+.f64 i alpha)) beta))
(*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i))
(*.f64 (+.f64 i alpha) (+.f64 i (+.f64 i alpha)))
(+.f64 (+.f64 alpha i) i)
(+.f64 i (+.f64 i alpha))
beta
(/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)
(.f64 (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64))) (/.f64 (+.f64 i alpha) beta))
(.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))
(.f64 (+.f64 i alpha) (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64))))
(fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))
(fma.f64 i #s(literal 8 binary64) (*.f64 alpha #s(literal 4 binary64)))
#s(literal 4 binary64)
(*.f64 i #s(literal 8 binary64))
#s(literal 8 binary64)
(*.f64 beta beta)
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(/.f64 (.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 (+.f64 i alpha) (+.f64 i beta)))) (.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (*.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (fma.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i))) #s(literal -1 binary64)))))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 i alpha) (+.f64 i beta)) (fma.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i))) #s(literal -1 binary64)))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(*.f64 (+.f64 i alpha) (+.f64 i beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(fma.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i))) #s(literal -1 binary64))
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))
(+.f64 alpha (+.f64 beta (+.f64 i i)))
#s(literal 2 binary64)
#s(literal -1 binary64)
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i)))))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))
(*.f64 (+.f64 alpha (+.f64 beta (+.f64 i i))) (+.f64 alpha (+.f64 beta (+.f64 i i))))

localize163.0ms (1.1%)

Memory

-26.8MiB live, 301.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))
✓	accuracy	99.8%	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
✓	accuracy	38.7%	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))
✓	accuracy	38.7%	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
✓	accuracy	83.7%	(/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)
✓	accuracy	83.7%	(/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)
✓	accuracy	70.9%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
✓	accuracy	58.9%	(-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta))
✓	accuracy	100.0%	(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
✓	accuracy	88.1%	(.f64 alpha (.f64 beta i))
✓	accuracy	83.0%	(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
✓	accuracy	78.0%	(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
✓	accuracy	100.0%	(+.f64 alpha i)
✓	accuracy	100.0%	(*.f64 i (+.f64 alpha i))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	69.8%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))

Samples

96.0ms

256×

valid

Compiler

Compiled 490 to 47 computations (90.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 33.0ms (44.6% of total)

ival-div: 20.0ms (27% of total)

ival-add: 15.0ms (20.3% of total)

ival-sub: 5.0ms (6.8% of total)

exact: 1.0ms (1.4% of total)

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

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

series134.0ms (0.9%)

Memory

-3.1MiB live, 150.2MiB allocated

Counts

21 → 684

Calls

Call 1

Inputs
#<alt (/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))>
#<alt (*.f64 i (+.f64 alpha i))>
#<alt (+.f64 alpha i)>
#<alt (*.f64 beta beta)>
#<alt (/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))>
#<alt (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))>
#<alt (*.f64 #s(literal 2 binary64) i)>
#<alt (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))>
#<alt (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta))>
#<alt (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta))))>
#<alt (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))>
#<alt (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))>
#<alt (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))>
#<alt (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))>
#<alt (+.f64 i (+.f64 alpha beta))>
#<alt (.f64 alpha (.f64 beta i))>
#<alt (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))>
#<alt (/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)>
#<alt (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)>
#<alt (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))>
#<alt (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))>

Outputs
#<alt (/ (* alpha i) (pow beta 2))>
#<alt (* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))>
#<alt (* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))>
#<alt (* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))>
#<alt (/ (pow i 2) (pow beta 2))>
#<alt (* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))>
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#<alt (* (pow alpha 2) (- (+ (* 2 (/ i (* alpha beta))) (+ (* 2 (/ (pow i 2) (* (pow alpha 2) beta))) (/ i (* alpha beta)))) (+ (* 3 (/ 1 beta)) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (* 8 (/ (pow i 2) (* (pow alpha 2) beta))))))))>
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#<alt (* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))>
#<alt (* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (+ (* -1 (/ i beta)) (* -1 (/ (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta))) alpha)))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))>
#<alt (* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (+ (* -1 (/ i beta)) (* -1 (/ (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta))) alpha)))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))>
#<alt (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta)))>
#<alt (- (+ (* i (- (+ (* 2 (/ alpha beta)) (/ alpha beta)) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))>
#<alt (- (+ (* i (- (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))>
#<alt (- (+ (* i (- (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))>
#<alt (* -6 (/ (pow i 2) beta))>
#<alt (* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (/ alpha (* beta i))) (+ (* 4 (/ alpha (* beta i))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i)))))))>
#<alt (* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))>
#<alt (* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))>
#<alt (* -6 (/ (pow i 2) beta))>
#<alt (* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))>
#<alt (* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) i)))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))>
#<alt (* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) i)))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)>
#<alt (* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))>
#<alt (* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))>
#<alt (* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))>
#<alt (* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))>
#<alt (* i (- (+ alpha (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta))))>
#<alt (* i (- (+ alpha (+ (* i (- (+ 1 (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))>
#<alt (* i (- (+ alpha (+ (* i (- (+ 1 (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta)))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))>
#<alt (* i (- (+ alpha (+ (* i (- (+ 1 (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta)))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))>
#<alt (* -6 (/ (pow i 3) beta))>
#<alt (* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (/ alpha (* beta i)))) (+ (* 4 (/ alpha (* beta i))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i)))))))>
#<alt (* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (+ (/ alpha (* beta i)) (+ (/ alpha (pow i 2)) (/ (pow alpha 2) (* beta (pow i 2))))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))>
#<alt (* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (+ (/ alpha (* beta i)) (+ (/ alpha (pow i 2)) (/ (pow alpha 2) (* beta (pow i 2))))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))>
#<alt (* -6 (/ (pow i 3) beta))>
#<alt (* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))))) i)) (* 6 (/ 1 beta)))))>
#<alt (* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (+ (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))))) (* -1 (/ (+ (* -1 alpha) (* -1 (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))))) i)))) i)) (* 6 (/ 1 beta)))))>
#<alt (* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (+ (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))))) (* -1 (/ (+ (* -1 alpha) (* -1 (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))))) i)))) i)) (* 6 (/ 1 beta)))))>
#<alt (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2))>
#<alt (+ (* alpha (+ i (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))>
#<alt (+ (* alpha (+ i (+ (* -3 (/ (* alpha i) beta)) (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))>
#<alt (+ (* alpha (+ i (+ (* -3 (/ (* alpha i) beta)) (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))>
#<alt (* -3 (/ (* (pow alpha 2) i) beta))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow alpha 2)) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha) (/ (pow i 2) (pow alpha 2)))))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow alpha 2)) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha) (/ (pow i 2) (pow alpha 2)))))))>
#<alt (* -3 (/ (* (pow alpha 2) i) beta))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))))) alpha))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (+ (* -1 (/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) alpha)) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))))) alpha))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (+ (* -1 (/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) alpha)) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))))) alpha))))>
#<alt (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)>
#<alt (/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)>
#<alt (/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)>
#<alt (/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)>
#<alt (* i (+ alpha i))>
#<alt (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))>
#<alt (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))>
#<alt (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))>
#<alt (* i (+ alpha i))>
#<alt (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))>
#<alt (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))>
#<alt (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))>
#<alt (/ (* i (- (+ alpha (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))) (pow beta 2))>
#<alt (* i (- (+ (* i (- (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3)))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))>
#<alt (* i (- (+ (* i (- (+ (* -6 (/ i (pow beta 3))) (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3))))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))>
#<alt (* i (- (+ (* i (- (+ (* -6 (/ i (pow beta 3))) (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3))))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))>
#<alt (* -6 (/ (pow i 3) (pow beta 3)))>
#<alt (* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (/ alpha (* (pow beta 3) i)))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3)))))))>
#<alt (* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (+ (/ alpha (* (pow beta 2) (pow i 2))) (+ (/ alpha (* (pow beta 3) i)) (/ (pow alpha 2) (* (pow beta 3) (pow i 2))))))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 4 (/ (pow alpha 2) (* (pow beta 3) (pow i 2)))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3))))))))>
#<alt (* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (+ (/ alpha (* (pow beta 2) (pow i 2))) (+ (/ alpha (* (pow beta 3) i)) (/ (pow alpha 2) (* (pow beta 3) (pow i 2))))))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 4 (/ (pow alpha 2) (* (pow beta 3) (pow i 2)))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3))))))))>
#<alt (* -6 (/ (pow i 3) (pow beta 3)))>
#<alt (* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2))) i)) (* 6 (/ 1 (pow beta 3))))))>
#<alt (* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ alpha (pow beta 2))) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) (pow beta 2)))) i)) (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2)))) i)) (* 6 (/ 1 (pow beta 3))))))>
#<alt (* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ alpha (pow beta 2))) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) (pow beta 2)))) i)) (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2)))) i)) (* 6 (/ 1 (pow beta 3))))))>
#<alt (/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) (pow beta 2))>
#<alt (+ (* alpha (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2)))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))>
#<alt (+ (* alpha (+ (* -3 (/ (* alpha i) (pow beta 3))) (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2))))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))>
#<alt (+ (* alpha (+ (* -3 (/ (* alpha i) (pow beta 3))) (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2))))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))>
#<alt (* -3 (/ (* (pow alpha 2) i) (pow beta 3)))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (* (pow alpha 2) (pow beta 2))) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))) (/ (pow i 2) (* (pow alpha 2) (pow beta 2))))))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (* (pow alpha 2) (pow beta 2))) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))) (/ (pow i 2) (* (pow alpha 2) (pow beta 2))))))))>
#<alt (* -3 (/ (* (pow alpha 2) i) (pow beta 3)))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2))) alpha))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (+ (* -1 (/ (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))) alpha)) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2)))) alpha))))>
#<alt (* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (+ (* -1 (/ (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))) alpha)) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2)))) alpha))))>
#<alt (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (pow beta 3))>
#<alt (/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))>
#<alt (/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))>
#<alt (/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
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#<alt (/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))>
#<alt (/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))>
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#<alt (/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
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#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt 1/16>
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#<alt (/ (* (+ alpha i) (+ alpha (* 2 i))) beta)>
#<alt (* 8 (/ (pow i 2) beta))>
#<alt (+ (* 8 (/ (pow i 2) beta)) (* alpha (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))>
#<alt (+ (* 8 (/ (pow i 2) beta)) (* alpha (+ (* 4 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))))>
#<alt (+ (* 8 (/ (pow i 2) beta)) (* alpha (+ (* 4 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))))>
#<alt (* 4 (/ (pow alpha 2) beta))>
#<alt (* (pow alpha 2) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (* 4 (/ 1 beta)))))>
#<alt (* (pow alpha 2) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (+ (* 8 (/ (pow i 2) (* (pow alpha 2) beta))) (* 4 (/ 1 beta))))))>
#<alt (* (pow alpha 2) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (+ (* 8 (/ (pow i 2) (* (pow alpha 2) beta))) (* 4 (/ 1 beta))))))>
#<alt (* 4 (/ (pow alpha 2) beta))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (+ (* -8 (/ i beta)) (* -4 (/ i beta))) alpha)) (* 4 (/ 1 beta))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (+ (* -8 (/ i beta)) (+ (* -8 (/ (pow i 2) (* alpha beta))) (* -4 (/ i beta)))) alpha)) (* 4 (/ 1 beta))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (+ (* -8 (/ i beta)) (+ (* -8 (/ (pow i 2) (* alpha beta))) (* -4 (/ i beta)))) alpha)) (* 4 (/ 1 beta))))>
#<alt (* 4 (/ (pow alpha 2) beta))>
#<alt (+ (* 4 (/ (pow alpha 2) beta)) (* i (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta)))))>
#<alt (+ (* 4 (/ (pow alpha 2) beta)) (* i (+ (* 4 (/ alpha beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ i beta))))))>
#<alt (+ (* 4 (/ (pow alpha 2) beta)) (* i (+ (* 4 (/ alpha beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ i beta))))))>
#<alt (* 8 (/ (pow i 2) beta))>
#<alt (* (pow i 2) (+ (* 4 (/ alpha (* beta i))) (+ (* 8 (/ alpha (* beta i))) (* 8 (/ 1 beta)))))>
#<alt (* (pow i 2) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 8 (/ alpha (* beta i))) (* 8 (/ 1 beta))))))>
#<alt (* (pow i 2) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 8 (/ alpha (* beta i))) (* 8 (/ 1 beta))))))>
#<alt (* 8 (/ (pow i 2) beta))>
#<alt (* (pow i 2) (+ (* -1 (/ (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))) i)) (* 8 (/ 1 beta))))>
#<alt (* (pow i 2) (+ (* -1 (/ (+ (* -8 (/ alpha beta)) (+ (* -4 (/ alpha beta)) (* -4 (/ (pow alpha 2) (* beta i))))) i)) (* 8 (/ 1 beta))))>
#<alt (* (pow i 2) (+ (* -1 (/ (+ (* -8 (/ alpha beta)) (+ (* -4 (/ alpha beta)) (* -4 (/ (pow alpha 2) (* beta i))))) i)) (* 8 (/ 1 beta))))>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)>
#<alt (/ i (+ alpha beta))>
#<alt (* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))))>
#<alt (+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))>
#<alt (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))>
#<alt (+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)))) (pow (+ beta (* 2 i)) 2))) (/ i (pow (+ beta (* 2 i)) 4))))) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))>
#<alt (/ i alpha)>
#<alt (/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (pow (+ beta (* 2 i)) 2)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)>
#<alt (/ i alpha)>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -1 (/ (* i (pow (+ beta (* 2 i)) 2)) alpha)) (* i (+ beta i)))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (* i (+ beta i))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))>
#<alt (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)))) (pow (+ alpha (* 2 i)) 2))) (/ i (pow (+ alpha (* 2 i)) 4))))) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (/ i beta)>
#<alt (/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (pow (+ alpha (* 2 i)) 2)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)>
#<alt (/ i beta)>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -1 (/ (* i (pow (+ alpha (* 2 i)) 2)) beta)) (* i (+ alpha i)))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (* i (+ alpha i))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))>
#<alt (pow (+ alpha beta) 2)>
#<alt (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))>
#<alt (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))>
#<alt (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))>
#<alt (pow (+ beta (* 2 i)) 2)>
#<alt (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))>
#<alt (pow (+ alpha (* 2 i)) 2)>
#<alt (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))>

Calls

171 calls:

Time	Variable		Point	Expression
15.0ms	alpha	@	inf	(/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))))
7.0ms	beta	@	0	(/ (/ (* alpha (* beta i)) (+ alpha beta)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
6.0ms	i	@	inf	(* 2 i)
4.0ms	alpha	@	-inf	(/ (/ (* alpha (* beta i)) (+ alpha beta)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
2.0ms	beta	@	inf	(+ (* i (+ alpha i)) (* i (- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta))))

rewrite513.0ms (3.5%)

Memory

23.3MiB live, 727.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 396×	`lower-fma.f32`
6 386×	`lower-fma.f64`
5 436×	`lower-*.f32`
5 410×	`lower-*.f64`
4 916×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	330
0	78	278
1	399	266
2	3879	266
0	10692	260

Stop Event

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

Counts

21 → 733

Calls

Call 1

Inputs
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(*.f64 i (+.f64 alpha i))
(+.f64 alpha i)
(*.f64 beta beta)
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) i)
(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
(-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta))
(fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta))))
(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(+.f64 i (+.f64 alpha beta))
(.f64 alpha (.f64 beta i))
(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
(/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)
(/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))))
(*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 beta beta) (*.f64 i (+.f64 i alpha)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 beta (neg.f64 beta))) (/.f64 (.f64 i (+.f64 i alpha)) (*.f64 beta (neg.f64 beta))))
(neg.f64 (/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta (neg.f64 beta))))
(neg.f64 (/.f64 (neg.f64 (.f64 i (+.f64 i alpha))) (.f64 beta beta)))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 beta beta) (.f64 i (+.f64 i alpha))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 beta beta) (.f64 i (+.f64 i alpha))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (/.f64 (+.f64 i alpha) beta))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 beta beta) (.f64 i (+.f64 i alpha)))))
(/.f64 (neg.f64 (.f64 i (+.f64 i alpha))) (.f64 beta (neg.f64 beta)))
(/.f64 (*.f64 i (/.f64 (+.f64 i alpha) beta)) beta)
(/.f64 (neg.f64 (neg.f64 (.f64 i (+.f64 i alpha)))) (neg.f64 (.f64 beta (neg.f64 beta))))
(/.f64 (neg.f64 (*.f64 i (/.f64 (+.f64 i alpha) beta))) (neg.f64 beta))
(/.f64 (.f64 (.f64 i (+.f64 i alpha)) #s(literal 1 binary64)) (*.f64 beta beta))
(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
(pow.f64 (/.f64 (.f64 beta beta) (.f64 i (+.f64 i alpha))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 beta beta) (.f64 i (+.f64 i alpha))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 beta (*.f64 i (/.f64 (+.f64 i alpha) beta))) #s(literal -1 binary64))
(.f64 i (/.f64 (+.f64 i alpha) (.f64 beta beta)))
(.f64 (+.f64 i alpha) (.f64 i (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
(.f64 (.f64 i (+.f64 i alpha)) (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 i (+.f64 i alpha)) (*.f64 beta beta)))
(.f64 (neg.f64 (.f64 i (+.f64 i alpha))) (/.f64 #s(literal 1 binary64) (*.f64 beta (neg.f64 beta))))
(*.f64 (/.f64 i beta) (/.f64 (+.f64 i alpha) beta))
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (+.f64 i alpha) beta)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 i (+.f64 i alpha))) #s(literal -1 binary64)))
(.f64 (.f64 i (/.f64 (+.f64 i alpha) beta)) (/.f64 #s(literal 1 binary64) beta))
(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
(+.f64 (.f64 i i) (.f64 i alpha))
(+.f64 (.f64 i alpha) (.f64 i i))
(-.f64 (/.f64 (.f64 (.f64 alpha alpha) (.f64 i i)) (-.f64 (.f64 i alpha) (.f64 i i))) (/.f64 (.f64 (.f64 i i) (.f64 i i)) (-.f64 (.f64 i alpha) (.f64 i i))))
(fma.f64 i i (*.f64 i alpha))
(fma.f64 i alpha (*.f64 i i))
(fma.f64 alpha i (*.f64 i i))
(/.f64 (fma.f64 (.f64 i (.f64 i i)) (.f64 alpha (.f64 alpha alpha)) (.f64 (.f64 i (.f64 i i)) (.f64 i (.f64 i i)))) (fma.f64 (.f64 alpha alpha) (.f64 i i) (-.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 i alpha) (*.f64 i i)))))
(/.f64 (-.f64 (.f64 (.f64 alpha alpha) (.f64 i i)) (.f64 (.f64 i i) (.f64 i i))) (-.f64 (.f64 i alpha) (.f64 i i)))
(/.f64 (.f64 i (fma.f64 i (.f64 i i) (.f64 alpha (.f64 alpha alpha)))) (fma.f64 i (-.f64 i alpha) (*.f64 alpha alpha)))
(/.f64 (.f64 i (.f64 (+.f64 i alpha) (-.f64 alpha i))) (-.f64 alpha i))
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(*.f64 (exp.f64 (log.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (exp.f64 (log.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))

simplify558.0ms (3.8%)

Memory

12.7MiB live, 799.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 648×	`lower-*.f64`
7 648×	`lower-*.f32`
6 888×	`lower-fma.f64`
6 888×	`lower-fma.f32`
4 500×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2159	22542
1	7405	22536
0	8794	20765

Stop Event

1×	iter limit
1×	node limit

Counts

684 → 672

Calls

Call 1

Inputs
(/ (* alpha i) (pow beta 2))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(/ (pow i 2) (pow beta 2))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(/ (pow i 2) (pow beta 2))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(/ (pow i 2) (pow beta 2))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(/ (* alpha i) (pow beta 2))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(/ (* alpha i) (pow beta 2))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(* alpha i)
(* i (+ alpha i))
(* i (+ alpha i))
(* i (+ alpha i))
(pow i 2)
(* (pow i 2) (+ 1 (/ alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(pow i 2)
(* (pow i 2) (+ 1 (/ alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(pow i 2)
(+ (* alpha i) (pow i 2))
(+ (* alpha i) (pow i 2))
(+ (* alpha i) (pow i 2))
(* alpha i)
(* alpha (+ i (/ (pow i 2) alpha)))
(* alpha (+ i (/ (pow i 2) alpha)))
(* alpha (+ i (/ (pow i 2) alpha)))
(* alpha i)
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))
i
(+ alpha i)
(+ alpha i)
(+ alpha i)
alpha
(* alpha (+ 1 (/ i alpha)))
(* alpha (+ 1 (/ i alpha)))
(* alpha (+ 1 (/ i alpha)))
alpha
(* -1 (* alpha (- (* -1 (/ i alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ i alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ i alpha)) 1)))
alpha
(+ alpha i)
(+ alpha i)
(+ alpha i)
i
(* i (+ 1 (/ alpha i)))
(* i (+ 1 (/ alpha i)))
(* i (+ 1 (/ alpha i)))
i
(* -1 (* i (- (* -1 (/ alpha i)) 1)))
(* -1 (* i (- (* -1 (/ alpha i)) 1)))
(* -1 (* i (- (* -1 (/ alpha i)) 1)))
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(pow beta 2)
(/ (* alpha i) (- (pow (+ beta (* 2 i)) 2) 1))
(* alpha (+ (* -1 (/ (* alpha (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ i (- (pow (+ beta (* 2 i)) 2) 1))))
(* alpha (+ (* alpha (- (* -1 (* alpha (+ (* -1 (/ (* i (pow (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) 2)) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (/ (* i (+ beta (+ (* 2 beta) (* 4 i)))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ beta (* 2 i)) 2) 1))))
(* alpha (+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (* -1 (/ (* i (* (+ beta (+ (* 2 beta) (* 4 i))) (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) 2)) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (/ (* i (+ beta (+ (* 2 beta) (* 4 i)))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* beta (- (pow (+ beta (* 2 i)) 2) 1)))) (/ i (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) 2)) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (/ (* i (+ beta (+ (* 2 beta) (* 4 i)))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ beta (* 2 i)) 2) 1))))
(/ (* beta i) (pow alpha 2))
(/ (+ (* -1 (/ (* beta (* i (+ beta (+ (* 2 beta) (* 4 i))))) alpha)) (* beta i)) (pow alpha 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* beta (* i (pow (+ beta (+ (* 2 beta) (* 4 i))) 2)))) (* beta (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)))) (pow alpha 2))) (* beta i)) (/ (* beta (* i (+ beta (+ (* 2 beta) (* 4 i))))) alpha)) (pow alpha 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* beta (* i (* (+ beta (+ (* 2 beta) (* 4 i))) (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))))) (+ (* -1 (* (+ beta (+ (* 2 beta) (* 4 i))) (+ (* -1 (* beta (* i (pow (+ beta (+ (* 2 beta) (* 4 i))) 2)))) (* beta (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)))))) (* (pow beta 2) (* i (- (pow (+ beta (* 2 i)) 2) 1))))) (pow alpha 3))) (* beta i)) (+ (* -1 (/ (* beta (* i (pow (+ beta (+ (* 2 beta) (* 4 i))) 2))) (pow alpha 2))) (+ (/ (* beta (* i (+ beta (+ (* 2 beta) (* 4 i))))) alpha) (/ (* beta (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (pow alpha 2))))) (pow alpha 2))
(/ (* beta i) (pow alpha 2))
(/ (+ (* -1 (/ (* beta (* i (+ beta (* 2 (+ beta (* 2 i)))))) alpha)) (* beta i)) (pow alpha 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))))) (* beta (* i (pow (+ beta (* 2 (+ beta (* 2 i)))) 2)))) alpha)) (* beta (* i (+ beta (* 2 (+ beta (* 2 i))))))) alpha)) (* beta i)) (pow alpha 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (* (+ beta (* 2 (+ beta (* 2 i)))) (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1)))))) (+ (* (+ beta (* 2 (+ beta (* 2 i)))) (+ (* beta (* i (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))))) (* beta (* i (pow (+ beta (* 2 (+ beta (* 2 i)))) 2))))) (* (pow beta 2) (* i (- (pow (+ beta (* 2 i)) 2) 1))))) alpha)) (+ (* beta (* i (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))))) (* beta (* i (pow (+ beta (* 2 (+ beta (* 2 i)))) 2))))) alpha)) (* beta (* i (+ beta (* 2 (+ beta (* 2 i))))))) alpha)) (* beta i)) (pow alpha 2))
(/ (* beta i) (- (pow (+ alpha (* 2 i)) 2) 1))
(* beta (+ (* -1 (/ (* beta (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))))
(* beta (+ (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (pow (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (+ alpha (+ (* 2 alpha) (* 4 i)))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))))
(* beta (+ (* beta (- (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (* (+ alpha (+ (* 2 alpha) (* 4 i))) (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (+ alpha (+ (* 2 alpha) (* 4 i)))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* alpha (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ i (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (+ alpha (+ (* 2 alpha) (* 4 i)))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))))
(/ (* alpha i) (pow beta 2))
(/ (+ (* -1 (/ (* alpha (* i (+ alpha (+ (* 2 alpha) (* 4 i))))) beta)) (* alpha i)) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* alpha (* i (pow (+ alpha (+ (* 2 alpha) (* 4 i))) 2)))) (* alpha (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)))) (pow beta 2))) (* alpha i)) (/ (* alpha (* i (+ alpha (+ (* 2 alpha) (* 4 i))))) beta)) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* alpha (* i (* (+ alpha (+ (* 2 alpha) (* 4 i))) (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))))) (+ (* -1 (* (+ alpha (+ (* 2 alpha) (* 4 i))) (+ (* -1 (* alpha (* i (pow (+ alpha (+ (* 2 alpha) (* 4 i))) 2)))) (* alpha (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)))))) (* (pow alpha 2) (* i (- (pow (+ alpha (* 2 i)) 2) 1))))) (pow beta 3))) (* alpha i)) (+ (* -1 (/ (* alpha (* i (pow (+ alpha (+ (* 2 alpha) (* 4 i))) 2))) (pow beta 2))) (+ (/ (* alpha (* i (+ alpha (+ (* 2 alpha) (* 4 i))))) beta) (/ (* alpha (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (pow beta 2))))) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (+ (* -1 (/ (* alpha (* i (+ alpha (* 2 (+ alpha (* 2 i)))))) beta)) (* alpha i)) (pow beta 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (+ (* -2 (* alpha (+ alpha (* 2 i)))) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 (+ alpha (* 2 i)))) 2)))) beta)) (* alpha (* i (+ alpha (* 2 (+ alpha (* 2 i))))))) beta)) (* alpha i)) (pow beta 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (* (+ alpha (* 2 (+ alpha (* 2 i)))) (+ (* -2 (* alpha (+ alpha (* 2 i)))) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1)))))) (+ (* (+ alpha (* 2 (+ alpha (* 2 i)))) (+ (* alpha (* i (+ (* -2 (* alpha (+ alpha (* 2 i)))) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 (+ alpha (* 2 i)))) 2))))) (* (pow alpha 2) (* i (- (pow (+ alpha (* 2 i)) 2) 1))))) beta)) (+ (* alpha (* i (+ (* -2 (* alpha (+ alpha (* 2 i)))) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 (+ alpha (* 2 i)))) 2))))) beta)) (* alpha (* i (+ alpha (* 2 (+ alpha (* 2 i))))))) beta)) (* alpha i)) (pow beta 2))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(* i (+ (* -4 (/ (* alpha (* beta i)) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (* -1 (* i (+ (* -16 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* 4 (/ (* alpha beta) (* (+ alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))))))) (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (* i (- (* -1 (* i (+ (* -16 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* -4 (/ (* (+ alpha beta) (+ (* -16 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* 4 (/ (* alpha beta) (* (+ alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2)))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (* -16 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* 4 (/ (* alpha beta) (* (+ alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))))))) (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* 1/4 (/ (* alpha beta) (* i (+ alpha beta))))
(/ (+ (* -1/4 (/ (* alpha beta) i)) (* 1/4 (/ (* alpha beta) (+ alpha beta)))) i)
(/ (- (+ (* -1 (/ (+ (* -1/4 (* alpha (* beta (+ alpha beta)))) (* 1/16 (/ (* alpha (* beta (- (pow (+ alpha beta) 2) 1))) (+ alpha beta)))) (pow i 2))) (* 1/4 (/ (* alpha beta) (+ alpha beta)))) (* 1/4 (/ (* alpha beta) i))) i)
(/ (- (+ (* -1 (/ (+ (* -1 (* (+ alpha beta) (+ (* -1/4 (* alpha (* beta (+ alpha beta)))) (* 1/16 (/ (* alpha (* beta (- (pow (+ alpha beta) 2) 1))) (+ alpha beta)))))) (* -1/16 (* alpha (* beta (- (pow (+ alpha beta) 2) 1))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (+ alpha beta)))) (+ (* -1/4 (/ (* alpha (* beta (+ alpha beta))) (pow i 2))) (+ (* 1/16 (/ (* alpha (* beta (- (pow (+ alpha beta) 2) 1))) (* (pow i 2) (+ alpha beta)))) (* 1/4 (/ (* alpha beta) i))))) i)
(* 1/4 (/ (* alpha beta) (* i (+ alpha beta))))
(* -1 (/ (+ (* -1/4 (/ (* alpha beta) (+ alpha beta))) (* 1/4 (/ (* alpha beta) i))) i))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* alpha (* beta (+ alpha beta)))) (* 1/16 (/ (* alpha (* beta (- (pow (+ alpha beta) 2) 1))) (+ alpha beta)))) i)) (* -1/4 (* alpha beta))) i)) (* -1/4 (/ (* alpha beta) (+ alpha beta)))) i))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/16 (* alpha (* beta (- (pow (+ alpha beta) 2) 1)))) (* (+ alpha beta) (+ (* -1/4 (* alpha (* beta (+ alpha beta)))) (* 1/16 (/ (* alpha (* beta (- (pow (+ alpha beta) 2) 1))) (+ alpha beta)))))) i)) (+ (* -1/4 (* alpha (* beta (+ alpha beta)))) (* 1/16 (/ (* alpha (* beta (- (pow (+ alpha beta) 2) 1))) (+ alpha beta))))) i)) (* -1/4 (* alpha beta))) i)) (* -1/4 (/ (* alpha beta) (+ alpha beta)))) i))
(- (pow (+ beta (* 2 i)) 2) 1)
(- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)
(pow alpha 2)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(- (pow (+ alpha (* 2 i)) 2) 1)
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(- (pow (+ alpha beta) 2) 1)
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* alpha i)
(* alpha (+ i (* -1 (/ (* alpha i) beta))))
(* alpha (+ i (* alpha (- (/ (* alpha i) (pow beta 2)) (/ i beta)))))
(* alpha (+ i (* alpha (- (* alpha (- (* -1 (/ (* alpha i) (pow beta 3))) (* -1 (/ i (pow beta 2))))) (/ i beta)))))
(* beta i)
(+ (* -1 (/ (* (pow beta 2) i) alpha)) (* beta i))
(- (+ (* beta i) (/ (* (pow beta 3) i) (pow alpha 2))) (/ (* (pow beta 2) i) alpha))
(- (+ (* -1 (/ (* (pow beta 4) i) (pow alpha 3))) (* beta i)) (+ (* -1 (/ (* (pow beta 3) i) (pow alpha 2))) (/ (* (pow beta 2) i) alpha)))
(* beta i)
(+ (* -1 (/ (* (pow beta 2) i) alpha)) (* beta i))
(+ (* -1 (/ (+ (* -1 (/ (* (pow beta 3) i) alpha)) (* (pow beta 2) i)) alpha)) (* beta i))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (pow beta 4) i) alpha)) (* (pow beta 3) i)) alpha)) (* (pow beta 2) i)) alpha)) (* beta i))
(* beta i)
(* beta (+ i (* -1 (/ (* beta i) alpha))))
(* beta (+ i (* beta (- (/ (* beta i) (pow alpha 2)) (/ i alpha)))))
(* beta (+ i (* beta (- (* beta (- (* -1 (/ (* beta i) (pow alpha 3))) (* -1 (/ i (pow alpha 2))))) (/ i alpha)))))
(* alpha i)
(+ (* -1 (/ (* (pow alpha 2) i) beta)) (* alpha i))
(- (+ (* alpha i) (/ (* (pow alpha 3) i) (pow beta 2))) (/ (* (pow alpha 2) i) beta))
(- (+ (* -1 (/ (* (pow alpha 4) i) (pow beta 3))) (* alpha i)) (+ (* -1 (/ (* (pow alpha 3) i) (pow beta 2))) (/ (* (pow alpha 2) i) beta)))
(* alpha i)
(+ (* -1 (/ (* (pow alpha 2) i) beta)) (* alpha i))
(+ (* -1 (/ (+ (* -1 (/ (* (pow alpha 3) i) beta)) (* (pow alpha 2) i)) beta)) (* alpha i))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (pow alpha 4) i) beta)) (* (pow alpha 3) i)) beta)) (* (pow alpha 2) i)) beta)) (* alpha i))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(/ (* alpha (* beta i)) (+ alpha beta))
(- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))
(- (+ (* 2 (/ (pow i 2) beta)) (* alpha (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))) (* 8 (/ (pow i 2) beta)))
(- (+ (* 2 (/ (pow i 2) beta)) (* alpha (- (+ (* -3 (/ alpha beta)) (+ (* 2 (/ i beta)) (/ i beta))) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))) (* 8 (/ (pow i 2) beta)))
(- (+ (* 2 (/ (pow i 2) beta)) (* alpha (- (+ (* -3 (/ alpha beta)) (+ (* 2 (/ i beta)) (/ i beta))) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))) (* 8 (/ (pow i 2) beta)))
(* -3 (/ (pow alpha 2) beta))
(* (pow alpha 2) (- (+ (* 2 (/ i (* alpha beta))) (/ i (* alpha beta))) (+ (* 3 (/ 1 beta)) (+ (* 4 (/ i (* alpha beta))) (* 8 (/ i (* alpha beta)))))))
(* (pow alpha 2) (- (+ (* 2 (/ i (* alpha beta))) (+ (* 2 (/ (pow i 2) (* (pow alpha 2) beta))) (/ i (* alpha beta)))) (+ (* 3 (/ 1 beta)) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (* 8 (/ (pow i 2) (* (pow alpha 2) beta))))))))
(* (pow alpha 2) (- (+ (* 2 (/ i (* alpha beta))) (+ (* 2 (/ (pow i 2) (* (pow alpha 2) beta))) (/ i (* alpha beta)))) (+ (* 3 (/ 1 beta)) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (* 8 (/ (pow i 2) (* (pow alpha 2) beta))))))))
(* -3 (/ (pow alpha 2) beta))
(* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))
(* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (+ (* -1 (/ i beta)) (* -1 (/ (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta))) alpha)))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))
(* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (+ (* -1 (/ i beta)) (* -1 (/ (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta))) alpha)))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))
(- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta)))
(- (+ (* i (- (+ (* 2 (/ alpha beta)) (/ alpha beta)) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))
(- (+ (* i (- (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))
(- (+ (* i (- (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))
(* -6 (/ (pow i 2) beta))
(* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (/ alpha (* beta i))) (+ (* 4 (/ alpha (* beta i))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i)))))))
(* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(* -6 (/ (pow i 2) beta))
(* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))
(* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) i)))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))
(* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) i)))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(* i (- (+ alpha (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta))))
(* i (- (+ alpha (+ (* i (- (+ 1 (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))
(* i (- (+ alpha (+ (* i (- (+ 1 (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta)))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))
(* i (- (+ alpha (+ (* i (- (+ 1 (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta)))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))
(* -6 (/ (pow i 3) beta))
(* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (/ alpha (* beta i)))) (+ (* 4 (/ alpha (* beta i))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i)))))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (+ (/ alpha (* beta i)) (+ (/ alpha (pow i 2)) (/ (pow alpha 2) (* beta (pow i 2))))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (+ (/ alpha (* beta i)) (+ (/ alpha (pow i 2)) (/ (pow alpha 2) (* beta (pow i 2))))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(* -6 (/ (pow i 3) beta))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))))) i)) (* 6 (/ 1 beta)))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (+ (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))))) (* -1 (/ (+ (* -1 alpha) (* -1 (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))))) i)))) i)) (* 6 (/ 1 beta)))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (+ (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))))) (* -1 (/ (+ (* -1 alpha) (* -1 (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))))) i)))) i)) (* 6 (/ 1 beta)))))
(+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2))
(+ (* alpha (+ i (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))
(+ (* alpha (+ i (+ (* -3 (/ (* alpha i) beta)) (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))
(+ (* alpha (+ i (+ (* -3 (/ (* alpha i) beta)) (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))
(* -3 (/ (* (pow alpha 2) i) beta))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow alpha 2)) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha) (/ (pow i 2) (pow alpha 2)))))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow alpha 2)) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha) (/ (pow i 2) (pow alpha 2)))))))
(* -3 (/ (* (pow alpha 2) i) beta))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (+ (* -1 (/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) alpha)) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (+ (* -1 (/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) alpha)) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))))) alpha))))
(/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)
(* i (+ alpha i))
(+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(* i (+ alpha i))
(+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(/ (* i (- (+ alpha (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))) (pow beta 2))
(* i (- (+ (* i (- (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3)))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))
(* i (- (+ (* i (- (+ (* -6 (/ i (pow beta 3))) (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3))))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))
(* i (- (+ (* i (- (+ (* -6 (/ i (pow beta 3))) (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3))))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))
(* -6 (/ (pow i 3) (pow beta 3)))
(* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (/ alpha (* (pow beta 3) i)))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3)))))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (+ (/ alpha (* (pow beta 2) (pow i 2))) (+ (/ alpha (* (pow beta 3) i)) (/ (pow alpha 2) (* (pow beta 3) (pow i 2))))))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 4 (/ (pow alpha 2) (* (pow beta 3) (pow i 2)))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3))))))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (+ (/ alpha (* (pow beta 2) (pow i 2))) (+ (/ alpha (* (pow beta 3) i)) (/ (pow alpha 2) (* (pow beta 3) (pow i 2))))))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 4 (/ (pow alpha 2) (* (pow beta 3) (pow i 2)))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3))))))))
(* -6 (/ (pow i 3) (pow beta 3)))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2))) i)) (* 6 (/ 1 (pow beta 3))))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ alpha (pow beta 2))) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) (pow beta 2)))) i)) (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2)))) i)) (* 6 (/ 1 (pow beta 3))))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ alpha (pow beta 2))) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) (pow beta 2)))) i)) (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2)))) i)) (* 6 (/ 1 (pow beta 3))))))
(/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) (pow beta 2))
(+ (* alpha (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2)))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
(+ (* alpha (+ (* -3 (/ (* alpha i) (pow beta 3))) (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2))))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
(+ (* alpha (+ (* -3 (/ (* alpha i) (pow beta 3))) (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2))))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
(* -3 (/ (* (pow alpha 2) i) (pow beta 3)))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (* (pow alpha 2) (pow beta 2))) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))) (/ (pow i 2) (* (pow alpha 2) (pow beta 2))))))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (* (pow alpha 2) (pow beta 2))) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))) (/ (pow i 2) (* (pow alpha 2) (pow beta 2))))))))
(* -3 (/ (* (pow alpha 2) i) (pow beta 3)))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (+ (* -1 (/ (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))) alpha)) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2)))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (+ (* -1 (/ (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))) alpha)) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2)))) alpha))))
(/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (pow beta 3))
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))))))
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3)))))))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i)))
(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i)))
(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
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(/ (* i (+ beta i)) (pow alpha 2))
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2))
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2)))
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
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(/ (* i (+ alpha i)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2))
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(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2)))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(* alpha beta)
(+ (* alpha beta) (* i (+ alpha beta)))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(* i (+ beta i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(* alpha (+ beta i))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* -1 (* alpha (+ (* -1 beta) (* -1 i))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* i (+ alpha i))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(* beta (+ alpha i))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* -1 (* beta (+ (* -1 alpha) (* -1 i))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))
(+ (* i (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (- (+ (* i (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (- (+ (* i (- (+ (* -1 (* i (+ (* 4 (/ (* (+ alpha beta) (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (- (pow (+ alpha beta) 2) 1)))))) (/ 1 (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
1/4
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (+ (* -1 (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))))) (* 1/4 (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)))) (pow i 4))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (+ (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))))
1/4
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (- (+ (* -1 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) i)) (* 1/4 (/ (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)) i))) (* -1 (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1))
(+ (* alpha (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1)))) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ i (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(/ (+ beta i) alpha)
(/ (- (+ beta (+ i (/ (* i (+ beta i)) alpha))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))))) (* (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (- (pow (+ beta (* 2 i)) 2) 1))) (pow alpha 3))) (/ (* i (+ beta i)) alpha)))) (+ (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)
(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)) (+ (* i (+ beta i)) (/ (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)) alpha))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (/ (* (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) (- (pow (+ beta (* 2 i)) 2) 1)) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (* i (+ beta i))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha))
(/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))
(+ (* beta (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1))))) (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ i (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (+ (/ (* i (+ alpha i)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (pow (+ alpha (* 2 i)) 2) 1))))) (+ (/ alpha (- (pow (+ alpha (* 2 i)) 2) 1)) (/ i (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(/ (+ alpha i) beta)
(/ (- (+ alpha (+ i (/ (* i (+ alpha i)) beta))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta)))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 3))) (/ (* i (+ alpha i)) beta)))) (+ (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)
(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta))
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta))
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)) (+ (* i (+ alpha i)) (/ (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) beta))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta))
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (/ (* (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) (- (pow (+ alpha (* 2 i)) 2) 1)) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (* i (+ alpha i))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta))
(+ alpha beta)
(+ alpha (+ beta i))
(+ alpha (+ beta i))
(+ alpha (+ beta i))
i
(* i (+ 1 (+ (/ alpha i) (/ beta i))))
(* i (+ 1 (+ (/ alpha i) (/ beta i))))
(* i (+ 1 (+ (/ alpha i) (/ beta i))))
i
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))
(+ beta i)
(+ alpha (+ beta i))
(+ alpha (+ beta i))
(+ alpha (+ beta i))
alpha
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))
alpha
(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1)))
(+ alpha i)
(+ alpha (+ beta i))
(+ alpha (+ beta i))
(+ alpha (+ beta i))
beta
(* beta (+ 1 (+ (/ alpha beta) (/ i beta))))
(* beta (+ 1 (+ (/ alpha beta) (/ i beta))))
(* beta (+ 1 (+ (/ alpha beta) (/ i beta))))
beta
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(* alpha (* beta i))
(pow (+ beta (* 2 i)) 2)
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(pow (+ alpha (* 2 i)) 2)
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(pow (+ alpha beta) 2)
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(* 2 (/ (pow i 2) beta))
(+ (* 2 (/ (pow i 2) beta)) (* alpha (+ (* 2 (/ i beta)) (/ i beta))))
(+ (* 2 (/ (pow i 2) beta)) (* alpha (+ (* 2 (/ i beta)) (+ (/ alpha beta) (/ i beta)))))
(+ (* 2 (/ (pow i 2) beta)) (* alpha (+ (* 2 (/ i beta)) (+ (/ alpha beta) (/ i beta)))))
(/ (pow alpha 2) beta)
(* (pow alpha 2) (+ (* 2 (/ i (* alpha beta))) (+ (/ 1 beta) (/ i (* alpha beta)))))
(* (pow alpha 2) (+ (* 2 (/ i (* alpha beta))) (+ (* 2 (/ (pow i 2) (* (pow alpha 2) beta))) (+ (/ 1 beta) (/ i (* alpha beta))))))
(* (pow alpha 2) (+ (* 2 (/ i (* alpha beta))) (+ (* 2 (/ (pow i 2) (* (pow alpha 2) beta))) (+ (/ 1 beta) (/ i (* alpha beta))))))
(/ (pow alpha 2) beta)
(* (pow alpha 2) (+ (* -1 (/ (+ (* -2 (/ i beta)) (* -1 (/ i beta))) alpha)) (/ 1 beta)))
(* (pow alpha 2) (+ (* -1 (/ (+ (* -2 (/ i beta)) (+ (* -2 (/ (pow i 2) (* alpha beta))) (* -1 (/ i beta)))) alpha)) (/ 1 beta)))
(* (pow alpha 2) (+ (* -1 (/ (+ (* -2 (/ i beta)) (+ (* -2 (/ (pow i 2) (* alpha beta))) (* -1 (/ i beta)))) alpha)) (/ 1 beta)))
(/ (pow alpha 2) beta)
(+ (* i (+ (* 2 (/ alpha beta)) (/ alpha beta))) (/ (pow alpha 2) beta))
(+ (* i (+ (* 2 (/ alpha beta)) (+ (* 2 (/ i beta)) (/ alpha beta)))) (/ (pow alpha 2) beta))
(+ (* i (+ (* 2 (/ alpha beta)) (+ (* 2 (/ i beta)) (/ alpha beta)))) (/ (pow alpha 2) beta))
(* 2 (/ (pow i 2) beta))
(* (pow i 2) (+ (* 2 (/ alpha (* beta i))) (+ (* 2 (/ 1 beta)) (/ alpha (* beta i)))))
(* (pow i 2) (+ (* 2 (/ alpha (* beta i))) (+ (* 2 (/ 1 beta)) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2)))))))
(* (pow i 2) (+ (* 2 (/ alpha (* beta i))) (+ (* 2 (/ 1 beta)) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2)))))))
(* 2 (/ (pow i 2) beta))
(* (pow i 2) (+ (* -1 (/ (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) i)) (* 2 (/ 1 beta))))
(* (pow i 2) (+ (* -1 (/ (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (pow alpha 2) (* beta i))))) i)) (* 2 (/ 1 beta))))
(* (pow i 2) (+ (* -1 (/ (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (pow alpha 2) (* beta i))))) i)) (* 2 (/ 1 beta))))
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(/ (* (+ alpha i) (+ alpha (* 2 i))) beta)
(* 8 (/ (pow i 2) beta))
(+ (* 8 (/ (pow i 2) beta)) (* alpha (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))
(+ (* 8 (/ (pow i 2) beta)) (* alpha (+ (* 4 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))))
(+ (* 8 (/ (pow i 2) beta)) (* alpha (+ (* 4 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))))
(* 4 (/ (pow alpha 2) beta))
(* (pow alpha 2) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (* 4 (/ 1 beta)))))
(* (pow alpha 2) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (+ (* 8 (/ (pow i 2) (* (pow alpha 2) beta))) (* 4 (/ 1 beta))))))
(* (pow alpha 2) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (+ (* 8 (/ (pow i 2) (* (pow alpha 2) beta))) (* 4 (/ 1 beta))))))
(* 4 (/ (pow alpha 2) beta))
(* (pow alpha 2) (+ (* -1 (/ (+ (* -8 (/ i beta)) (* -4 (/ i beta))) alpha)) (* 4 (/ 1 beta))))
(* (pow alpha 2) (+ (* -1 (/ (+ (* -8 (/ i beta)) (+ (* -8 (/ (pow i 2) (* alpha beta))) (* -4 (/ i beta)))) alpha)) (* 4 (/ 1 beta))))
(* (pow alpha 2) (+ (* -1 (/ (+ (* -8 (/ i beta)) (+ (* -8 (/ (pow i 2) (* alpha beta))) (* -4 (/ i beta)))) alpha)) (* 4 (/ 1 beta))))
(* 4 (/ (pow alpha 2) beta))
(+ (* 4 (/ (pow alpha 2) beta)) (* i (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta)))))
(+ (* 4 (/ (pow alpha 2) beta)) (* i (+ (* 4 (/ alpha beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ i beta))))))
(+ (* 4 (/ (pow alpha 2) beta)) (* i (+ (* 4 (/ alpha beta)) (+ (* 8 (/ alpha beta)) (* 8 (/ i beta))))))
(* 8 (/ (pow i 2) beta))
(* (pow i 2) (+ (* 4 (/ alpha (* beta i))) (+ (* 8 (/ alpha (* beta i))) (* 8 (/ 1 beta)))))
(* (pow i 2) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 8 (/ alpha (* beta i))) (* 8 (/ 1 beta))))))
(* (pow i 2) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 8 (/ alpha (* beta i))) (* 8 (/ 1 beta))))))
(* 8 (/ (pow i 2) beta))
(* (pow i 2) (+ (* -1 (/ (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))) i)) (* 8 (/ 1 beta))))
(* (pow i 2) (+ (* -1 (/ (+ (* -8 (/ alpha beta)) (+ (* -4 (/ alpha beta)) (* -4 (/ (pow alpha 2) (* beta i))))) i)) (* 8 (/ 1 beta))))
(* (pow i 2) (+ (* -1 (/ (+ (* -8 (/ alpha beta)) (+ (* -4 (/ alpha beta)) (* -4 (/ (pow alpha 2) (* beta i))))) i)) (* 8 (/ 1 beta))))
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ (* (+ alpha i) (+ (* 4 alpha) (* 8 i))) beta)
(/ i (+ alpha beta))
(* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta))))
(* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))
(* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))
1/4
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))
(- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))
(- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))
1/4
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))
(+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))))
(+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))
(/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)))) (pow (+ beta (* 2 i)) 2))) (/ i (pow (+ beta (* 2 i)) 4))))) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))
(/ i alpha)
(/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (pow (+ beta (* 2 i)) 2)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)
(/ i alpha)
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -1 (/ (* i (pow (+ beta (* 2 i)) 2)) alpha)) (* i (+ beta i)))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (* i (+ beta i))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))
(/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)))) (pow (+ alpha (* 2 i)) 2))) (/ i (pow (+ alpha (* 2 i)) 4))))) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))
(/ i beta)
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (pow (+ alpha (* 2 i)) 2)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)
(/ i beta)
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -1 (/ (* i (pow (+ alpha (* 2 i)) 2)) beta)) (* i (+ alpha i)))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (* i (+ alpha i))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))
(pow (+ alpha beta) 2)
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(pow (+ beta (* 2 i)) 2)
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(pow (+ alpha (* 2 i)) 2)
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))

Outputs
(/ (* alpha i) (pow beta 2))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(.f64 i (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 i (*.f64 beta beta))))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(.f64 i (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 i (*.f64 beta beta))))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(.f64 i (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 i (*.f64 beta beta))))
(/ (pow i 2) (pow beta 2))
(/.f64 (.f64 i i) (.f64 beta beta))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(/ (pow i 2) (pow beta 2))
(/.f64 (.f64 i i) (.f64 beta beta))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(/ (pow i 2) (pow beta 2))
(/.f64 (.f64 i i) (.f64 beta beta))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(fma.f64 alpha (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta)))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(fma.f64 alpha (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta)))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(fma.f64 alpha (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta)))
(/ (* alpha i) (pow beta 2))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(.f64 alpha (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 alpha (*.f64 beta beta)))))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(.f64 alpha (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 alpha (*.f64 beta beta)))))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(.f64 alpha (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 alpha (*.f64 beta beta)))))
(/ (* alpha i) (pow beta 2))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 i (.f64 beta beta))) (neg.f64 (/.f64 (.f64 i i) (.f64 alpha (*.f64 beta beta))))))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 i (.f64 beta beta))) (neg.f64 (/.f64 (.f64 i i) (.f64 alpha (*.f64 beta beta))))))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(.f64 (neg.f64 alpha) (+.f64 (neg.f64 (/.f64 i (.f64 beta beta))) (neg.f64 (/.f64 (.f64 i i) (.f64 alpha (*.f64 beta beta))))))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(* alpha i)
(*.f64 alpha i)
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(pow i 2)
(*.f64 i i)
(* (pow i 2) (+ 1 (/ alpha i)))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(pow i 2)
(*.f64 i i)
(* (pow i 2) (+ 1 (/ alpha i)))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(* (pow i 2) (+ 1 (/ alpha i)))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(pow i 2)
(*.f64 i i)
(+ (* alpha i) (pow i 2))
(*.f64 i (+.f64 alpha i))
(+ (* alpha i) (pow i 2))
(*.f64 i (+.f64 alpha i))
(+ (* alpha i) (pow i 2))
(*.f64 i (+.f64 alpha i))
(* alpha i)
(*.f64 alpha i)
(* alpha (+ i (/ (pow i 2) alpha)))
(.f64 alpha (+.f64 i (/.f64 (.f64 i i) alpha)))
(* alpha (+ i (/ (pow i 2) alpha)))
(.f64 alpha (+.f64 i (/.f64 (.f64 i i) alpha)))
(* alpha (+ i (/ (pow i 2) alpha)))
(.f64 alpha (+.f64 i (/.f64 (.f64 i i) alpha)))
(* alpha i)
(*.f64 alpha i)
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))
(.f64 (neg.f64 alpha) (+.f64 (neg.f64 i) (neg.f64 (/.f64 (.f64 i i) alpha))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))
(.f64 (neg.f64 alpha) (+.f64 (neg.f64 i) (neg.f64 (/.f64 (.f64 i i) alpha))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))
(.f64 (neg.f64 alpha) (+.f64 (neg.f64 i) (neg.f64 (/.f64 (.f64 i i) alpha))))
i
(+ alpha i)
(+.f64 alpha i)
(+ alpha i)
(+.f64 alpha i)
(+ alpha i)
(+.f64 alpha i)
alpha
(* alpha (+ 1 (/ i alpha)))
(*.f64 alpha (+.f64 #s(literal 1 binary64) (/.f64 i alpha)))
(* alpha (+ 1 (/ i alpha)))
(*.f64 alpha (+.f64 #s(literal 1 binary64) (/.f64 i alpha)))
(* alpha (+ 1 (/ i alpha)))
(*.f64 alpha (+.f64 #s(literal 1 binary64) (/.f64 i alpha)))
alpha
(* -1 (* alpha (- (* -1 (/ i alpha)) 1)))
(neg.f64 (*.f64 alpha (+.f64 (/.f64 (neg.f64 i) alpha) #s(literal -1 binary64))))
(* -1 (* alpha (- (* -1 (/ i alpha)) 1)))
(neg.f64 (*.f64 alpha (+.f64 (/.f64 (neg.f64 i) alpha) #s(literal -1 binary64))))
(* -1 (* alpha (- (* -1 (/ i alpha)) 1)))
(neg.f64 (*.f64 alpha (+.f64 (/.f64 (neg.f64 i) alpha) #s(literal -1 binary64))))
alpha
(+ alpha i)
(+.f64 alpha i)
(+ alpha i)
(+.f64 alpha i)
(+ alpha i)
(+.f64 alpha i)
i
(* i (+ 1 (/ alpha i)))
(*.f64 i (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(* i (+ 1 (/ alpha i)))
(*.f64 i (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
(* i (+ 1 (/ alpha i)))
(*.f64 i (+.f64 #s(literal 1 binary64) (/.f64 alpha i)))
i
(* -1 (* i (- (* -1 (/ alpha i)) 1)))
(*.f64 (neg.f64 i) (+.f64 (/.f64 (neg.f64 alpha) i) #s(literal -1 binary64)))
(* -1 (* i (- (* -1 (/ alpha i)) 1)))
(*.f64 (neg.f64 i) (+.f64 (/.f64 (neg.f64 alpha) i) #s(literal -1 binary64)))
(* -1 (* i (- (* -1 (/ alpha i)) 1)))
(*.f64 (neg.f64 i) (+.f64 (/.f64 (neg.f64 alpha) i) #s(literal -1 binary64)))
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(pow beta 2)
(*.f64 beta beta)
(/ (* alpha i) (- (pow (+ beta (* 2 i)) 2) 1))
(/.f64 (*.f64 alpha i) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
(* alpha (+ (* -1 (/ (* alpha (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ i (- (pow (+ beta (* 2 i)) 2) 1))))
(.f64 alpha (+.f64 (neg.f64 (/.f64 (.f64 (.f64 alpha i) (fma.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 beta #s(literal 2 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 beta (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))) (/.f64 i (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
(* alpha (+ (* alpha (- (* -1 (* alpha (+ (* -1 (/ (* i (pow (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) 2)) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (/ (* i (+ beta (+ (* 2 beta) (* 4 i)))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ beta (* 2 i)) 2) 1))))
(.f64 alpha (fma.f64 alpha (fma.f64 (neg.f64 alpha) (fma.f64 i (/.f64 (+.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 beta #s(literal 2 binary64)))) (.f64 beta (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 i (.f64 (fma.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 beta #s(literal 2 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (fma.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 beta #s(literal 2 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) (.f64 (.f64 beta beta) (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))))) (neg.f64 (/.f64 (.f64 i (fma.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 beta #s(literal 2 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 beta (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))) (/.f64 i (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
(* alpha (+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (* -1 (/ (* i (* (+ beta (+ (* 2 beta) (* 4 i))) (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) 2)) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (/ (* i (+ beta (+ (* 2 beta) (* 4 i)))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* beta (- (pow (+ beta (* 2 i)) 2) 1)))) (/ i (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) 2)) (* (pow beta 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))) (/ (* i (+ beta (+ (* 2 beta) (* 4 i)))) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ beta (* 2 i)) 2) 1))))
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(/ (* beta i) (pow alpha 2))
(.f64 beta (/.f64 i (.f64 alpha alpha)))
(/ (+ (* -1 (/ (* beta (* i (+ beta (+ (* 2 beta) (* 4 i))))) alpha)) (* beta i)) (pow alpha 2))
(/.f64 (fma.f64 i beta (neg.f64 (/.f64 (.f64 (.f64 i beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 beta #s(literal 2 binary64))))) alpha))) (.f64 alpha alpha))
(/ (- (+ (* -1 (/ (+ (* -1 (* beta (* i (pow (+ beta (+ (* 2 beta) (* 4 i))) 2)))) (* beta (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)))) (pow alpha 2))) (* beta i)) (/ (* beta (* i (+ beta (+ (* 2 beta) (* 4 i))))) alpha)) (pow alpha 2))
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(/ (- (+ (* -1 (/ (+ (* -1 (* beta (* i (* (+ beta (+ (* 2 beta) (* 4 i))) (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))))) (+ (* -1 (* (+ beta (+ (* 2 beta) (* 4 i))) (+ (* -1 (* beta (* i (pow (+ beta (+ (* 2 beta) (* 4 i))) 2)))) (* beta (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)))))) (* (pow beta 2) (* i (- (pow (+ beta (* 2 i)) 2) 1))))) (pow alpha 3))) (* beta i)) (+ (* -1 (/ (* beta (* i (pow (+ beta (+ (* 2 beta) (* 4 i))) 2))) (pow alpha 2))) (+ (/ (* beta (* i (+ beta (+ (* 2 beta) (* 4 i))))) alpha) (/ (* beta (* i (- (+ (* beta (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (pow alpha 2))))) (pow alpha 2))
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(/ (* beta i) (pow alpha 2))
(.f64 beta (/.f64 i (.f64 alpha alpha)))
(/ (+ (* -1 (/ (* beta (* i (+ beta (* 2 (+ beta (* 2 i)))))) alpha)) (* beta i)) (pow alpha 2))
(/.f64 (fma.f64 i beta (neg.f64 (/.f64 (.f64 beta (.f64 i (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta))) alpha))) (*.f64 alpha alpha))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))))) (* beta (* i (pow (+ beta (* 2 (+ beta (* 2 i)))) 2)))) alpha)) (* beta (* i (+ beta (* 2 (+ beta (* 2 i))))))) alpha)) (* beta i)) (pow alpha 2))
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(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (* (+ beta (* 2 (+ beta (* 2 i)))) (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1)))))) (+ (* (+ beta (* 2 (+ beta (* 2 i)))) (+ (* beta (* i (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))))) (* beta (* i (pow (+ beta (* 2 (+ beta (* 2 i)))) 2))))) (* (pow beta 2) (* i (- (pow (+ beta (* 2 i)) 2) 1))))) alpha)) (+ (* beta (* i (+ (* -2 (* beta (+ beta (* 2 i)))) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))))) (* beta (* i (pow (+ beta (* 2 (+ beta (* 2 i)))) 2))))) alpha)) (* beta (* i (+ beta (* 2 (+ beta (* 2 i))))))) alpha)) (* beta i)) (pow alpha 2))
(/.f64 (fma.f64 i beta (neg.f64 (/.f64 (fma.f64 beta (.f64 i (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta)) (neg.f64 (/.f64 (fma.f64 beta (fma.f64 i (fma.f64 #s(literal -2 binary64) (.f64 beta (fma.f64 i #s(literal 2 binary64) beta)) (neg.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 i (.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta) (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta)))) (neg.f64 (/.f64 (fma.f64 beta (.f64 (.f64 i (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta)) (fma.f64 #s(literal -2 binary64) (.f64 beta (fma.f64 i #s(literal 2 binary64) beta)) (neg.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) (fma.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta) (.f64 beta (fma.f64 i (fma.f64 #s(literal -2 binary64) (.f64 beta (fma.f64 i #s(literal 2 binary64) beta)) (neg.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 i (.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta) (fma.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 2 binary64) beta) beta))))) (.f64 (.f64 i (.f64 beta beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) alpha))) alpha))) alpha))) (*.f64 alpha alpha))
(/ (* beta i) (- (pow (+ alpha (* 2 i)) 2) 1))
(/.f64 (*.f64 i beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)))
(* beta (+ (* -1 (/ (* beta (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))))
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(* beta (+ (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (pow (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (+ alpha (+ (* 2 alpha) (* 4 i)))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))))
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(* beta (+ (* beta (- (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (* (+ alpha (+ (* 2 alpha) (* 4 i))) (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (+ alpha (+ (* 2 alpha) (* 4 i)))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* alpha (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ i (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (+ alpha (+ (* 2 alpha) (* 4 i)))) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (- (+ (* alpha (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* alpha (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ i (- (pow (+ alpha (* 2 i)) 2) 1))))
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(+.f64 (fma.f64 alpha (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 i beta) (.f64 (/.f64 alpha beta) #s(literal -3 binary64))) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 #s(literal 2 binary64) (/.f64 (.f64 i i) beta))) (.f64 #s(literal -8 binary64) (/.f64 (.f64 i i) beta)))
(- (+ (* 2 (/ (pow i 2) beta)) (* alpha (- (+ (* -3 (/ alpha beta)) (+ (* 2 (/ i beta)) (/ i beta))) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))) (* 8 (/ (pow i 2) beta)))
(+.f64 (fma.f64 alpha (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 i beta) (.f64 (/.f64 alpha beta) #s(literal -3 binary64))) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 #s(literal 2 binary64) (/.f64 (.f64 i i) beta))) (.f64 #s(literal -8 binary64) (/.f64 (.f64 i i) beta)))
(* -3 (/ (pow alpha 2) beta))
(/.f64 (.f64 #s(literal -3 binary64) (.f64 alpha alpha)) beta)
(* (pow alpha 2) (- (+ (* 2 (/ i (* alpha beta))) (/ i (* alpha beta))) (+ (* 3 (/ 1 beta)) (+ (* 4 (/ i (* alpha beta))) (* 8 (/ i (* alpha beta)))))))
(.f64 (.f64 alpha alpha) (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i (.f64 alpha beta))) (fma.f64 (/.f64 i (*.f64 alpha beta)) #s(literal 12 binary64) (/.f64 #s(literal 3 binary64) beta))))
(* (pow alpha 2) (- (+ (* 2 (/ i (* alpha beta))) (+ (* 2 (/ (pow i 2) (* (pow alpha 2) beta))) (/ i (* alpha beta)))) (+ (* 3 (/ 1 beta)) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (* 8 (/ (pow i 2) (* (pow alpha 2) beta))))))))
(.f64 (.f64 alpha alpha) (-.f64 (fma.f64 #s(literal 2 binary64) (/.f64 i (.f64 alpha beta)) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 i i) (.f64 beta (.f64 alpha alpha))) (/.f64 i (.f64 alpha beta)))) (+.f64 (/.f64 #s(literal 3 binary64) beta) (fma.f64 (/.f64 i (.f64 alpha beta)) #s(literal 12 binary64) (/.f64 (.f64 #s(literal 8 binary64) (.f64 i i)) (.f64 beta (.f64 alpha alpha)))))))
(* (pow alpha 2) (- (+ (* 2 (/ i (* alpha beta))) (+ (* 2 (/ (pow i 2) (* (pow alpha 2) beta))) (/ i (* alpha beta)))) (+ (* 3 (/ 1 beta)) (+ (* 4 (/ i (* alpha beta))) (+ (* 8 (/ i (* alpha beta))) (* 8 (/ (pow i 2) (* (pow alpha 2) beta))))))))
(.f64 (.f64 alpha alpha) (-.f64 (fma.f64 #s(literal 2 binary64) (/.f64 i (.f64 alpha beta)) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 i i) (.f64 beta (.f64 alpha alpha))) (/.f64 i (.f64 alpha beta)))) (+.f64 (/.f64 #s(literal 3 binary64) beta) (fma.f64 (/.f64 i (.f64 alpha beta)) #s(literal 12 binary64) (/.f64 (.f64 #s(literal 8 binary64) (.f64 i i)) (.f64 beta (.f64 alpha alpha)))))))
(* -3 (/ (pow alpha 2) beta))
(/.f64 (.f64 #s(literal -3 binary64) (.f64 alpha alpha)) beta)
(* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))
(.f64 (.f64 alpha alpha) (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64))) alpha)) (/.f64 #s(literal 3 binary64) beta)))
(* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (+ (* -1 (/ i beta)) (* -1 (/ (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta))) alpha)))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))
(.f64 (.f64 alpha alpha) (-.f64 (neg.f64 (/.f64 (-.f64 (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (neg.f64 (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) alpha))) (*.f64 (/.f64 i beta) #s(literal -12 binary64))) alpha)) (/.f64 #s(literal 3 binary64) beta)))
(* (pow alpha 2) (- (* -1 (/ (- (+ (* -2 (/ i beta)) (+ (* -1 (/ i beta)) (* -1 (/ (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta))) alpha)))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))) alpha)) (* 3 (/ 1 beta))))
(.f64 (.f64 alpha alpha) (-.f64 (neg.f64 (/.f64 (-.f64 (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (neg.f64 (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) alpha))) (*.f64 (/.f64 i beta) #s(literal -12 binary64))) alpha)) (/.f64 #s(literal 3 binary64) beta)))
(- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta)))
(+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha alpha) beta)))
(- (+ (* i (- (+ (* 2 (/ alpha beta)) (/ alpha beta)) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))
(fma.f64 i (-.f64 (.f64 #s(literal 3 binary64) (/.f64 alpha beta)) (.f64 (/.f64 alpha beta) #s(literal 12 binary64))) (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha alpha) beta))))
(- (+ (* i (- (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))
(+.f64 (fma.f64 i (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 alpha beta) (.f64 (/.f64 i beta) #s(literal -6 binary64))) (.f64 (/.f64 alpha beta) #s(literal 12 binary64))) (/.f64 (.f64 alpha alpha) beta)) (.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha alpha) beta)))
(- (+ (* i (- (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))
(+.f64 (fma.f64 i (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 alpha beta) (.f64 (/.f64 i beta) #s(literal -6 binary64))) (.f64 (/.f64 alpha beta) #s(literal 12 binary64))) (/.f64 (.f64 alpha alpha) beta)) (.f64 #s(literal -4 binary64) (/.f64 (*.f64 alpha alpha) beta)))
(* -6 (/ (pow i 2) beta))
(.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64))
(* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (/ alpha (* beta i))) (+ (* 4 (/ alpha (* beta i))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i)))))))
(.f64 (.f64 i i) (-.f64 (.f64 #s(literal 3 binary64) (/.f64 alpha (.f64 i beta))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i beta)) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 #s(literal 6 binary64) beta)))))
(* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(.f64 (.f64 i i) (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i)))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i beta)) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i))) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (*.f64 i beta)) (/.f64 #s(literal 6 binary64) beta))))))
(* (pow i 2) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ alpha (* beta i)) (/ (pow alpha 2) (* beta (pow i 2))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(.f64 (.f64 i i) (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i)))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i beta)) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i))) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (*.f64 i beta)) (/.f64 #s(literal 6 binary64) beta))))))
(* -6 (/ (pow i 2) beta))
(.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64))
(* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))
(.f64 (.f64 i i) (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) i)) (/.f64 #s(literal 6 binary64) beta)))
(* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) i)))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))
(.f64 (.f64 i i) (-.f64 (neg.f64 (/.f64 (-.f64 (fma.f64 (/.f64 alpha beta) #s(literal -3 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta))) i))) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) i)) (/.f64 #s(literal 6 binary64) beta)))
(* (pow i 2) (- (* -1 (/ (- (+ (* -2 (/ alpha beta)) (+ (* -1 (/ alpha beta)) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) i)))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) i)) (* 6 (/ 1 beta))))
(.f64 (.f64 i i) (-.f64 (neg.f64 (/.f64 (-.f64 (fma.f64 (/.f64 alpha beta) #s(literal -3 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta))) i))) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) i)) (/.f64 #s(literal 6 binary64) beta)))
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(/ (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)
(/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta)
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))))) beta))
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))))) beta))
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))))) beta))
(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))))) beta))
(* i (- (+ alpha (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta))))
(.f64 i (+.f64 (+.f64 alpha (/.f64 (.f64 alpha alpha) beta)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta))))
(* i (- (+ alpha (+ (* i (- (+ 1 (+ (* 2 (/ alpha beta)) (/ alpha beta))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))
(.f64 i (+.f64 alpha (-.f64 (fma.f64 i (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 alpha beta) #s(literal 1 binary64)) (.f64 (/.f64 alpha beta) #s(literal 12 binary64))) (/.f64 (.f64 alpha alpha) beta)) (/.f64 (.f64 #s(literal 4 binary64) (*.f64 alpha alpha)) beta))))
(* i (- (+ alpha (+ (* i (- (+ 1 (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta)))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))
(.f64 i (+.f64 alpha (-.f64 (fma.f64 i (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 alpha beta) (.f64 (/.f64 i beta) #s(literal -6 binary64))) (.f64 (/.f64 alpha beta) #s(literal 12 binary64)))) (/.f64 (.f64 alpha alpha) beta)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 alpha alpha)) beta))))
(* i (- (+ alpha (+ (* i (- (+ 1 (+ (* -6 (/ i beta)) (+ (* 2 (/ alpha beta)) (/ alpha beta)))) (+ (* 4 (/ alpha beta)) (* 8 (/ alpha beta))))) (/ (pow alpha 2) beta))) (* 4 (/ (pow alpha 2) beta))))
(.f64 i (+.f64 alpha (-.f64 (fma.f64 i (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 3 binary64) (/.f64 alpha beta) (.f64 (/.f64 i beta) #s(literal -6 binary64))) (.f64 (/.f64 alpha beta) #s(literal 12 binary64)))) (/.f64 (.f64 alpha alpha) beta)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 alpha alpha)) beta))))
(* -6 (/ (pow i 3) beta))
(/.f64 (.f64 #s(literal -6 binary64) (.f64 i (*.f64 i i))) beta)
(* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (/ alpha (* beta i)))) (+ (* 4 (/ alpha (* beta i))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i)))))))
(.f64 (.f64 i (.f64 i i)) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 #s(literal 1 binary64) i)) (/.f64 alpha (.f64 i beta))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i beta)) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (*.f64 i beta)) (/.f64 #s(literal 6 binary64) beta)))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (+ (/ alpha (* beta i)) (+ (/ alpha (pow i 2)) (/ (pow alpha 2) (* beta (pow i 2))))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(.f64 (.f64 i (.f64 i i)) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 #s(literal 1 binary64) i)) (+.f64 (/.f64 alpha (.f64 i beta)) (+.f64 (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i))) (/.f64 alpha (.f64 i i))))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i beta)) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i))) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 #s(literal 6 binary64) beta))))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* beta i))) (+ (/ 1 i) (+ (/ alpha (* beta i)) (+ (/ alpha (pow i 2)) (/ (pow alpha 2) (* beta (pow i 2))))))) (+ (* 4 (/ alpha (* beta i))) (+ (* 4 (/ (pow alpha 2) (* beta (pow i 2)))) (+ (* 6 (/ 1 beta)) (* 8 (/ alpha (* beta i))))))))
(.f64 (.f64 i (.f64 i i)) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 #s(literal 1 binary64) i)) (+.f64 (/.f64 alpha (.f64 i beta)) (+.f64 (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i))) (/.f64 alpha (.f64 i i))))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i beta)) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 i i))) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (.f64 i beta)) (/.f64 #s(literal 6 binary64) beta))))))
(* -6 (/ (pow i 3) beta))
(/.f64 (.f64 #s(literal -6 binary64) (.f64 i (*.f64 i i))) beta)
(* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))))) i)) (* 6 (/ 1 beta)))))
(neg.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 (/.f64 #s(literal 6 binary64) beta) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (*.f64 (/.f64 alpha beta) #s(literal -12 binary64))))) i)))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (+ (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))))) (* -1 (/ (+ (* -1 alpha) (* -1 (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))))) i)))) i)) (* 6 (/ 1 beta)))))
(neg.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 (/.f64 #s(literal 6 binary64) beta) (neg.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (+.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) (/.f64 (+.f64 (neg.f64 alpha) (neg.f64 (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta))))) i)) #s(literal 1 binary64)) i)))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ 1 (+ (* -1 (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta))))) (* -1 (/ (+ (* -1 alpha) (* -1 (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))))) i)))) i)) (* 6 (/ 1 beta)))))
(neg.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 (/.f64 #s(literal 6 binary64) beta) (neg.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (+.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) (/.f64 (+.f64 (neg.f64 alpha) (neg.f64 (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta))))) i)) #s(literal 1 binary64)) i)))))
(+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2))
(fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i))
(+ (* alpha (+ i (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))
(fma.f64 alpha (fma.f64 i (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) i) (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i)))
(+ (* alpha (+ i (+ (* -3 (/ (* alpha i) beta)) (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))
(fma.f64 alpha (+.f64 i (fma.f64 i (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (/.f64 (.f64 #s(literal -3 binary64) (.f64 alpha i)) beta))) (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i)))
(+ (* alpha (+ i (+ (* -3 (/ (* alpha i) beta)) (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta)))))))) (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)))
(fma.f64 alpha (+.f64 i (fma.f64 i (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (/.f64 (.f64 #s(literal -3 binary64) (.f64 alpha i)) beta))) (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i)))
(* -3 (/ (* (pow alpha 2) i) beta))
(/.f64 (.f64 #s(literal -3 binary64) (.f64 i (*.f64 alpha alpha))) beta)
(* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) alpha) (/.f64 i alpha))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow alpha 2)) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha) (/ (pow i 2) (pow alpha 2)))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (/.f64 i alpha)) (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 alpha alpha)) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) alpha) (/.f64 (.f64 i i) (*.f64 alpha alpha))))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (+ (/ i alpha) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow alpha 2)) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) alpha) (/ (pow i 2) (pow alpha 2)))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (/.f64 i alpha)) (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 alpha alpha)) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) alpha) (/.f64 (.f64 i i) (*.f64 alpha alpha))))))
(* -3 (/ (* (pow alpha 2) i) beta))
(/.f64 (.f64 #s(literal -3 binary64) (.f64 i (*.f64 alpha alpha))) beta)
(* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta)))))) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (neg.f64 (/.f64 (fma.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64))) (neg.f64 i)) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (+ (* -1 (/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) alpha)) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))))) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 i) (fma.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64))) (neg.f64 (/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i)) alpha)))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i beta)) (* -1 (/ (+ (* -1 i) (+ (* -1 (/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) alpha)) (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))))) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 (/.f64 i beta) #s(literal -3 binary64) (neg.f64 (/.f64 (+.f64 (neg.f64 i) (fma.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64))) (neg.f64 (/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i)) alpha)))) alpha))))
(/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)
(/.f64 (.f64 i (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))))) beta)
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)
(/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) (.f64 beta (.f64 i (+.f64 alpha i)))) beta)
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)
(/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) (.f64 beta (.f64 i (+.f64 alpha i)))) beta)
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)
(/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) (.f64 beta (.f64 i (+.f64 alpha i)))) beta)
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(fma.f64 i (/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta) (*.f64 i (+.f64 alpha i)))
(+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(fma.f64 i (/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta) (*.f64 i (+.f64 alpha i)))
(+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(fma.f64 i (/.f64 (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))) beta) (*.f64 i (+.f64 alpha i)))
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(fma.f64 i (+.f64 alpha i) (neg.f64 (/.f64 (.f64 i (.f64 #s(literal -1 binary64) (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))))) beta)))
(+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(fma.f64 i (+.f64 alpha i) (neg.f64 (/.f64 (.f64 i (.f64 #s(literal -1 binary64) (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))))) beta)))
(+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(fma.f64 i (+.f64 alpha i) (neg.f64 (/.f64 (.f64 i (.f64 #s(literal -1 binary64) (.f64 (+.f64 alpha i) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64))))))) beta)))
(/ (* i (- (+ alpha (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))) (pow beta 2))
(/.f64 (.f64 i (+.f64 (+.f64 alpha (/.f64 (.f64 alpha alpha) beta)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta)))) (*.f64 beta beta))
(* i (- (+ (* i (- (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3)))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))
(.f64 i (fma.f64 i (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 beta (.f64 beta beta))) (/.f64 #s(literal 1 binary64) (.f64 beta beta))) (/.f64 alpha (.f64 beta (.f64 beta beta)))) (.f64 (/.f64 alpha (.f64 beta (.f64 beta beta))) #s(literal 12 binary64))) (-.f64 (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 beta beta)))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 alpha alpha)) (.f64 beta (*.f64 beta beta))))))
(* i (- (+ (* i (- (+ (* -6 (/ i (pow beta 3))) (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3))))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))
(.f64 i (fma.f64 i (-.f64 (fma.f64 #s(literal -6 binary64) (/.f64 i (.f64 beta (.f64 beta beta))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 beta (.f64 beta beta))) (/.f64 #s(literal 1 binary64) (.f64 beta beta))) (/.f64 alpha (.f64 beta (.f64 beta beta))))) (.f64 (/.f64 alpha (.f64 beta (.f64 beta beta))) #s(literal 12 binary64))) (-.f64 (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 beta beta)))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 alpha alpha)) (.f64 beta (*.f64 beta beta))))))
(* i (- (+ (* i (- (+ (* -6 (/ i (pow beta 3))) (+ (* 2 (/ alpha (pow beta 3))) (+ (/ 1 (pow beta 2)) (/ alpha (pow beta 3))))) (+ (* 4 (/ alpha (pow beta 3))) (* 8 (/ alpha (pow beta 3)))))) (+ (/ alpha (pow beta 2)) (/ (pow alpha 2) (pow beta 3)))) (* 4 (/ (pow alpha 2) (pow beta 3)))))
(.f64 i (fma.f64 i (-.f64 (fma.f64 #s(literal -6 binary64) (/.f64 i (.f64 beta (.f64 beta beta))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 beta (.f64 beta beta))) (/.f64 #s(literal 1 binary64) (.f64 beta beta))) (/.f64 alpha (.f64 beta (.f64 beta beta))))) (.f64 (/.f64 alpha (.f64 beta (.f64 beta beta))) #s(literal 12 binary64))) (-.f64 (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 beta beta)))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 alpha alpha)) (.f64 beta (*.f64 beta beta))))))
(* -6 (/ (pow i 3) (pow beta 3)))
(/.f64 (.f64 #s(literal -6 binary64) (.f64 i (.f64 i i))) (.f64 beta (*.f64 beta beta)))
(* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (/ alpha (* (pow beta 3) i)))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3)))))))
(.f64 (.f64 i (.f64 i i)) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 #s(literal 1 binary64) (.f64 i (.f64 beta beta)))) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta))))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 #s(literal 6 binary64) (.f64 beta (*.f64 beta beta)))))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (+ (/ alpha (* (pow beta 2) (pow i 2))) (+ (/ alpha (* (pow beta 3) i)) (/ (pow alpha 2) (* (pow beta 3) (pow i 2))))))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 4 (/ (pow alpha 2) (* (pow beta 3) (pow i 2)))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3))))))))
(.f64 (.f64 i (.f64 i i)) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 #s(literal 1 binary64) (.f64 i (.f64 beta beta)))) (+.f64 (+.f64 (/.f64 alpha (.f64 (.f64 beta beta) (.f64 i i))) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta))))) (/.f64 (.f64 alpha alpha) (.f64 (.f64 i i) (.f64 beta (.f64 beta beta)))))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 alpha alpha) (.f64 (.f64 i i) (.f64 beta (.f64 beta beta)))) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))))))))
(* (pow i 3) (- (+ (* 2 (/ alpha (* (pow beta 3) i))) (+ (/ 1 (* (pow beta 2) i)) (+ (/ alpha (* (pow beta 2) (pow i 2))) (+ (/ alpha (* (pow beta 3) i)) (/ (pow alpha 2) (* (pow beta 3) (pow i 2))))))) (+ (* 4 (/ alpha (* (pow beta 3) i))) (+ (* 4 (/ (pow alpha 2) (* (pow beta 3) (pow i 2)))) (+ (* 8 (/ alpha (* (pow beta 3) i))) (* 6 (/ 1 (pow beta 3))))))))
(.f64 (.f64 i (.f64 i i)) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 #s(literal 1 binary64) (.f64 i (.f64 beta beta)))) (+.f64 (+.f64 (/.f64 alpha (.f64 (.f64 beta beta) (.f64 i i))) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta))))) (/.f64 (.f64 alpha alpha) (.f64 (.f64 i i) (.f64 beta (.f64 beta beta)))))) (fma.f64 #s(literal 4 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 alpha alpha) (.f64 (.f64 i i) (.f64 beta (.f64 beta beta)))) (fma.f64 #s(literal 8 binary64) (/.f64 alpha (.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))))))))
(* -6 (/ (pow i 3) (pow beta 3)))
(/.f64 (.f64 #s(literal -6 binary64) (.f64 i (.f64 i i))) (.f64 beta (*.f64 beta beta)))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2))) i)) (* 6 (/ 1 (pow beta 3))))))
(neg.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) (*.f64 beta beta)))) i)))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ alpha (pow beta 2))) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) (pow beta 2)))) i)) (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2)))) i)) (* 6 (/ 1 (pow beta 3))))))
(neg.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))) (neg.f64 (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) (.f64 beta beta)))) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 alpha (.f64 beta beta))) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta))) (.f64 beta beta)))) i))) i)))))
(* -1 (* (pow i 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ alpha (pow beta 2))) (* -1 (/ (- (/ (pow alpha 2) beta) (* 4 (/ (pow alpha 2) beta))) (pow beta 2)))) i)) (+ (* -1 (/ (- (+ (* -2 (/ alpha beta)) (* -1 (/ alpha beta))) (+ (* -8 (/ alpha beta)) (* -4 (/ alpha beta)))) (pow beta 2))) (/ 1 (pow beta 2)))) i)) (* 6 (/ 1 (pow beta 3))))))
(neg.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))) (neg.f64 (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) (.f64 beta beta)))) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 alpha (.f64 beta beta))) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta))) (.f64 beta beta)))) i))) i)))))
(/ (+ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow i 2)) (pow beta 2))
(/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 i i)) (.f64 beta beta))
(+ (* alpha (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2)))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
(fma.f64 alpha (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 beta beta)) (/.f64 i (.f64 beta beta))) (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta))))
(+ (* alpha (+ (* -3 (/ (* alpha i) (pow beta 3))) (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2))))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
(fma.f64 alpha (fma.f64 (/.f64 (.f64 alpha i) (.f64 beta (.f64 beta beta))) #s(literal -3 binary64) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 beta beta)) (/.f64 i (.f64 beta beta)))) (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 beta beta))))
(+ (* alpha (+ (* -3 (/ (* alpha i) (pow beta 3))) (+ (/ i (pow beta 2)) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (pow beta 2))))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
(fma.f64 alpha (fma.f64 (/.f64 (.f64 alpha i) (.f64 beta (.f64 beta beta))) #s(literal -3 binary64) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 beta beta)) (/.f64 i (.f64 beta beta)))) (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 beta beta))))
(* -3 (/ (* (pow alpha 2) i) (pow beta 3)))
(/.f64 (.f64 #s(literal -3 binary64) (.f64 i (.f64 alpha alpha))) (.f64 beta (*.f64 beta beta)))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta))) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 alpha (.f64 beta beta))) (/.f64 i (.f64 alpha (.f64 beta beta))))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (* (pow alpha 2) (pow beta 2))) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))) (/ (pow i 2) (* (pow alpha 2) (pow beta 2))))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta))) (/.f64 i (.f64 alpha (.f64 beta beta)))) (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 (.f64 beta beta) (.f64 alpha alpha))) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 alpha (.f64 beta beta))) (/.f64 (.f64 i i) (.f64 (.f64 beta beta) (*.f64 alpha alpha)))))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (+ (/ i (* alpha (pow beta 2))) (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (* (pow alpha 2) (pow beta 2))) (+ (/ (* i (- (+ (* 2 (/ i beta)) (/ i beta)) (+ (* 4 (/ i beta)) (* 8 (/ i beta))))) (* alpha (pow beta 2))) (/ (pow i 2) (* (pow alpha 2) (pow beta 2))))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta))) (/.f64 i (.f64 alpha (.f64 beta beta)))) (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 (.f64 beta beta) (.f64 alpha alpha))) (fma.f64 i (/.f64 (-.f64 (.f64 #s(literal 3 binary64) (/.f64 i beta)) (.f64 (/.f64 i beta) #s(literal 12 binary64))) (.f64 alpha (.f64 beta beta))) (/.f64 (.f64 i i) (.f64 (.f64 beta beta) (*.f64 alpha alpha)))))))
(* -3 (/ (* (pow alpha 2) i) (pow beta 3)))
(/.f64 (.f64 #s(literal -3 binary64) (.f64 i (.f64 alpha alpha))) (.f64 beta (*.f64 beta beta)))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2))) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta))) (neg.f64 (/.f64 (fma.f64 i (/.f64 (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64))) (.f64 beta beta)) (neg.f64 (/.f64 i (.f64 beta beta)))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (+ (* -1 (/ (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))) alpha)) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2)))) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta))) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 i (.f64 beta beta))) (fma.f64 i (/.f64 (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64))) (.f64 beta beta)) (neg.f64 (/.f64 (fma.f64 i (/.f64 (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta))) alpha)))) alpha))))
(* (pow alpha 2) (+ (* -3 (/ i (pow beta 3))) (* -1 (/ (+ (* -1 (/ i (pow beta 2))) (+ (* -1 (/ (+ (/ (* i (- (* 2 (/ (pow i 2) beta)) (* 8 (/ (pow i 2) beta)))) (pow beta 2)) (/ (pow i 2) (pow beta 2))) alpha)) (/ (* i (- (+ (* -2 (/ i beta)) (* -1 (/ i beta))) (+ (* -8 (/ i beta)) (* -4 (/ i beta))))) (pow beta 2)))) alpha))))
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(/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (pow beta 3))
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(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))
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(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
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(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
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(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
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(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
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(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
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(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
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(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/.f64 (.f64 alpha (.f64 i beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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1/16
#s(literal 1/16 binary64)
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(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -2 binary64) (neg.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -2 binary64) (neg.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha))) alpha))))
(pow (+ alpha (* 2 i)) 2)
(*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (+.f64 beta (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (+.f64 beta (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (*.f64 #s(literal 2 binary64) (/.f64 alpha beta)))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta))))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta))))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (neg.f64 (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) beta))) beta))))

eval555.0ms (3.8%)

Memory: -6.2MiB live, 395.6MiB allocated
Compiler: Compiled 82 499 to 5 386 computations (93.5% saved)

prune276.0ms (1.9%)

Memory

-2.6MiB live, 488.9MiB allocated

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	1 617	24	1 641
Fresh	11	4	15
Picked	4	1	5
Done	0	0	0
Total	1 632	29	1 661

Accuracy

99.4%

Counts

1 661 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	16.1%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (/.f64 (.f64 #s(literal -3 binary64) (.f64 alpha alpha)) beta))) (.f64 beta beta))
	13.8%	(/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 i i)) (.f64 beta beta))
	16.5%	(/.f64 (fma.f64 i i (.f64 i alpha)) (.f64 beta beta))
	5.0%	(/.f64 (/.f64 (.f64 (.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (.f64 alpha alpha))))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	22.4%	(/.f64 (/.f64 (.f64 i (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha))) beta) beta)
▶	6.1%	(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
	5.2%	(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (*.f64 beta beta))
	23.6%	(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
	33.3%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	13.4%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	36.9%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	6.8%	(/.f64 (.f64 (.f64 alpha beta) #s(literal 1/4 binary64)) (*.f64 i (+.f64 alpha beta)))
	19.4%	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	15.3%	(/.f64 (.f64 i i) (.f64 beta beta))
	6.0%	(/.f64 (.f64 alpha (.f64 i beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	33.0%	(/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (/.f64 (+.f64 i alpha) beta))))
▶	39.3%	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
▶	31.9%	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
	39.3%	(.f64 (/.f64 (fma.f64 i i (fma.f64 i (+.f64 alpha beta) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
▶	33.4%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	38.2%	(.f64 (/.f64 (.f64 i (+.f64 i beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
	32.3%	(.f64 (/.f64 i beta) (pow.f64 (/.f64 beta (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha))) #s(literal -1 binary64)))
	32.3%	(.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha)) beta))
	16.5%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
	33.3%	(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (+.f64 i alpha) beta)))
	17.3%	(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
▶	10.8%	(.f64 alpha (/.f64 i (.f64 beta beta)))
	31.9%	(.f64 #s(literal 1/4 binary64) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
✓	68.2%	#s(literal 1/16 binary64)

Compiler

Compiled 1 450 to 680 computations (53.1% saved)

simplify388.0ms (2.6%)

Memory

42.7MiB live, 664.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 i (+.f64 alpha beta))
✓	cost-diff	0	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
✓	cost-diff	0	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
✓	cost-diff	384	(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
✓	cost-diff	0	(*.f64 beta i)
✓	cost-diff	0	(.f64 alpha (.f64 beta i))
✓	cost-diff	0	(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
✓	cost-diff	384	(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
✓	cost-diff	0	(/.f64 i beta)
✓	cost-diff	0	(+.f64 i alpha)
✓	cost-diff	0	(/.f64 (+.f64 i alpha) beta)
✓	cost-diff	384	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
✓	cost-diff	0	(*.f64 beta beta)
✓	cost-diff	0	(/.f64 i (*.f64 beta beta))
✓	cost-diff	0	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	cost-diff	0	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
✓	cost-diff	320	(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
✓	cost-diff	384	(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
✓	cost-diff	384	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))

Rules

12 966×	`lower-fma.f32`
12 956×	`lower-fma.f64`
4 648×	`lower-*.f32`
4 632×	`lower-+.f32`
4 626×	`lower-*.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	373
0	62	373
1	135	373
2	426	373
3	1749	371
4	5540	343
5	7524	343
0	8487	343

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))
#s(literal 2 binary64)
#s(literal -1 binary64)
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta)))
#s(literal 4 binary64)
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(.f64 alpha (/.f64 i (.f64 beta beta)))
alpha
(/.f64 i (*.f64 beta beta))
i
(*.f64 beta beta)
beta
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(/.f64 (+.f64 i alpha) beta)
(+.f64 i alpha)
i
alpha
beta
(/.f64 i beta)
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
(.f64 alpha (.f64 beta i))
alpha
(*.f64 beta i)
beta
i
(+.f64 alpha beta)
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
#s(literal -1 binary64)
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(literal 1/4 binary64)

Outputs
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 (+.f64 i alpha) (+.f64 i beta)))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 i alpha) (+.f64 i beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(*.f64 (+.f64 i alpha) (+.f64 i beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))
#s(literal 2 binary64)
#s(literal -1 binary64)
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
(*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta)))
(*.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(.f64 i (/.f64 alpha (.f64 beta beta)))
alpha
(/.f64 i (*.f64 beta beta))
i
(*.f64 beta beta)
beta
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/.f64 (+.f64 i alpha) beta)
(+.f64 i alpha)
i
alpha
beta
(/.f64 i beta)
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(/.f64 (.f64 i (.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
(.f64 i (.f64 alpha (/.f64 beta (+.f64 alpha beta))))
(.f64 alpha (.f64 beta i))
(.f64 i (.f64 alpha beta))
alpha
(*.f64 beta i)
(*.f64 i beta)
beta
i
(+.f64 alpha beta)
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
#s(literal -1 binary64)
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(/.f64 (.f64 (.f64 (+.f64 i alpha) (+.f64 i beta)) #s(literal 1/4 binary64)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 i alpha) (+.f64 i beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(*.f64 (+.f64 i alpha) (+.f64 i beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))
(fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(literal 1/4 binary64)

localize161.0ms (1.1%)

Memory

-22.0MiB live, 287.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 alpha beta)
✓	accuracy	100.0%	(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
✓	accuracy	100.0%	(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
✓	accuracy	38.7%	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
✓	accuracy	100.0%	(*.f64 beta i)
✓	accuracy	88.8%	(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
✓	accuracy	88.1%	(.f64 alpha (.f64 beta i))
✓	accuracy	78.0%	(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
✓	accuracy	100.0%	(/.f64 i beta)
✓	accuracy	100.0%	(+.f64 i alpha)
✓	accuracy	100.0%	(/.f64 (+.f64 i alpha) beta)
✓	accuracy	99.5%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	87.0%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	accuracy	84.8%	(/.f64 i (*.f64 beta beta))
✓	accuracy	100.0%	(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
✓	accuracy	99.8%	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
✓	accuracy	38.7%	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
✓	accuracy	38.7%	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))

Samples

103.0ms

256×

valid

Compiler

Compiled 406 to 38 computations (90.6% saved)

Precisions

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

ival-mult: 61.0ms (75.6% of total)

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

ival-add: 9.0ms (11.2% of total)

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

exact: 0.0ms (0% of total)

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

series119.0ms (0.8%)

Memory

6.3MiB live, 186.0MiB allocated

Counts

21 → 660

Calls

Call 1

Inputs
#<alt (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))>
#<alt (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))>
#<alt (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))>
#<alt (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))>
#<alt (.f64 alpha (/.f64 i (.f64 beta beta)))>
#<alt (/.f64 i (*.f64 beta beta))>
#<alt (*.f64 beta beta)>
#<alt (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))>
#<alt (/.f64 (+.f64 i alpha) beta)>
#<alt (+.f64 i alpha)>
#<alt (/.f64 i beta)>
#<alt (/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))>
#<alt (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))>
#<alt (.f64 alpha (.f64 beta i))>
#<alt (*.f64 beta i)>
#<alt (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))>
#<alt (+.f64 i (+.f64 alpha beta))>
#<alt (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))>
#<alt (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))>
#<alt (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))>
#<alt (*.f64 alpha beta)>

Outputs
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt 1/16>
#<alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))>
#<alt (- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))))))>
#<alt (- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3)))))))))>
#<alt 1/16>
#<alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))>
#<alt (+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i)))>
#<alt (+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i)))>
#<alt (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))>
#<alt (+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))))>
#<alt (+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))))>
#<alt (+ (* alpha (- (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 4 beta) (* 8 i)))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))))) (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))))>
#<alt (/ (* i (+ beta i)) (pow alpha 2))>
#<alt (/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2))>
#<alt (/ (- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2))>
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#<alt (* -1 (/ (+ (* -1/4 (/ (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)) (* 1/4 (+ (* -1 alpha) (* -1 i)))) beta))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (* 1/4 (/ (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) beta))) beta)) (* 1/4 (+ (* -1 alpha) (* -1 i)))) beta))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) (* 1/4 (/ (+ (* 2 (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) (* (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) (- (pow (+ alpha (* 2 i)) 2) 1))) beta))) beta)) (* 1/4 (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta)) (* 1/4 (+ (* -1 alpha) (* -1 i)))) beta))>
#<alt (+ alpha beta)>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt i>
#<alt (* i (+ 1 (+ (/ alpha i) (/ beta i))))>
#<alt (* i (+ 1 (+ (/ alpha i) (/ beta i))))>
#<alt (* i (+ 1 (+ (/ alpha i) (/ beta i))))>
#<alt i>
#<alt (* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))>
#<alt (* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))>
#<alt (* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))>
#<alt (+ beta i)>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt alpha>
#<alt (* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))>
#<alt (* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))>
#<alt (* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))>
#<alt alpha>
#<alt (* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ (+ beta i) alpha)) 1)))>
#<alt (+ alpha i)>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt beta>
#<alt (* beta (+ 1 (+ (/ alpha beta) (/ i beta))))>
#<alt (* beta (+ 1 (+ (/ alpha beta) (/ i beta))))>
#<alt (* beta (+ 1 (+ (/ alpha beta) (/ i beta))))>
#<alt beta>
#<alt (* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))>
#<alt (/ i (+ alpha beta))>
#<alt (* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))))>
#<alt (+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2)))>
#<alt (+ (* alpha (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))>
#<alt (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))))) (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))>
#<alt (+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2))))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ i (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2))))) (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))))) (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))>
#<alt (/ i alpha)>
#<alt (/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)>
#<alt (/ i alpha)>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta))))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) alpha)) (+ (* i (+ beta i)) (/ (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))) alpha))) (* -1 (* i (+ (* -4 i) (* -2 beta))))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 beta)) (+ (* -1 (* i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))))) alpha)) (/ (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))) alpha)) (+ (* -1 (* i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))))) alpha)) (* i (+ beta i))) (* -1 (* i (+ (* -4 i) (* -2 beta))))) alpha))) alpha))>
#<alt (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))>
#<alt (+ (* beta (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))>
#<alt (+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))))) (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))>
#<alt (+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 3)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ i (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2))))) (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))))) (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))>
#<alt (/ i beta)>
#<alt (/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)>
#<alt (/ i beta)>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) beta)) (+ (* i (+ alpha i)) (/ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (/ (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (* i (+ alpha i))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))>
#<alt (pow beta 2)>
#<alt (+ (* 2 (* alpha beta)) (pow beta 2))>
#<alt (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))>
#<alt (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) alpha))) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) alpha))) alpha))))>
#<alt (pow alpha 2)>
#<alt (+ (* 2 (* alpha beta)) (pow alpha 2))>
#<alt (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))>
#<alt (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))>
#<alt (- (pow (+ alpha beta) 2) 1)>
#<alt (- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1)>
#<alt (- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)>
#<alt (- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))>
#<alt (* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))>
#<alt (- (pow (+ beta (* 2 i)) 2) 1)>
#<alt (- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)>
#<alt (- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)>
#<alt (- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))>
#<alt (* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))>
#<alt (- (pow (+ alpha (* 2 i)) 2) 1)>
#<alt (- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)>
#<alt (- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)>
#<alt (- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))>
#<alt (* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))>
#<alt (* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>

Calls

165 calls:

Time	Variable		Point	Expression
15.0ms	i	@	inf	(+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))
15.0ms	i	@	-inf	(/ (/ (* alpha (* beta i)) (+ alpha beta)) (+ (* (+ alpha beta) (+ alpha beta)) -1))
3.0ms	alpha	@	0	(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) (/ (* i (+ i (+ alpha beta))) (+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))))
3.0ms	beta	@	0	(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) (/ (* i (+ i (+ alpha beta))) (+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))))
2.0ms	alpha	@	-inf	(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* (+ (* i 2) (+ alpha beta)) (+ (* i 2) (+ alpha beta))) -1)) (/ (* i (+ i (+ alpha beta))) (+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))))

rewrite382.0ms (2.6%)

Memory

-26.9MiB live, 670.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 702×	`lower-/.f32`
6 688×	`lower-/.f64`
5 142×	`lower-*.f32`
5 120×	`lower-*.f64`
2 346×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	251
0	62	226
1	271	226
2	2609	226
0	9326	226

Stop Event

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

Counts

21 → 1 020

Calls

Call 1

Inputs
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 i (*.f64 beta beta))
(*.f64 beta beta)
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(/.f64 (+.f64 i alpha) beta)
(+.f64 i alpha)
(/.f64 i beta)
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta))
(.f64 alpha (.f64 beta i))
(*.f64 beta i)
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(+.f64 i (+.f64 alpha beta))
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(*.f64 alpha beta)

Outputs
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i #s(literal 4 binary64))))) (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i #s(literal 4 binary64)))) (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (*.f64 i (+.f64 i (+.f64 alpha beta)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 (+.f64 i (+.f64 alpha beta)) (*.f64 i #s(literal 4 binary64))))))))
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(*.f64 alpha beta)
(*.f64 beta alpha)

simplify553.0ms (3.7%)

Memory

39.9MiB live, 781.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 546×	`lower-*.f64`
6 546×	`lower-*.f32`
5 772×	`lower-fma.f64`
5 772×	`lower-fma.f32`
4 184×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1836	21137
1	6244	20803
0	8239	19433

Stop Event

1×	iter limit
1×	node limit

Counts

660 → 648

Calls

Call 1

Inputs
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))))))
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3)))))))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
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(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i)))
(/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))))
(+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))))
(+ (* alpha (- (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 4 beta) (* 8 i)))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))))) (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (pow (+ beta (* 2 i)) 2) 1))))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2))
(/ (- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2))
(/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (+ (pow (+ beta (* 2 i)) 2) (pow (+ (* 2 beta) (* 4 i)) 2)))) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2))
(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2)))
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* -2 (* (+ beta (* 2 i)) (+ (* -4 i) (* -2 beta)))) (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (pow (+ beta (* 2 i)) 2)))) 1)))) (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (+ (* -1 beta) (* -1 i))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (* (+ (* -4 i) (* -2 beta)) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (+ (/ (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* -2 (* (+ beta (* 2 i)) (+ (* -4 i) (* -2 beta)))) (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (pow (+ beta (* 2 i)) 2)))) 1)))) (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (+ (* -1 beta) (* -1 i)))))))))) alpha) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (+ (* -1 beta) (* -1 i)))))) (- (+ (* -2 (* (+ beta (* 2 i)) (+ (* -4 i) (* -2 beta)))) (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (pow (+ beta (* 2 i)) 2)))) 1)) alpha)))) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* -2 (* (+ beta (* 2 i)) (+ (* -4 i) (* -2 beta)))) (+ (* 4 (* i (+ beta i))) (+ (pow beta 2) (pow (+ beta (* 2 i)) 2)))) 1)))) (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (+ (* -1 beta) (* -1 i))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 beta) (* -2 (+ beta (* 2 i))))) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1))))
(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (+ (pow (+ alpha (* 2 i)) 2) (pow (+ (* 2 alpha) (* 4 i)) 2)))) 1))) (* (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) (* (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (pow (+ alpha (* 2 i)) 2) 1))))
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(/ (* i (+ alpha i)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (+ (pow (+ alpha (* 2 i)) 2) (pow (+ (* 2 alpha) (* 4 i)) 2)))) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (+ (pow (+ alpha (* 2 i)) 2) (pow (+ (* 2 alpha) (* 4 i)) 2)))) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (+ (pow (+ alpha (* 2 i)) 2) (pow (+ (* 2 alpha) (* 4 i)) 2)))) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (+ (pow (+ alpha (* 2 i)) 2) (pow (+ (* 2 alpha) (* 4 i)) 2)))) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2))
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2)))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* -2 (* (+ alpha (* 2 i)) (+ (* -4 i) (* -2 alpha)))) (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (pow (+ alpha (* 2 i)) 2)))) 1)))) (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (+ (* -1 alpha) (* -1 i))))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (+ (/ (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* -2 (* (+ alpha (* 2 i)) (+ (* -4 i) (* -2 alpha)))) (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (pow (+ alpha (* 2 i)) 2)))) 1)))) (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (+ (* -1 alpha) (* -1 i)))))))))) beta) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* -2 (* (+ alpha (* 2 i)) (+ (* -4 i) (* -2 alpha)))) (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (pow (+ alpha (* 2 i)) 2)))) 1)) beta)))) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* -2 (* (+ alpha (* 2 i)) (+ (* -4 i) (* -2 alpha)))) (+ (* 4 (* i (+ alpha i))) (+ (pow alpha 2) (pow (+ alpha (* 2 i)) 2)))) 1)))) (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (+ (* -1 alpha) (* -1 i))))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* -1 (* i (* (+ (* -4 i) (+ (* -2 alpha) (* -2 (+ alpha (* 2 i))))) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(* alpha beta)
(+ (* alpha beta) (* i (+ alpha beta)))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(* i (+ beta i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(* alpha (+ beta i))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* -1 (* alpha (+ (* -1 beta) (* -1 i))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* i (+ alpha i))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(* beta (+ alpha i))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* -1 (* beta (+ (* -1 alpha) (* -1 i))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(pow (+ alpha beta) 2)
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(+ (* 4 (* i (+ beta i))) (pow beta 2))
(+ (* 4 (* i (+ beta i))) (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow beta 2)))
(+ (* 4 (* i (+ beta i))) (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow beta 2)))
(+ (* 4 (* i (+ beta i))) (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow beta 2)))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (+ (* 4 (/ (* i (+ beta i)) (pow alpha 2))) (/ (pow beta 2) (pow alpha 2)))))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (+ (* 4 (/ (* i (+ beta i)) (pow alpha 2))) (/ (pow beta 2) (pow alpha 2)))))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -2 beta)) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -4 i) (+ (* -2 beta) (* -1 (/ (+ (* 4 (* i (+ beta i))) (pow beta 2)) alpha)))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -4 i) (+ (* -2 beta) (* -1 (/ (+ (* 4 (* i (+ beta i))) (pow beta 2)) alpha)))) alpha))))
(+ (* 4 (* i (+ alpha i))) (pow alpha 2))
(+ (* 4 (* i (+ alpha i))) (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow alpha 2)))
(+ (* 4 (* i (+ alpha i))) (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow alpha 2)))
(+ (* 4 (* i (+ alpha i))) (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow alpha 2)))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 4 (/ (* i (+ alpha i)) (pow beta 2))) (/ (pow alpha 2) (pow beta 2)))))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 4 (/ (* i (+ alpha i)) (pow beta 2))) (/ (pow alpha 2) (pow beta 2)))))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -2 alpha)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (+ (* -2 alpha) (* -1 (/ (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) beta)))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (+ (* -2 alpha) (* -1 (/ (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) beta)))) beta))))
(/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))
(+ (* i (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (- (+ (* i (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (- (+ (* i (- (+ (* -1 (* i (+ (* 4 (/ (* (+ alpha beta) (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (- (pow (+ alpha beta) 2) 1)))))) (/ 1 (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
1/4
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (+ (* -1 (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))))) (* 1/4 (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)))) (pow i 4))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (+ (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))))
1/4
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (- (+ (* -1 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) i)) (* 1/4 (/ (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)) i))) (* -1 (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1))
(+ (* alpha (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1)))) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ beta (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ i (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))) (+ (/ (* i (+ beta i)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (- (pow (+ beta (* 2 i)) 2) 1))))) (+ (/ beta (- (pow (+ beta (* 2 i)) 2) 1)) (/ i (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))) (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(/ (+ beta i) alpha)
(/ (- (+ beta (+ i (/ (* i (+ beta i)) alpha))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))))) (* (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (- (pow (+ beta (* 2 i)) 2) 1))) (pow alpha 3))) (/ (* i (+ beta i)) alpha)))) (+ (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* (+ beta i) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)
(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) alpha)) (+ (* i (+ beta i)) (/ (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)) alpha))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (/ (* (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) (- (pow (+ beta (* 2 i)) 2) 1)) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))))) (* (+ (* -1 beta) (* -1 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (* i (+ beta i))) (* -2 (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i))))) alpha)))) alpha))
(/ (* i (+ alpha i)) (- (pow (+ alpha (* 2 i)) 2) 1))
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(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 3))) (/ (* i (+ alpha i)) beta)))) (+ (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)
(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta))
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(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (/ (* (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) (- (pow (+ alpha (* 2 i)) 2) 1)) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) (* (+ (* -1 alpha) (* -1 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) beta)) (* i (+ alpha i))) (* -2 (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))) beta)))) beta))
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(/ (* alpha i) (pow beta 2))
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(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (* (+ alpha (* 2 alpha)) (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1)))))) (+ (* (+ alpha (* 2 alpha)) (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))))) (* (pow alpha 2) (* i (- (pow alpha 2) 1))))) beta)) (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))))) beta)) (* alpha (* i (+ alpha (* 2 alpha))))) beta)) (* alpha i)) (pow beta 2))
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(/ (* alpha (* beta i)) (+ alpha beta))
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(* 1/4 (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
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1/16
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1/16
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(* 1/4 (/ (* i (+ beta i)) (- (pow (+ beta (* 2 i)) 2) 1)))
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(* 1/4 (/ (+ beta i) alpha))
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(* 1/4 (/ (+ alpha i) beta))
(/ (+ (* 1/4 (+ alpha i)) (* 1/4 (/ (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta))) beta)
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(/ (+ (* -1/4 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 3))) (+ (* -1/4 (/ (+ (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (+ (* 1/4 (+ alpha i)) (* 1/4 (/ (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta))))) beta)
(* -1/4 (/ (+ (* -1 alpha) (* -1 i)) beta))
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(+ alpha beta)
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(+ alpha (+ beta i))
(+ alpha (+ beta i))
i
(* i (+ 1 (+ (/ alpha i) (/ beta i))))
(* i (+ 1 (+ (/ alpha i) (/ beta i))))
(* i (+ 1 (+ (/ alpha i) (/ beta i))))
i
(* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))
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(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))
(* alpha (+ 1 (+ (/ beta alpha) (/ i alpha))))
alpha
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beta
(* beta (+ 1 (+ (/ alpha beta) (/ i beta))))
(* beta (+ 1 (+ (/ alpha beta) (/ i beta))))
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beta
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))
(* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))
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(/ i (+ alpha beta))
(* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta))))
(* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))
(* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))
1/4
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(- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))
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1/4
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(/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2)))
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(/ i alpha)
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(/ i alpha)
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(/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))
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(/ i beta)
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ i (+ (* -1 (/ (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)
(/ i beta)
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) beta)) (+ (* i (+ alpha i)) (/ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (/ (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (* i (+ alpha i))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))
(pow beta 2)
(+ (* 2 (* alpha beta)) (pow beta 2))
(+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))
(+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) alpha))) alpha))))
(pow alpha 2)
(+ (* 2 (* alpha beta)) (pow alpha 2))
(+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))
(+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))
(- (pow (+ alpha beta) 2) 1)
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(- (pow (+ beta (* 2 i)) 2) 1)
(- (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)
(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)
(pow alpha 2)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))) (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
(- (pow (+ alpha (* 2 i)) 2) 1)
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)

Outputs
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(.f64 i (fma.f64 i (-.f64 (fma.f64 alpha (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(.f64 i (fma.f64 i (fma.f64 i (-.f64 (.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (fma.f64 (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (-.f64 (fma.f64 alpha (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (fma.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64)))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))) (-.f64 (fma.f64 alpha (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))) (/.f64 (.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(.f64 i (fma.f64 i (-.f64 (fma.f64 i (-.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))) (.f64 i (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (fma.f64 #s(literal 32 binary64) (/.f64 (.f64 alpha beta) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))) (fma.f64 (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (-.f64 (.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (fma.f64 (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (-.f64 (fma.f64 alpha (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (fma.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal 20 binary64) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) #s(literal 4 binary64)))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (-.f64 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#s(literal -1 binary64))))))))) (fma.f64 (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (-.f64 (fma.f64 alpha (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (.f64 (.f64 (+.f64 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(+.f64 alpha beta) (+.f64 alpha beta)))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (.f64 alpha beta) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
1/16
#s(literal 1/16 binary64)
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (.f64 #s(literal -1/8 binary64) (+.f64 alpha beta))) i))
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1/4
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(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)))
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(fma.f64 beta (+.f64 (fma.f64 alpha #s(literal 2 binary64) beta) (*.f64 i #s(literal 4 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)))
(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
(fma.f64 beta (+.f64 (fma.f64 alpha #s(literal 2 binary64) beta) (*.f64 i #s(literal 4 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (/.f64 (*.f64 i #s(literal 4 binary64)) beta))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) #s(literal 1 binary64)) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta)))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (-.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) #s(literal 1 binary64)) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta)))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta)))
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)
(* alpha beta)
(*.f64 alpha beta)

eval381.0ms (2.6%)

Memory: 23.1MiB live, 591.8MiB allocated
Compiler: Compiled 107 990 to 5 540 computations (94.9% saved)

prune338.0ms (2.3%)

Memory

-11.5MiB live, 746.5MiB allocated

Pruning

30 alts after pruning (28 fresh and 2 done)

	Pruned	Kept	Total
New	2 120	18	2 138
Fresh	13	10	23
Picked	4	1	5
Done	0	1	1
Total	2 137	30	2 167

Accuracy

99.4%

Counts

2 167 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	13.8%	(/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 i i)) (.f64 beta beta))
	16.5%	(/.f64 (fma.f64 i i (.f64 i alpha)) (.f64 beta beta))
	23.8%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
▶	12.0%	(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
▶	33.5%	(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
	33.3%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	12.6%	(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
▶	5.1%	(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
	13.4%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha i)) (.f64 alpha alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	13.4%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	8.8%	(/.f64 (.f64 i (.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	15.3%	(/.f64 (.f64 i i) (.f64 beta beta))
	12.2%	(/.f64 (*.f64 alpha i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
	32.4%	(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 i (+.f64 beta i))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	33.0%	(/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (/.f64 (+.f64 i alpha) beta))))
▶	39.3%	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
	39.3%	(.f64 (/.f64 (fma.f64 i i (fma.f64 i (+.f64 alpha beta) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
	38.2%	(.f64 (/.f64 (.f64 i (+.f64 i beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
	38.2%	(.f64 (/.f64 (.f64 i (+.f64 beta i)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
	5.5%	(.f64 (/.f64 (.f64 beta (+.f64 alpha i)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
▶	9.9%	(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
	26.2%	(*.f64 (/.f64 (neg.f64 i) #s(literal -1 binary64)) (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
	32.3%	(.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha)) beta))
	30.3%	(*.f64 (/.f64 i beta) (/.f64 i beta))
	12.6%	(*.f64 (/.f64 i beta) (/.f64 alpha beta))
	17.3%	(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
	8.8%	(.f64 (.f64 i (.f64 alpha beta)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
	26.2%	(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (+.f64 i alpha) beta)))
✓	10.8%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	68.2%	#s(literal 1/16 binary64)

Compiler

Compiled 1 216 to 594 computations (51.2% saved)

simplify430.0ms (2.9%)

Memory

-29.5MiB live, 704.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 alpha beta)
✓	cost-diff	0	(/.f64 (*.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
✓	cost-diff	384	(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
✓	cost-diff	0	(+.f64 i alpha)
✓	cost-diff	0	(/.f64 beta (+.f64 i alpha))
✓	cost-diff	0	(/.f64 i beta)
✓	cost-diff	768	(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
✓	cost-diff	0	(*.f64 i alpha)
✓	cost-diff	0	(/.f64 (*.f64 i alpha) beta)
✓	cost-diff	384	(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
✓	cost-diff	0	(+.f64 alpha i)
✓	cost-diff	0	(*.f64 (+.f64 alpha i) #s(literal 1/4 binary64))
✓	cost-diff	0	(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
✓	cost-diff	0	(+.f64 i (+.f64 alpha beta))
✓	cost-diff	0	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
✓	cost-diff	384	(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
✓	cost-diff	384	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))

Rules

10 778×	`lower-fma.f32`
10 770×	`lower-fma.f64`
5 566×	`lower-*.f32`
5 550×	`lower-*.f64`
4 284×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	306
0	59	306
1	122	306
2	341	306
3	1133	306
4	4295	295
5	6778	294
0	8166	288

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta)))
#s(literal 4 binary64)
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
#s(literal -1 binary64)
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(*.f64 (+.f64 alpha i) #s(literal 1/4 binary64))
(+.f64 alpha i)
alpha
i
#s(literal 1/4 binary64)
beta
(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
(/.f64 (*.f64 i alpha) beta)
(*.f64 i alpha)
i
alpha
beta
(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
(/.f64 i beta)
i
beta
(/.f64 beta (+.f64 i alpha))
(+.f64 i alpha)
alpha
(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
(/.f64 (*.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(*.f64 alpha beta)
alpha
beta
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
(+.f64 alpha beta)
#s(literal -1 binary64)
(/.f64 i (+.f64 alpha beta))
i

Outputs
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 (.f64 i (+.f64 i alpha)) (+.f64 i beta))) (.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64))))))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 (+.f64 i alpha) (+.f64 i beta)) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(*.f64 (+.f64 i alpha) (+.f64 i beta))
i
(+.f64 i (+.f64 alpha beta))
(+.f64 alpha beta)
alpha
beta
(*.f64 alpha beta)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(fma.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(*.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta)))
(*.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64))
#s(literal 4 binary64)
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
#s(literal -1 binary64)
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 i (*.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)))))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64))))
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 i alpha)) beta)
(*.f64 (+.f64 alpha i) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/4 binary64) (+.f64 i alpha))
(+.f64 alpha i)
(+.f64 i alpha)
alpha
i
#s(literal 1/4 binary64)
beta
(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (*.f64 i alpha) beta)
(*.f64 i alpha)
i
alpha
beta
(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/.f64 i beta)
i
beta
(/.f64 beta (+.f64 i alpha))
(+.f64 i alpha)
alpha
(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
(/.f64 (.f64 alpha (.f64 i beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (*.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(*.f64 alpha (/.f64 beta (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(*.f64 alpha beta)
alpha
beta
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
(+.f64 alpha beta)
#s(literal -1 binary64)
(/.f64 i (+.f64 alpha beta))
i

localize103.0ms (0.7%)

Memory

35.8MiB live, 273.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 alpha beta)
✓	accuracy	100.0%	(*.f64 alpha beta)
✓	accuracy	84.4%	(/.f64 (*.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
✓	accuracy	76.5%	(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
✓	accuracy	100.0%	(/.f64 i beta)
✓	accuracy	100.0%	(+.f64 i alpha)
✓	accuracy	100.0%	(/.f64 beta (+.f64 i alpha))
✓	accuracy	99.7%	(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
✓	accuracy	100.0%	(*.f64 i alpha)
✓	accuracy	99.8%	(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
✓	accuracy	96.4%	(/.f64 (*.f64 i alpha) beta)
✓	accuracy	100.0%	(+.f64 alpha i)
✓	accuracy	100.0%	(*.f64 (+.f64 alpha i) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
✓	accuracy	100.0%	(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
✓	accuracy	99.8%	(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
✓	accuracy	38.7%	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
✓	accuracy	38.7%	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))

Samples

59.0ms

256×

valid

Compiler

Compiled 324 to 35 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-div: 15.0ms (38% of total)

ival-mult: 15.0ms (38% of total)

ival-add: 9.0ms (22.8% of total)

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

exact: 0.0ms (0% of total)

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

series78.0ms (0.5%)

Memory

-45.5MiB live, 94.7MiB allocated

Counts

21 → 636

Calls

Call 1

Inputs
#<alt (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))>
#<alt (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))>
#<alt (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))>
#<alt (+.f64 i (+.f64 alpha beta))>
#<alt (/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)>
#<alt (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64))>
#<alt (+.f64 alpha i)>
#<alt (/.f64 (/.f64 (*.f64 i alpha) beta) beta)>
#<alt (/.f64 (*.f64 i alpha) beta)>
#<alt (*.f64 i alpha)>
#<alt (/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))>
#<alt (/.f64 i beta)>
#<alt (/.f64 beta (+.f64 i alpha))>
#<alt (+.f64 i alpha)>
#<alt (.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))>
#<alt (/.f64 (*.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))>
#<alt (*.f64 alpha beta)>
#<alt (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))>
#<alt (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))>
#<alt (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))>
#<alt (+.f64 alpha beta)>

Outputs
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt (* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))>
#<alt 1/16>
#<alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))>
#<alt (- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))))))>
#<alt (- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3)))))))))>
#<alt 1/16>
#<alt (- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))>
#<alt (+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i)))>
#<alt (+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i)))>
#<alt (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))>
#<alt (+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))>
#<alt (+ (* alpha (- (+ (* alpha (- (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))>
#<alt (+ (* alpha (- (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (- (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (+ (/ (* (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* 4 beta) (* 8 i)))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))))) (/ (* i (+ beta i)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) (+ (/ (* (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (* (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))>
#<alt (/ (* i (+ beta i)) (pow alpha 2))>
#<alt (/ (- (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)) (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha)) (pow alpha 2))>
#<alt (/ (- (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* i (* (+ beta i) (+ (* (+ (* 2 beta) (* 4 i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (+ (* (+ (* 4 beta) (* 8 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1))) (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))))))) (* (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i))))) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1)))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))) alpha) (+ (/ (* i (* (+ beta i) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1))) (pow alpha 2)) (/ (* (+ (* 4 beta) (* 8 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 4 beta) (* 8 i)))))) (pow alpha 2))))) (pow alpha 2))>
#<alt (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2)))>
#<alt (/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 beta)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))>
#<alt (/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* -4 i) (* -2 beta)) 2))) 1)))) (* (+ (* -8 i) (* -4 beta)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 beta)) (+ (* -1 beta) (* -1 i))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -8 i) (* -4 beta)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))>
#<alt (/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -1 beta) (* -1 i)) (+ (* (+ (* -4 i) (* -2 beta)) (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* -4 i) (* -2 beta)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (+ (/ (* (+ (* -8 i) (* -4 beta)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* -4 i) (* -2 beta)) 2))) 1)))) (* (+ (* -8 i) (* -4 beta)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 beta)) (+ (* -1 beta) (* -1 i)))))))))) alpha) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 beta)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* -4 i) (* -2 beta)) 2))) 1)) alpha)))) (+ (* -1 (* i (* (+ (* -1 beta) (* -1 i)) (- (+ (* 2 (pow beta 2)) (+ (* 8 (* i (+ beta i))) (pow (+ (* -4 i) (* -2 beta)) 2))) 1)))) (* (+ (* -8 i) (* -4 beta)) (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 beta)) (+ (* -1 beta) (* -1 i))))))))) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) (* -1 (* i (* (+ (* -8 i) (* -4 beta)) (+ (* -1 beta) (* -1 i)))))) alpha))) (pow alpha 2))>
#<alt (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))>
#<alt (+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))))) (* (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))))>
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#<alt (* alpha beta)>
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#<alt 1/4>
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#<alt (/ (+ beta i) alpha)>
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#<alt (* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 beta)) (+ (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i))))) (* (+ (* -1 beta) (* -1 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) alpha)) (/ (* (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i)))) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) alpha)) (+ (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i))))) (* (+ (* -1 beta) (* -1 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) alpha)) (* i (+ beta i))) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i)))) alpha)))) alpha))>
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#<alt (/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (pow beta 3))) (/ (* i (+ alpha i)) beta)))) (+ (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)>
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#<alt (* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 alpha)) (+ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i))))) (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))) beta)) (/ (* (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) beta)) (+ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i))))) (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))) beta)) (* i (+ alpha i))) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i)))) beta)))) beta))>
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#<alt (* alpha (+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (* -1 (/ (* i (* (+ beta (* 2 beta)) (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1))) (* (pow beta 2) (pow (- (pow beta 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1) 2)) (* (pow beta 2) (pow (- (pow beta 2) 1) 3)))) (/ (* i (+ beta (* 2 beta))) (* beta (pow (- (pow beta 2) 1) 2)))) (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1)) (* beta (- (pow beta 2) 1)))) (/ i (* beta (pow (- (pow beta 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1) 2)) (* (pow beta 2) (pow (- (pow beta 2) 1) 3)))) (/ (* i (+ beta (* 2 beta))) (* beta (pow (- (pow beta 2) 1) 2)))))) (/ (* i (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1)) (* beta (pow (- (pow beta 2) 1) 2))))) (/ i (- (pow beta 2) 1))))>
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#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* beta (* i (* (+ beta (* 2 beta)) (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1))))) (+ (* -1 (* (+ beta (* 2 beta)) (+ (* -1 (* beta (* i (pow (+ beta (* 2 beta)) 2)))) (* beta (* i (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1)))))) (* (pow beta 2) (* i (- (pow beta 2) 1))))) (pow alpha 3))) (* beta i)) (+ (* -1 (/ (* beta (* i (pow (+ beta (* 2 beta)) 2))) (pow alpha 2))) (+ (/ (* beta (* i (+ beta (* 2 beta)))) alpha) (/ (* beta (* i (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1))) (pow alpha 2))))) (pow alpha 2))>
#<alt (/ (* beta i) (pow alpha 2))>
#<alt (/ (+ (* -1 (/ (* beta (* i (+ beta (* 2 beta)))) alpha)) (* beta i)) (pow alpha 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1))))) (* beta (* i (pow (+ beta (* 2 beta)) 2)))) alpha)) (* beta (* i (+ beta (* 2 beta))))) alpha)) (* beta i)) (pow alpha 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (* (+ beta (* 2 beta)) (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1)))))) (+ (* (+ beta (* 2 beta)) (+ (* beta (* i (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1))))) (* beta (* i (pow (+ beta (* 2 beta)) 2))))) (* (pow beta 2) (* i (- (pow beta 2) 1))))) alpha)) (+ (* beta (* i (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1))))) (* beta (* i (pow (+ beta (* 2 beta)) 2))))) alpha)) (* beta (* i (+ beta (* 2 beta))))) alpha)) (* beta i)) (pow alpha 2))>
#<alt (/ (* beta i) (- (pow alpha 2) 1))>
#<alt (* beta (+ (* -1 (/ (* beta (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))) (* alpha (pow (- (pow alpha 2) 1) 2)))) (/ i (- (pow alpha 2) 1))))>
#<alt (* beta (+ (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (/ (* i (+ alpha (* 2 alpha))) (* alpha (pow (- (pow alpha 2) 1) 2)))))) (/ (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)) (* alpha (pow (- (pow alpha 2) 1) 2))))) (/ i (- (pow alpha 2) 1))))>
#<alt (* beta (+ (* beta (- (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (* (+ alpha (* 2 alpha)) (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (/ (* i (+ alpha (* 2 alpha))) (* alpha (pow (- (pow alpha 2) 1) 2)))) (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)) (* alpha (- (pow alpha 2) 1)))) (/ i (* alpha (pow (- (pow alpha 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (/ (* i (+ alpha (* 2 alpha))) (* alpha (pow (- (pow alpha 2) 1) 2)))))) (/ (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)) (* alpha (pow (- (pow alpha 2) 1) 2))))) (/ i (- (pow alpha 2) 1))))>
#<alt (/ (* alpha i) (pow beta 2))>
#<alt (/ (+ (* -1 (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (* alpha i)) (pow beta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)))) (pow beta 2))) (* alpha i)) (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (pow beta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* alpha (* i (* (+ alpha (* 2 alpha)) (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))))) (+ (* -1 (* (+ alpha (* 2 alpha)) (+ (* -1 (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)))))) (* (pow alpha 2) (* i (- (pow alpha 2) 1))))) (pow beta 3))) (* alpha i)) (+ (* -1 (/ (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))) (pow beta 2))) (+ (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta) (/ (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))) (pow beta 2))))) (pow beta 2))>
#<alt (/ (* alpha i) (pow beta 2))>
#<alt (/ (+ (* -1 (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (* alpha i)) (pow beta 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) beta)) (* alpha (* i (+ alpha (* 2 alpha))))) beta)) (* alpha i)) (pow beta 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (* (+ alpha (* 2 alpha)) (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1)))))) (+ (* (+ alpha (* 2 alpha)) (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))))) (* (pow alpha 2) (* i (- (pow alpha 2) 1))))) beta)) (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))))) beta)) (* alpha (* i (+ alpha (* 2 alpha))))) beta)) (* alpha i)) (pow beta 2))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))>
#<alt (/ (* alpha beta) (- (pow beta 2) 1))>
#<alt (* alpha (+ (* -2 (/ (* alpha (pow beta 2)) (pow (- (pow beta 2) 1) 2))) (/ beta (- (pow beta 2) 1))))>
#<alt (* alpha (+ (* alpha (- (* -1 (* alpha (+ (* -4 (/ (pow beta 3) (pow (- (pow beta 2) 1) 3))) (/ beta (pow (- (pow beta 2) 1) 2))))) (* 2 (/ (pow beta 2) (pow (- (pow beta 2) 1) 2))))) (/ beta (- (pow beta 2) 1))))>
#<alt (* alpha (+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (* -2 (/ (* beta (+ (* -4 (/ (pow beta 3) (pow (- (pow beta 2) 1) 3))) (/ beta (pow (- (pow beta 2) 1) 2)))) (- (pow beta 2) 1))) (* -2 (/ (pow beta 2) (pow (- (pow beta 2) 1) 3)))))) (+ (* -4 (/ (pow beta 3) (pow (- (pow beta 2) 1) 3))) (/ beta (pow (- (pow beta 2) 1) 2))))) (* 2 (/ (pow beta 2) (pow (- (pow beta 2) 1) 2))))) (/ beta (- (pow beta 2) 1))))>
#<alt (/ beta alpha)>
#<alt (/ (+ beta (* -2 (/ (pow beta 2) alpha))) alpha)>
#<alt (/ (- (+ beta (* -1 (/ (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))) (pow alpha 2)))) (* 2 (/ (pow beta 2) alpha))) alpha)>
#<alt (/ (- (+ beta (* -1 (/ (+ (* -2 (* beta (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))))) (* -2 (* (pow beta 2) (- (pow beta 2) 1)))) (pow alpha 3)))) (+ (* -4 (/ (pow beta 3) (pow alpha 2))) (+ (* 2 (/ (pow beta 2) alpha)) (/ (* beta (- (pow beta 2) 1)) (pow alpha 2))))) alpha)>
#<alt (/ beta alpha)>
#<alt (* -1 (/ (+ (* -1 beta) (* 2 (/ (pow beta 2) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 beta) (* -1 (/ (+ (* -2 (pow beta 2)) (* -1 (/ (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))) alpha))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 beta) (* -1 (/ (+ (* -2 (pow beta 2)) (* -1 (/ (+ (* -4 (pow beta 3)) (+ (* -1 (/ (+ (* 2 (* beta (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))))) (* 2 (* (pow beta 2) (- (pow beta 2) 1)))) alpha)) (* beta (- (pow beta 2) 1)))) alpha))) alpha))) alpha))>
#<alt (/ (* alpha beta) (- (pow alpha 2) 1))>
#<alt (* beta (+ (* -2 (/ (* (pow alpha 2) beta) (pow (- (pow alpha 2) 1) 2))) (/ alpha (- (pow alpha 2) 1))))>
#<alt (* beta (+ (* beta (- (* -1 (* beta (+ (* -4 (/ (pow alpha 3) (pow (- (pow alpha 2) 1) 3))) (/ alpha (pow (- (pow alpha 2) 1) 2))))) (* 2 (/ (pow alpha 2) (pow (- (pow alpha 2) 1) 2))))) (/ alpha (- (pow alpha 2) 1))))>
#<alt (* beta (+ (* beta (- (* beta (- (* -1 (* beta (+ (* -2 (/ (* alpha (+ (* -4 (/ (pow alpha 3) (pow (- (pow alpha 2) 1) 3))) (/ alpha (pow (- (pow alpha 2) 1) 2)))) (- (pow alpha 2) 1))) (* -2 (/ (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))))) (+ (* -4 (/ (pow alpha 3) (pow (- (pow alpha 2) 1) 3))) (/ alpha (pow (- (pow alpha 2) 1) 2))))) (* 2 (/ (pow alpha 2) (pow (- (pow alpha 2) 1) 2))))) (/ alpha (- (pow alpha 2) 1))))>
#<alt (/ alpha beta)>
#<alt (/ (+ alpha (* -2 (/ (pow alpha 2) beta))) beta)>
#<alt (/ (- (+ alpha (* -1 (/ (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))) (pow beta 2)))) (* 2 (/ (pow alpha 2) beta))) beta)>
#<alt (/ (- (+ alpha (* -1 (/ (+ (* -2 (* alpha (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))))) (* -2 (* (pow alpha 2) (- (pow alpha 2) 1)))) (pow beta 3)))) (+ (* -4 (/ (pow alpha 3) (pow beta 2))) (+ (* 2 (/ (pow alpha 2) beta)) (/ (* alpha (- (pow alpha 2) 1)) (pow beta 2))))) beta)>
#<alt (/ alpha beta)>
#<alt (* -1 (/ (+ (* -1 alpha) (* 2 (/ (pow alpha 2) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 alpha) (* -1 (/ (+ (* -2 (pow alpha 2)) (* -1 (/ (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))) beta))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 alpha) (* -1 (/ (+ (* -2 (pow alpha 2)) (* -1 (/ (+ (* -4 (pow alpha 3)) (+ (* -1 (/ (+ (* 2 (* alpha (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))))) (* 2 (* (pow alpha 2) (- (pow alpha 2) 1)))) beta)) (* alpha (- (pow alpha 2) 1)))) beta))) beta))) beta))>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (* alpha beta)>
#<alt (- (pow beta 2) 1)>
#<alt (- (+ (* 2 (* alpha beta)) (pow beta 2)) 1)>
#<alt (- (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2)) 1)>
#<alt (- (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2)) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))>
#<alt (* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (- (pow beta 2) 1) alpha))) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (- (pow beta 2) 1) alpha))) alpha))))>
#<alt (- (pow alpha 2) 1)>
#<alt (- (+ (* 2 (* alpha beta)) (pow alpha 2)) 1)>
#<alt (- (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2)) 1)>
#<alt (- (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2)) 1)>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))>
#<alt (* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))) (/ 1 (pow beta 2))))>
#<alt (* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))) (/ 1 (pow beta 2))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (- (pow alpha 2) 1) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (- (pow alpha 2) 1) beta))) beta))))>
#<alt (/ i (+ alpha beta))>
#<alt (* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))))>
#<alt (+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2)))>
#<alt (+ (* alpha (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))>
#<alt (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))))) (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))>
#<alt (+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2))))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ i (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2))))) (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))))) (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))>
#<alt (/ i alpha)>
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#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)>
#<alt (/ i alpha)>
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#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 beta)) (+ (* -1 (* i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))))) alpha)) (/ (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))) alpha)) (+ (* -1 (* i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))))) alpha)) (* i (+ beta i))) (* -1 (* i (+ (* -4 i) (* -2 beta))))) alpha))) alpha))>
#<alt (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))>
#<alt (+ (* beta (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))>
#<alt (+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))))) (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))>
#<alt (+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 3)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ i (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2))))) (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))))) (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))>
#<alt (/ i beta)>
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#<alt (/ (- (+ i (+ (* -1 (/ (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)>
#<alt (/ i beta)>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) beta)) (+ (* i (+ alpha i)) (/ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (/ (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (* i (+ alpha i))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))>
#<alt (pow beta 2)>
#<alt (+ (* 2 (* alpha beta)) (pow beta 2))>
#<alt (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))>
#<alt (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))>
#<alt (pow alpha 2)>
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#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))>
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#<alt (pow alpha 2)>
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#<alt (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))>
#<alt (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))>
#<alt beta>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt alpha>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt alpha>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt beta>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt beta>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>

Calls

159 calls:

Time	Variable		Point	Expression
21.0ms	i	@	-inf	(* i alpha)
8.0ms	alpha	@	0	(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i (* 4 (+ i (+ alpha beta)))) (+ (* (+ alpha beta) (+ alpha beta)) -1))) (/ (* i (+ i (+ alpha beta))) (+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))))
3.0ms	beta	@	0	(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i (* 4 (+ i (+ alpha beta)))) (+ (* (+ alpha beta) (+ alpha beta)) -1))) (/ (* i (+ i (+ alpha beta))) (+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))))
2.0ms	alpha	@	-inf	(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i (* 4 (+ i (+ alpha beta)))) (+ (* (+ alpha beta) (+ alpha beta)) -1))) (/ (* i (+ i (+ alpha beta))) (+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))))
2.0ms	beta	@	-inf	(* (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ (* i (* 4 (+ i (+ alpha beta)))) (+ (* (+ alpha beta) (+ alpha beta)) -1))) (/ (* i (+ i (+ alpha beta))) (+ (* i (* 4 (+ i (+ alpha beta)))) (* (+ alpha beta) (+ alpha beta)))))

rewrite325.0ms (2.2%)

Memory

26.2MiB live, 529.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 250×	`lower-/.f32`
6 230×	`lower-/.f64`
4 640×	`lower-*.f32`
4 624×	`lower-*.f64`
2 076×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	221
0	59	210
1	271	210
2	2547	210
0	8501	210

Stop Event

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

Counts

21 → 1 083

Calls

Call 1

Inputs
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(+.f64 i (+.f64 alpha beta))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(*.f64 (+.f64 alpha i) #s(literal 1/4 binary64))
(+.f64 alpha i)
(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
(/.f64 (*.f64 i alpha) beta)
(*.f64 i alpha)
(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
(/.f64 i beta)
(/.f64 beta (+.f64 i alpha))
(+.f64 i alpha)
(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
(/.f64 (*.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(*.f64 alpha beta)
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(+.f64 alpha beta)

Outputs
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (*.f64 i (+.f64 i (+.f64 alpha beta)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (.f64 i (+.f64 i (+.f64 alpha beta)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))))
(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (*.f64 i (+.f64 i (+.f64 alpha beta))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (.f64 i (+.f64 i (+.f64 alpha beta))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))
(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(/.f64 (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i (+.f64 i (+.f64 alpha beta))))))
(/.f64 (.f64 (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 i (+.f64 i (+.f64 alpha beta)))) (.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (.f64 (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))
(/.f64 (.f64 (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) #s(literal 1 binary64)) (.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (*.f64 i (+.f64 i (+.f64 alpha beta))))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 i (+.f64 i (+.f64 alpha beta)))) (.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) #s(literal 1 binary64)) (.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))
(/.f64 (.f64 (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
(/.f64 (.f64 (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
(/.f64 (.f64 (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal 1 binary64)) (.f64 (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 i (+.f64 i (+.f64 alpha beta)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta))))) (neg.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))
(/.f64 (neg.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (.f64 i (+.f64 i (+.f64 alpha beta))))) (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (neg.f64 (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta))))) (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 i (+.f64 i (+.f64 alpha beta)))))
(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))))
(/.f64 (.f64 (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
(/.f64 (.f64 (neg.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))) (neg.f64 (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (neg.f64 (.f64 (neg.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 i (+.f64 i (+.f64 alpha beta))))) (neg.f64 (.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) #s(literal 4 binary64)) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))
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(*.f64 (exp.f64 (log.f64 (+.f64 alpha beta))) (exp.f64 (log.f64 (+.f64 alpha beta))))
(+.f64 alpha beta)
(+.f64 beta alpha)
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(-.f64 (/.f64 (.f64 alpha alpha) (-.f64 alpha beta)) (/.f64 (.f64 beta beta) (-.f64 alpha beta)))
(-.f64 (/.f64 (.f64 beta beta) (-.f64 beta alpha)) (/.f64 (.f64 alpha alpha) (-.f64 beta alpha)))
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(/.f64 (neg.f64 (*.f64 (+.f64 alpha beta) (-.f64 alpha beta))) (neg.f64 (-.f64 alpha beta)))
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(.f64 (pow.f64 (.f64 (+.f64 alpha beta) (-.f64 alpha beta)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 alpha beta)) #s(literal 1 binary64)))

simplify494.0ms (3.3%)

Memory

9.2MiB live, 729.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6 406×	`lower-*.f64`
6 406×	`lower-*.f32`
5 316×	`lower-fma.f64`
5 316×	`lower-fma.f32`
3 846×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1778	18414
1	6032	18125
0	8189	16872

Stop Event

1×	iter limit
1×	node limit

Counts

636 → 612

Calls

Call 1

Inputs
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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1/16
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1/16
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2)))
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(/ (* i (+ alpha i)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* 2 alpha) (* 4 i)) 2))) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* (+ (* 2 alpha) (* 4 i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))))) (+ (* (+ (* 4 alpha) (* 8 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* 2 alpha) (* 4 i)) 2))) 1))) (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* 2 alpha) (* 4 i)) 2))) 1)))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta) (+ (/ (* i (* (+ alpha i) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* 2 alpha) (* 4 i)) 2))) 1))) (pow beta 2)) (/ (* (+ (* 4 alpha) (* 8 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 2))))) (pow beta 2))
(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2)))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 alpha)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* -4 i) (* -2 alpha)) 2))) 1)))) (* (+ (* -8 i) (* -4 alpha)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 alpha)) (+ (* -1 alpha) (* -1 i))))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* -1 (* i (* (+ (* -8 i) (* -4 alpha)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* i (* (+ (* -1 alpha) (* -1 i)) (+ (* (+ (* -4 i) (* -2 alpha)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* -4 i) (* -2 alpha)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (+ (/ (* (+ (* -8 i) (* -4 alpha)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* -4 i) (* -2 alpha)) 2))) 1)))) (* (+ (* -8 i) (* -4 alpha)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 alpha)) (+ (* -1 alpha) (* -1 i)))))))))) beta) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 alpha)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* -4 i) (* -2 alpha)) 2))) 1)) beta)))) (+ (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow alpha 2)) (+ (* 8 (* i (+ alpha i))) (pow (+ (* -4 i) (* -2 alpha)) 2))) 1)))) (* (+ (* -8 i) (* -4 alpha)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* -1 (* i (* (+ (* -8 i) (* -4 alpha)) (+ (* -1 alpha) (* -1 i))))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* -1 (* i (* (+ (* -8 i) (* -4 alpha)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(* alpha beta)
(+ (* alpha beta) (* i (+ alpha beta)))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(* i (+ beta i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(* alpha (+ beta i))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(* -1 (* alpha (+ (* -1 beta) (* -1 i))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(* i (+ alpha i))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(* beta (+ alpha i))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(* -1 (* beta (+ (* -1 alpha) (* -1 i))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(/ (* alpha beta) (- (pow (+ alpha beta) 2) 1))
(+ (* i (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (- (+ (* i (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (- (+ (* i (- (+ (* -1 (* i (+ (* 4 (/ (* (+ alpha beta) (- (/ 1 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (- (pow (+ alpha beta) 2) 1)))))) (/ 1 (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (/ (* alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 4 (/ (* (+ alpha beta) (- (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ alpha (- (pow (+ alpha beta) 2) 1)) (/ beta (- (pow (+ alpha beta) 2) 1)))) (* 4 (/ (* alpha (* beta (+ alpha beta))) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (- (pow (+ alpha beta) 2) 1)))
1/4
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (+ (* -1 (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))))) (* 1/4 (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)))) (pow i 4))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (+ (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))))
1/4
(- (+ 1/4 (* 1/4 (/ (* alpha beta) (pow i 2)))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(- (+ 1/4 (+ (* -1 (/ (- (+ (* -1 (/ (* (pow (+ alpha beta) 2) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))) i)) (* 1/4 (/ (* (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1))) (- (pow (+ alpha beta) 2) 1)) i))) (* -1 (* (+ alpha beta) (- (* 1/4 (* alpha beta)) (* 1/16 (- (pow (+ alpha beta) 2) 1)))))) (pow i 3))) (* 1/4 (/ (* alpha beta) (pow i 2))))) (* 1/16 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))))
(/ (* i (+ beta i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))
(+ (* alpha (- (+ (/ beta (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (/ i (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))) (/ (* i (+ beta i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (/ i (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (+ (/ beta (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (/ i (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))) (/ (* i (+ beta i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (/ i (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (+ (/ beta (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)) (/ i (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))))) (+ (/ (* i (+ beta i)) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (+ (/ beta (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (/ i (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))))) (+ (/ beta (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (/ i (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1) 2)))) (/ (* i (+ beta i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))
(/ (+ beta i) alpha)
(/ (- (+ beta (+ i (/ (* i (+ beta i)) alpha))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* (+ beta i) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha)))) (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ beta (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* (+ beta i) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))))))) (* (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1))) (pow alpha 3))) (/ (* i (+ beta i)) alpha)))) (+ (/ (* (+ beta i) (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* (+ beta i) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* (+ beta i) (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)
(* -1 (/ (+ (* -1 beta) (* -1 i)) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i)))) alpha)))) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* i (+ beta i)) (+ (/ (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i))))) alpha) (/ (* (+ (* -1 beta) (* -1 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) alpha))) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i)))) alpha)))) alpha))
(* -1 (/ (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 beta)) (+ (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i))))) (* (+ (* -1 beta) (* -1 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) alpha)) (/ (* (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i)))) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)) alpha)) (+ (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i))))) (* (+ (* -1 beta) (* -1 i)) (- (+ (* 4 (* i (+ beta i))) (pow beta 2)) 1)))) alpha)) (* i (+ beta i))) (* (+ (* -4 i) (* -2 beta)) (+ (* -1 beta) (* -1 i)))) alpha)))) alpha))
(/ (* i (+ alpha i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))
(+ (* beta (- (+ (/ alpha (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (/ i (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)))) (/ (* i (+ alpha i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (/ i (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))))) (+ (/ alpha (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (/ i (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)))) (/ (* i (+ alpha i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 3)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (/ i (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (+ (/ alpha (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)) (/ i (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)))))) (+ (/ (* i (+ alpha i)) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (+ (/ alpha (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (/ i (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))))) (+ (/ alpha (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (/ i (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1) 2)))) (/ (* i (+ alpha i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))
(/ (+ alpha i) beta)
(/ (- (+ alpha (+ i (/ (* i (+ alpha i)) beta))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta)))) (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ alpha (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))))) (* (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1))) (pow beta 3))) (/ (* i (+ alpha i)) beta)))) (+ (/ (* (+ alpha i) (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* (+ alpha i) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)
(* -1 (/ (+ (* -1 alpha) (* -1 i)) beta))
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i)))) beta)))) beta))
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* i (+ alpha i)) (+ (/ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i))))) beta) (/ (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) beta))) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i)))) beta)))) beta))
(* -1 (/ (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 alpha)) (+ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i))))) (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))) beta)) (/ (* (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i)))) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)) beta)) (+ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i))))) (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 1)))) beta)) (* i (+ alpha i))) (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 alpha) (* -1 i)))) beta)))) beta))
(+ alpha beta)
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i
(* i (+ 1 (+ (/ alpha i) (/ beta i))))
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(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
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(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
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(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
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(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
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(+ (* i (- (* i (- (* -1 (/ (* beta i) (pow alpha 4))) (* -1 (/ beta (pow alpha 3))))) (/ beta (pow alpha 2)))) (/ beta alpha))
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(/ (- (+ beta (* -1 (/ (* (pow alpha 3) beta) (pow i 3)))) (+ (* -1 (/ (* (pow alpha 2) beta) (pow i 2))) (/ (* alpha beta) i))) i)
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(* -1 (/ (+ (* -1 beta) (* -1 (/ (- (* -1 (/ (- (/ (* (pow alpha 3) beta) i) (* (pow alpha 2) beta)) i)) (* alpha beta)) i))) i))
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(+ (* alpha (- (* alpha (- (* -1 (/ (* alpha beta) (pow i 4))) (* -1 (/ beta (pow i 3))))) (/ beta (pow i 2)))) (/ beta i))
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(/ (- (+ beta (* -1 (/ (* beta (pow i 3)) (pow alpha 3)))) (+ (* -1 (/ (* beta (pow i 2)) (pow alpha 2))) (/ (* beta i) alpha))) alpha)
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(+ alpha i)
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i
(* i (+ 1 (/ alpha i)))
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(* -1 (* i (- (* -1 (/ alpha i)) 1)))
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(* alpha (+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (* -1 (/ (* i (* (+ beta (* 2 beta)) (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1))) (* (pow beta 2) (pow (- (pow beta 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1) 2)) (* (pow beta 2) (pow (- (pow beta 2) 1) 3)))) (/ (* i (+ beta (* 2 beta))) (* beta (pow (- (pow beta 2) 1) 2)))) (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1)) (* beta (- (pow beta 2) 1)))) (/ i (* beta (pow (- (pow beta 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1) 2)) (* (pow beta 2) (pow (- (pow beta 2) 1) 3)))) (/ (* i (+ beta (* 2 beta))) (* beta (pow (- (pow beta 2) 1) 2)))))) (/ (* i (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1)) (* beta (pow (- (pow beta 2) 1) 2))))) (/ i (- (pow beta 2) 1))))
(/ (* beta i) (pow alpha 2))
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(/ (- (+ (* -1 (/ (+ (* -1 (* beta (* i (* (+ beta (* 2 beta)) (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1))))) (+ (* -1 (* (+ beta (* 2 beta)) (+ (* -1 (* beta (* i (pow (+ beta (* 2 beta)) 2)))) (* beta (* i (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1)))))) (* (pow beta 2) (* i (- (pow beta 2) 1))))) (pow alpha 3))) (* beta i)) (+ (* -1 (/ (* beta (* i (pow (+ beta (* 2 beta)) 2))) (pow alpha 2))) (+ (/ (* beta (* i (+ beta (* 2 beta)))) alpha) (/ (* beta (* i (- (+ (* 2 (pow beta 2)) (pow beta 2)) 1))) (pow alpha 2))))) (pow alpha 2))
(/ (* beta i) (pow alpha 2))
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(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1))))) (* beta (* i (pow (+ beta (* 2 beta)) 2)))) alpha)) (* beta (* i (+ beta (* 2 beta))))) alpha)) (* beta i)) (pow alpha 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* beta (* i (* (+ beta (* 2 beta)) (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1)))))) (+ (* (+ beta (* 2 beta)) (+ (* beta (* i (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1))))) (* beta (* i (pow (+ beta (* 2 beta)) 2))))) (* (pow beta 2) (* i (- (pow beta 2) 1))))) alpha)) (+ (* beta (* i (+ (* -2 (pow beta 2)) (* -1 (- (pow beta 2) 1))))) (* beta (* i (pow (+ beta (* 2 beta)) 2))))) alpha)) (* beta (* i (+ beta (* 2 beta))))) alpha)) (* beta i)) (pow alpha 2))
(/ (* beta i) (- (pow alpha 2) 1))
(* beta (+ (* -1 (/ (* beta (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))) (* alpha (pow (- (pow alpha 2) 1) 2)))) (/ i (- (pow alpha 2) 1))))
(* beta (+ (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (/ (* i (+ alpha (* 2 alpha))) (* alpha (pow (- (pow alpha 2) 1) 2)))))) (/ (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)) (* alpha (pow (- (pow alpha 2) 1) 2))))) (/ i (- (pow alpha 2) 1))))
(* beta (+ (* beta (- (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (* (+ alpha (* 2 alpha)) (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (/ (* i (+ alpha (* 2 alpha))) (* alpha (pow (- (pow alpha 2) 1) 2)))) (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)) (* alpha (- (pow alpha 2) 1)))) (/ i (* alpha (pow (- (pow alpha 2) 1) 2))))))) (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (/ (* i (+ alpha (* 2 alpha))) (* alpha (pow (- (pow alpha 2) 1) 2)))))) (/ (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)) (* alpha (pow (- (pow alpha 2) 1) 2))))) (/ i (- (pow alpha 2) 1))))
(/ (* alpha i) (pow beta 2))
(/ (+ (* -1 (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (* alpha i)) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)))) (pow beta 2))) (* alpha i)) (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* alpha (* i (* (+ alpha (* 2 alpha)) (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))))) (+ (* -1 (* (+ alpha (* 2 alpha)) (+ (* -1 (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)))))) (* (pow alpha 2) (* i (- (pow alpha 2) 1))))) (pow beta 3))) (* alpha i)) (+ (* -1 (/ (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))) (pow beta 2))) (+ (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta) (/ (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))) (pow beta 2))))) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (+ (* -1 (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (* alpha i)) (pow beta 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) beta)) (* alpha (* i (+ alpha (* 2 alpha))))) beta)) (* alpha i)) (pow beta 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (* (+ alpha (* 2 alpha)) (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1)))))) (+ (* (+ alpha (* 2 alpha)) (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))))) (* (pow alpha 2) (* i (- (pow alpha 2) 1))))) beta)) (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))))) beta)) (* alpha (* i (+ alpha (* 2 alpha))))) beta)) (* alpha i)) (pow beta 2))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/ (* alpha beta) (- (pow beta 2) 1))
(* alpha (+ (* -2 (/ (* alpha (pow beta 2)) (pow (- (pow beta 2) 1) 2))) (/ beta (- (pow beta 2) 1))))
(* alpha (+ (* alpha (- (* -1 (* alpha (+ (* -4 (/ (pow beta 3) (pow (- (pow beta 2) 1) 3))) (/ beta (pow (- (pow beta 2) 1) 2))))) (* 2 (/ (pow beta 2) (pow (- (pow beta 2) 1) 2))))) (/ beta (- (pow beta 2) 1))))
(* alpha (+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (* -2 (/ (* beta (+ (* -4 (/ (pow beta 3) (pow (- (pow beta 2) 1) 3))) (/ beta (pow (- (pow beta 2) 1) 2)))) (- (pow beta 2) 1))) (* -2 (/ (pow beta 2) (pow (- (pow beta 2) 1) 3)))))) (+ (* -4 (/ (pow beta 3) (pow (- (pow beta 2) 1) 3))) (/ beta (pow (- (pow beta 2) 1) 2))))) (* 2 (/ (pow beta 2) (pow (- (pow beta 2) 1) 2))))) (/ beta (- (pow beta 2) 1))))
(/ beta alpha)
(/ (+ beta (* -2 (/ (pow beta 2) alpha))) alpha)
(/ (- (+ beta (* -1 (/ (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))) (pow alpha 2)))) (* 2 (/ (pow beta 2) alpha))) alpha)
(/ (- (+ beta (* -1 (/ (+ (* -2 (* beta (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))))) (* -2 (* (pow beta 2) (- (pow beta 2) 1)))) (pow alpha 3)))) (+ (* -4 (/ (pow beta 3) (pow alpha 2))) (+ (* 2 (/ (pow beta 2) alpha)) (/ (* beta (- (pow beta 2) 1)) (pow alpha 2))))) alpha)
(/ beta alpha)
(* -1 (/ (+ (* -1 beta) (* 2 (/ (pow beta 2) alpha))) alpha))
(* -1 (/ (+ (* -1 beta) (* -1 (/ (+ (* -2 (pow beta 2)) (* -1 (/ (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))) alpha))) alpha))) alpha))
(* -1 (/ (+ (* -1 beta) (* -1 (/ (+ (* -2 (pow beta 2)) (* -1 (/ (+ (* -4 (pow beta 3)) (+ (* -1 (/ (+ (* 2 (* beta (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))))) (* 2 (* (pow beta 2) (- (pow beta 2) 1)))) alpha)) (* beta (- (pow beta 2) 1)))) alpha))) alpha))) alpha))
(/ (* alpha beta) (- (pow alpha 2) 1))
(* beta (+ (* -2 (/ (* (pow alpha 2) beta) (pow (- (pow alpha 2) 1) 2))) (/ alpha (- (pow alpha 2) 1))))
(* beta (+ (* beta (- (* -1 (* beta (+ (* -4 (/ (pow alpha 3) (pow (- (pow alpha 2) 1) 3))) (/ alpha (pow (- (pow alpha 2) 1) 2))))) (* 2 (/ (pow alpha 2) (pow (- (pow alpha 2) 1) 2))))) (/ alpha (- (pow alpha 2) 1))))
(* beta (+ (* beta (- (* beta (- (* -1 (* beta (+ (* -2 (/ (* alpha (+ (* -4 (/ (pow alpha 3) (pow (- (pow alpha 2) 1) 3))) (/ alpha (pow (- (pow alpha 2) 1) 2)))) (- (pow alpha 2) 1))) (* -2 (/ (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))))) (+ (* -4 (/ (pow alpha 3) (pow (- (pow alpha 2) 1) 3))) (/ alpha (pow (- (pow alpha 2) 1) 2))))) (* 2 (/ (pow alpha 2) (pow (- (pow alpha 2) 1) 2))))) (/ alpha (- (pow alpha 2) 1))))
(/ alpha beta)
(/ (+ alpha (* -2 (/ (pow alpha 2) beta))) beta)
(/ (- (+ alpha (* -1 (/ (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))) (pow beta 2)))) (* 2 (/ (pow alpha 2) beta))) beta)
(/ (- (+ alpha (* -1 (/ (+ (* -2 (* alpha (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))))) (* -2 (* (pow alpha 2) (- (pow alpha 2) 1)))) (pow beta 3)))) (+ (* -4 (/ (pow alpha 3) (pow beta 2))) (+ (* 2 (/ (pow alpha 2) beta)) (/ (* alpha (- (pow alpha 2) 1)) (pow beta 2))))) beta)
(/ alpha beta)
(* -1 (/ (+ (* -1 alpha) (* 2 (/ (pow alpha 2) beta))) beta))
(* -1 (/ (+ (* -1 alpha) (* -1 (/ (+ (* -2 (pow alpha 2)) (* -1 (/ (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))) beta))) beta))) beta))
(* -1 (/ (+ (* -1 alpha) (* -1 (/ (+ (* -2 (pow alpha 2)) (* -1 (/ (+ (* -4 (pow alpha 3)) (+ (* -1 (/ (+ (* 2 (* alpha (+ (* -4 (pow alpha 3)) (* alpha (- (pow alpha 2) 1))))) (* 2 (* (pow alpha 2) (- (pow alpha 2) 1)))) beta)) (* alpha (- (pow alpha 2) 1)))) beta))) beta))) beta))
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(* alpha beta)
(- (pow beta 2) 1)
(- (+ (* 2 (* alpha beta)) (pow beta 2)) 1)
(- (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2)) 1)
(- (+ (* alpha (+ alpha (* 2 beta))) (pow beta 2)) 1)
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (- (pow beta 2) 1) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (- (pow beta 2) 1) alpha))) alpha))))
(- (pow alpha 2) 1)
(- (+ (* 2 (* alpha beta)) (pow alpha 2)) 1)
(- (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2)) 1)
(- (+ (* beta (+ beta (* 2 alpha))) (pow alpha 2)) 1)
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))) (/ 1 (pow beta 2))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))) (/ 1 (pow beta 2))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (- (pow alpha 2) 1) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (- (pow alpha 2) 1) beta))) beta))))
(/ i (+ alpha beta))
(* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta))))
(* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))
(* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))
1/4
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))
(- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))
(- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))
1/4
(+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))
(+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))))
(+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))
(/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2)))
(+ (* alpha (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))))) (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))
(+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 3)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2))))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ i (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2))))) (+ (/ (* i (+ beta i)) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (+ (* 4 (* i (+ beta i))) (pow beta 2)))))) (/ i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ (* 4 (* i (+ beta i))) (pow beta 2)) 2)))) (/ (* i (+ beta i)) (+ (* 4 (* i (+ beta i))) (pow beta 2))))
(/ i alpha)
(/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ i (+ (* -1 (/ (+ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)
(/ i alpha)
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta))))) alpha))) alpha))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (* i (+ (* 4 (* i (+ beta i))) (pow beta 2))) alpha)) (+ (* i (+ beta i)) (/ (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))) alpha))) (* -1 (* i (+ (* -4 i) (* -2 beta))))) alpha))) alpha))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 beta)) (+ (* -1 (* i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))))) alpha)) (/ (* (+ (* 4 (* i (+ beta i))) (pow beta 2)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))) alpha)) (+ (* -1 (* i (+ (* 4 (* i (+ beta i))) (pow beta 2)))) (* (+ (* -4 i) (* -2 beta)) (- (* i (+ beta i)) (* -1 (* i (+ (* -4 i) (* -2 beta)))))))) alpha)) (* i (+ beta i))) (* -1 (* i (+ (* -4 i) (* -2 beta))))) alpha))) alpha))
(/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))
(+ (* beta (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))
(+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))))) (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))
(+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 3)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ i (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2))))) (+ (/ (* i (+ alpha i)) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))))) (/ i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) 2)))) (/ (* i (+ alpha i)) (+ (* 4 (* i (+ alpha i))) (pow alpha 2))))
(/ i beta)
(/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ i (+ (* -1 (/ (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)
(/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)
(/ i beta)
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2))) beta)) (+ (* i (+ alpha i)) (/ (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))
(* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -4 i) (* -2 alpha)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (/ (* (+ (* 4 (* i (+ alpha i))) (pow alpha 2)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))) beta)) (+ (* -1 (* i (+ (* 4 (* i (+ alpha i))) (pow alpha 2)))) (* (+ (* -4 i) (* -2 alpha)) (- (* i (+ alpha i)) (* -1 (* i (+ (* -4 i) (* -2 alpha)))))))) beta)) (* i (+ alpha i))) (* -1 (* i (+ (* -4 i) (* -2 alpha))))) beta))) beta))
(pow beta 2)
(+ (* 2 (* alpha beta)) (pow beta 2))
(+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))
(+ (* alpha (+ alpha (* 2 beta))) (pow beta 2))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))))
(pow alpha 2)
(* (pow alpha 2) (+ 1 (* 2 (/ beta alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) alpha))) alpha))))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 beta) (* -1 (/ (pow beta 2) alpha))) alpha))))
(pow alpha 2)
(+ (* 2 (* alpha beta)) (pow alpha 2))
(+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))
(+ (* beta (+ beta (* 2 alpha))) (pow alpha 2))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (/ (pow alpha 2) (pow beta 2)))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 2 (/ alpha beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))
beta
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
alpha
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
alpha
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
alpha
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
beta
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
beta
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))

Outputs
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(.f64 i (fma.f64 i (-.f64 (fma.f64 alpha (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha beta) (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(* beta (+ (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (pow (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1) 2)) (* (pow alpha 2) (pow (- (pow alpha 2) 1) 3)))) (/ (* i (+ alpha (* 2 alpha))) (* alpha (pow (- (pow alpha 2) 1) 2)))))) (/ (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)) (* alpha (pow (- (pow alpha 2) 1) 2))))) (/ i (- (pow alpha 2) 1))))
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(/ (* alpha i) (pow beta 2))
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(/ (+ (* -1 (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (* alpha i)) (pow beta 2))
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(/ (- (+ (* -1 (/ (+ (* -1 (* alpha (* i (* (+ alpha (* 2 alpha)) (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))))) (+ (* -1 (* (+ alpha (* 2 alpha)) (+ (* -1 (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1)))))) (* (pow alpha 2) (* i (- (pow alpha 2) 1))))) (pow beta 3))) (* alpha i)) (+ (* -1 (/ (* alpha (* i (pow (+ alpha (* 2 alpha)) 2))) (pow beta 2))) (+ (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta) (/ (* alpha (* i (- (+ (* 2 (pow alpha 2)) (pow alpha 2)) 1))) (pow beta 2))))) (pow beta 2))
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(/ (* alpha i) (pow beta 2))
(/.f64 (.f64 alpha i) (.f64 beta beta))
(/ (+ (* -1 (/ (* alpha (* i (+ alpha (* 2 alpha)))) beta)) (* alpha i)) (pow beta 2))
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(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* alpha (* i (+ (* -2 (pow alpha 2)) (* -1 (- (pow alpha 2) 1))))) (* alpha (* i (pow (+ alpha (* 2 alpha)) 2)))) beta)) (* alpha (* i (+ alpha (* 2 alpha))))) beta)) (* alpha i)) (pow beta 2))
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(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
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(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
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(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
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(/ (* alpha beta) (- (pow beta 2) 1))
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(/ (+ beta (* -2 (/ (pow beta 2) alpha))) alpha)
(/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 beta beta) alpha) beta) alpha)
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(/ beta alpha)
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(* -1 (/ (+ (* -1 beta) (* 2 (/ (pow beta 2) alpha))) alpha))
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(* -1 (/ (+ (* -1 beta) (* -1 (/ (+ (* -2 (pow beta 2)) (* -1 (/ (+ (* -4 (pow beta 3)) (+ (* -1 (/ (+ (* 2 (* beta (+ (* -4 (pow beta 3)) (* beta (- (pow beta 2) 1))))) (* 2 (* (pow beta 2) (- (pow beta 2) 1)))) alpha)) (* beta (- (pow beta 2) 1)))) alpha))) alpha))) alpha))
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(/ (* alpha beta) (- (pow alpha 2) 1))
(*.f64 alpha (/.f64 beta (fma.f64 alpha alpha #s(literal -1 binary64))))
(* beta (+ (* -2 (/ (* (pow alpha 2) beta) (pow (- (pow alpha 2) 1) 2))) (/ alpha (- (pow alpha 2) 1))))
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(* beta (+ (* beta (- (* -1 (* beta (+ (* -4 (/ (pow alpha 3) (pow (- (pow alpha 2) 1) 3))) (/ alpha (pow (- (pow alpha 2) 1) 2))))) (* 2 (/ (pow alpha 2) (pow (- (pow alpha 2) 1) 2))))) (/ alpha (- (pow alpha 2) 1))))
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(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 alpha #s(literal -2 binary64)) (/.f64 (.f64 alpha alpha) beta)) beta)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 alpha) (* -1 (/ (pow alpha 2) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 alpha #s(literal -2 binary64)) (/.f64 (.f64 alpha alpha) beta)) beta)))
beta
(+ alpha beta)
(+.f64 alpha beta)
(+ alpha beta)
(+.f64 alpha beta)
(+ alpha beta)
(+.f64 alpha beta)
alpha
(* alpha (+ 1 (/ beta alpha)))
(*.f64 alpha (+.f64 #s(literal 1 binary64) (/.f64 beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
(*.f64 alpha (+.f64 #s(literal 1 binary64) (/.f64 beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
(*.f64 alpha (+.f64 #s(literal 1 binary64) (/.f64 beta alpha)))
alpha
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(*.f64 (neg.f64 alpha) (+.f64 (/.f64 (neg.f64 beta) alpha) #s(literal -1 binary64)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(*.f64 (neg.f64 alpha) (+.f64 (/.f64 (neg.f64 beta) alpha) #s(literal -1 binary64)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(*.f64 (neg.f64 alpha) (+.f64 (/.f64 (neg.f64 beta) alpha) #s(literal -1 binary64)))
alpha
(+ alpha beta)
(+.f64 alpha beta)
(+ alpha beta)
(+.f64 alpha beta)
(+ alpha beta)
(+.f64 alpha beta)
beta
(* beta (+ 1 (/ alpha beta)))
(*.f64 beta (+.f64 #s(literal 1 binary64) (/.f64 alpha beta)))
(* beta (+ 1 (/ alpha beta)))
(*.f64 beta (+.f64 #s(literal 1 binary64) (/.f64 alpha beta)))
(* beta (+ 1 (/ alpha beta)))
(*.f64 beta (+.f64 #s(literal 1 binary64) (/.f64 alpha beta)))
beta
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 alpha beta)) #s(literal -1 binary64)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 alpha beta)) #s(literal -1 binary64)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(*.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 alpha beta)) #s(literal -1 binary64)))

eval682.0ms (4.6%)

Memory: -68.2MiB live, 781.9MiB allocated
Compiler: Compiled 112 673 to 6 469 computations (94.3% saved)

prune316.0ms (2.1%)

Memory

37.7MiB live, 831.1MiB allocated

Pruning

32 alts after pruning (27 fresh and 5 done)

	Pruned	Kept	Total
New	2 437	7	2 444
Fresh	3	20	23
Picked	2	3	5
Done	0	2	2
Total	2 442	32	2 474

Accuracy

99.4%

Counts

2 474 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	13.8%	(/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 i i)) (.f64 beta beta))
	16.5%	(/.f64 (fma.f64 i i (.f64 i alpha)) (.f64 beta beta))
	23.8%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
✓	12.0%	(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
✓	33.5%	(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
	30.4%	(/.f64 (/.f64 i beta) (/.f64 beta i))
	33.3%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	12.6%	(/.f64 (*.f64 (/.f64 alpha beta) i) beta)
	13.4%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha i)) (.f64 alpha alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	13.4%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha i)) (.f64 alpha alpha)) (fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 alpha i)) (fma.f64 alpha alpha #s(literal -1 binary64)))))
	13.4%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	8.8%	(/.f64 (.f64 i (.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	15.3%	(/.f64 (.f64 i i) (.f64 beta beta))
	5.2%	(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
	12.2%	(/.f64 (*.f64 alpha i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
	8.9%	(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
	32.4%	(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 i (+.f64 beta i))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	33.0%	(/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (/.f64 (+.f64 i alpha) beta))))
	39.3%	(.f64 (/.f64 (fma.f64 i i (fma.f64 i (+.f64 alpha beta) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
	38.2%	(.f64 (/.f64 (.f64 i (+.f64 i beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
	38.2%	(.f64 (/.f64 (.f64 i (+.f64 beta i)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
	5.5%	(.f64 (/.f64 (.f64 beta (+.f64 alpha i)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
✓	9.9%	(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
	26.2%	(*.f64 (/.f64 (neg.f64 i) #s(literal -1 binary64)) (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
	17.3%	(.f64 (/.f64 i (.f64 beta beta)) (+.f64 i alpha))
	32.3%	(.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha)) beta))
	30.3%	(*.f64 (/.f64 i beta) (/.f64 i beta))
	5.1%	(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
	8.8%	(.f64 (.f64 i (.f64 alpha beta)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
	26.2%	(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (+.f64 i alpha) beta)))
✓	10.8%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	68.2%	#s(literal 1/16 binary64)

Compiler

Compiled 2 313 to 562 computations (75.7% saved)

regimes84.0ms (0.6%)

Memory

-13.1MiB live, 224.4MiB allocated

Counts

70 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
(.f64 (/.f64 i (.f64 beta beta)) (+.f64 i alpha))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))
(*.f64 (/.f64 i beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 alpha beta) i) beta)
(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
(/.f64 (fma.f64 i i (.f64 i alpha)) (.f64 beta beta))
(/.f64 (*.f64 alpha i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
(/.f64 (.f64 (.f64 alpha beta) #s(literal 1/4 binary64)) (*.f64 i (+.f64 alpha beta)))
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
(/.f64 (/.f64 i beta) (/.f64 beta i))
(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (+.f64 i alpha) beta)))
(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (+.f64 i alpha) beta)))
(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (*.f64 beta beta))
(/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (/.f64 (+.f64 i alpha) beta))))
(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 alpha (.f64 i beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 i (.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 i (+.f64 beta i))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 i) #s(literal -1 binary64)) (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
(.f64 (.f64 i (.f64 alpha beta)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 beta (+.f64 alpha i)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 i i)) (.f64 beta beta))
(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(.f64 #s(literal 1/4 binary64) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (/.f64 (.f64 #s(literal -3 binary64) (.f64 alpha alpha)) beta))) (.f64 beta beta))
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha)) beta))
(/.f64 (/.f64 (.f64 i (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha))) beta) beta)
(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha i)) (.f64 alpha alpha)) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha i)) (.f64 alpha alpha)) (fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 alpha i)) (fma.f64 alpha alpha #s(literal -1 binary64)))))
(/.f64 (.f64 (.f64 i i) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))) i))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 i (+.f64 i beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
(.f64 (/.f64 (.f64 i (+.f64 beta i)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))))
(.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)))))
(.f64 (/.f64 i (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(.f64 (/.f64 (fma.f64 i i (fma.f64 i (+.f64 alpha beta) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(.f64 (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))
(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))))
(.f64 (/.f64 (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))) #s(literal -1 binary64))) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal 1 binary64)))
(/.f64 (/.f64 (.f64 (.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (.f64 alpha alpha))))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(.f64 (/.f64 i beta) (pow.f64 (/.f64 beta (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha))) #s(literal -1 binary64)))

Outputs

#s(literal 1/16 binary64)

(*.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (*.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha)) beta))

Calls

4 calls:

22.0ms	beta
21.0ms	alpha
20.0ms	i
17.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
73.6%	2	`alpha`
85.2%	2	`beta`
82.0%	2	`i`
76.2%	2	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`

Compiler

Compiled 68 to 26 computations (61.8% saved)

regimes40.0ms (0.3%)

Memory

-8.6MiB live, 30.4MiB allocated

Counts

44 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
(.f64 (/.f64 i (.f64 beta beta)) (+.f64 i alpha))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))
(*.f64 (/.f64 i beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 alpha beta) i) beta)
(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
(/.f64 (fma.f64 i i (.f64 i alpha)) (.f64 beta beta))
(/.f64 (*.f64 alpha i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
(/.f64 (.f64 (.f64 alpha beta) #s(literal 1/4 binary64)) (*.f64 i (+.f64 alpha beta)))
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
(/.f64 (/.f64 i beta) (/.f64 beta i))
(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (+.f64 i alpha) beta)))
(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (+.f64 i alpha) beta)))
(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (*.f64 beta beta))
(/.f64 #s(literal 1 binary64) (/.f64 beta (*.f64 i (/.f64 (+.f64 i alpha) beta))))
(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 alpha (.f64 i beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 i (.f64 alpha beta)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 i (+.f64 beta i))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 i) #s(literal -1 binary64)) (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
(.f64 (.f64 i (.f64 alpha beta)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
(.f64 (/.f64 (.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 beta (+.f64 alpha i)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 i i)) (.f64 beta beta))
(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(.f64 #s(literal 1/4 binary64) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)))))
(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (/.f64 (.f64 #s(literal -3 binary64) (.f64 alpha alpha)) beta))) (.f64 beta beta))
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 i #s(literal 2 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(/.f64 (/.f64 (.f64 alpha (.f64 beta i)) (+.f64 alpha beta)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Outputs
#s(literal 1/16 binary64)
(/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha)))

Calls

1 calls:

38.0ms

beta

Results

Accuracy	Segments	Branch
85.0%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes9.0ms (0.1%)

Memory

17.3MiB live, 17.3MiB allocated

Counts

25 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
(.f64 (/.f64 i (.f64 beta beta)) (+.f64 i alpha))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))
(*.f64 (/.f64 i beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 alpha beta) i) beta)
(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
(/.f64 (fma.f64 i i (.f64 i alpha)) (.f64 beta beta))
(/.f64 (*.f64 alpha i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
(/.f64 (.f64 (.f64 alpha beta) #s(literal 1/4 binary64)) (*.f64 i (+.f64 alpha beta)))
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
(/.f64 (/.f64 i beta) (/.f64 beta i))
(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (+.f64 i alpha) beta)))
(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (+.f64 i alpha) beta)))

Outputs
#s(literal 1/16 binary64)
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))

Calls

1 calls:

8.0ms

beta

Results

Accuracy	Segments	Branch
85.0%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes32.0ms (0.2%)

Memory

-44.2MiB live, 14.0MiB allocated

Counts

19 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
(.f64 (/.f64 i (.f64 beta beta)) (+.f64 i alpha))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))
(*.f64 (/.f64 i beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 alpha beta) i) beta)
(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
(/.f64 (/.f64 (*.f64 i alpha) beta) beta)
(/.f64 (fma.f64 i i (.f64 i alpha)) (.f64 beta beta))
(/.f64 (*.f64 alpha i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
(/.f64 (.f64 (.f64 alpha beta) #s(literal 1/4 binary64)) (*.f64 i (+.f64 alpha beta)))

Outputs
#s(literal 1/16 binary64)
(*.f64 (/.f64 i beta) (/.f64 i beta))

Calls

1 calls:

31.0ms

beta

Results

Accuracy	Segments	Branch
83.1%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes12.0ms (0.1%)

Memory

27.9MiB live, 27.9MiB allocated

Counts

11 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
(.f64 (/.f64 i (.f64 beta beta)) (+.f64 i alpha))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))

Outputs
#s(literal 1/16 binary64)
(*.f64 (/.f64 i beta) (/.f64 alpha beta))

Calls

3 calls:

4.0ms

beta

4.0ms

3.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
71.5%	2	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`
72.4%	3	`i`
74.7%	2	`beta`

Compiler

Compiled 64 to 23 computations (64.1% saved)

regimes5.0ms (0%)

Memory

-27.8MiB live, 11.1MiB allocated

Counts

10 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))
(.f64 (/.f64 i (.f64 beta beta)) (+.f64 i alpha))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))

Outputs
#s(literal 1/16 binary64)
(.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta)))

Calls

1 calls:

5.0ms

beta

Results

Accuracy	Segments	Branch
73.9%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes3.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i i) (.f64 beta beta))

Outputs
#s(literal 1/16 binary64)
(.f64 alpha (/.f64 i (.f64 beta beta)))

Calls

1 calls:

3.0ms

beta

Results

Accuracy	Segments	Branch
73.9%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes5.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(*.f64 (/.f64 #s(literal 1/4 binary64) beta) (+.f64 i alpha))
(/.f64 (*.f64 (+.f64 alpha i) #s(literal 1/4 binary64)) beta)

Outputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta)

Calls

2 calls:

2.0ms	alpha
2.0ms	beta

Results

Accuracy	Segments	Branch
68.2%	1	`alpha`
71.8%	2	`beta`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes4.0ms (0%)

Memory

8.6MiB live, 8.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/16 binary64)

Outputs
#s(literal 1/16 binary64)

Calls

3 calls:

1.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

1.0ms

beta

Results

Accuracy	Segments	Branch
68.2%	1	`i`
68.2%	1	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`
68.2%	1	`beta`

Compiler

Compiled 64 to 23 computations (64.1% saved)

bsearch23.0ms (0.2%)

Memory

-9.6MiB live, 28.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	1.0241298304357072e+141	2.741336370554807e+144

Samples

15.0ms

128×

valid

Compiler

Compiled 339 to 199 computations (41.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 5.0ms (41.2% of total)

ival-mult: 3.0ms (24.7% of total)

ival-add: 2.0ms (16.5% of total)

ival-div: 1.0ms (8.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch16.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	5.993944775294195e+103	2.004014758466534e+105

Samples

9.0ms

112×

valid

Compiler

Compiled 185 to 114 computations (38.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 3.0ms (44.4% of total)

ival-add: 2.0ms (29.6% of total)

ival-sub: 1.0ms (14.8% of total)

ival-div: 1.0ms (14.8% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	5.993944775294195e+103	2.004014758466534e+105

Compiler

Compiled 185 to 114 computations (38.4% saved)

bsearch17.0ms (0.1%)

Memory

-27.6MiB live, 10.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.0241298304357072e+141	2.741336370554807e+144

Samples

13.0ms

64×

valid

Compiler

Compiled 187 to 111 computations (40.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-add: 9.0ms (76.2% of total)

ival-mult: 2.0ms (16.9% of total)

ival-div: 1.0ms (8.5% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch11.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	7.126875958133584e+244	1.4835474422081003e+245

Samples

7.0ms

80×

valid

Compiler

Compiled 139 to 83 computations (40.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (40.7% of total)

ival-div: 1.0ms (20.4% of total)

ival-add: 1.0ms (20.4% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	7.126875958133584e+244	1.4835474422081003e+245

Compiler

Compiled 149 to 88 computations (40.9% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	7.126875958133584e+244	1.4835474422081003e+245

Compiler

Compiled 139 to 83 computations (40.3% saved)

bsearch30.0ms (0.2%)

Memory

-22.5MiB live, 18.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
28.0ms	2.1314037445021358e+245	9.659836959061829e+249

Samples

23.0ms

128×

valid

Compiler

Compiled 171 to 119 computations (30.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sub: 12.0ms (60.7% of total)

ival-mult: 3.0ms (15.2% of total)

ival-add: 2.0ms (10.1% of total)

ival-div: 1.0ms (5.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	120
1	59	120
2	64	120
3	66	120
4	67	120

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 beta #s(literal 32000000000000000543239015623646710532513445554339415668179233123711927810150941086664394430600163612141070535396979175566700865076828561211392 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha)) beta)))
(if (<=.f64 beta #s(literal 839999999999999937951792811564431542532474544109693756509967650202970799951961512683022744286599403536384 binary64)) #s(literal 1/16 binary64) (/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha))))
(if (<=.f64 beta #s(literal 839999999999999937951792811564431542532474544109693756509967650202970799951961512683022744286599403536384 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 40999999999999998157570068613242727894428069270656583383780659856916025453704519413570517016770891659329178534970685753944581307289990705709056 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 101999999999999997001442069695955482642568148700562229176260251178583536419487980908091559857835435061107738342577721238867472906707137018972732922561558182733697896925585927432185838349248083245871485535732440027050682150220713528243639428317184 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 alpha beta)))
(if (<=.f64 beta #s(literal 101999999999999997001442069695955482642568148700562229176260251178583536419487980908091559857835435061107738342577721238867472906707137018972732922561558182733697896925585927432185838349248083245871485535732440027050682150220713528243639428317184 binary64)) #s(literal 1/16 binary64) (.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta))))
(if (<=.f64 beta #s(literal 101999999999999997001442069695955482642568148700562229176260251178583536419487980908091559857835435061107738342577721238867472906707137018972732922561558182733697896925585927432185838349248083245871485535732440027050682150220713528243639428317184 binary64)) #s(literal 1/16 binary64) (.f64 alpha (/.f64 i (.f64 beta beta))))
(if (<=.f64 beta #s(literal 379999999999999995012337857663000865769106016608875589804792548054115118771032580325078355635471327403336217223697703315247846080962848600165126504853288783951440258011789119863141691972397507482612125406031327652376006269913593831203941344346112 binary64)) #s(literal 1/16 binary64) (/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta))
#s(literal 1/16 binary64)

Outputs
(if (<=.f64 beta #s(literal 32000000000000000543239015623646710532513445554339415668179233123711927810150941086664394430600163612141070535396979175566700865076828561211392 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta) (+.f64 i alpha)) beta)))
(if (<=.f64 beta #s(literal 839999999999999937951792811564431542532474544109693756509967650202970799951961512683022744286599403536384 binary64)) #s(literal 1/16 binary64) (/.f64 (/.f64 i beta) (/.f64 beta (+.f64 i alpha))))
(if (<=.f64 beta #s(literal 839999999999999937951792811564431542532474544109693756509967650202970799951961512683022744286599403536384 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 839999999999999937951792811564431542532474544109693756509967650202970799951961512683022744286599403536384 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 (+.f64 i alpha) beta)))
(if (<=.f64 beta #s(literal 40999999999999998157570068613242727894428069270656583383780659856916025453704519413570517016770891659329178534970685753944581307289990705709056 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 101999999999999997001442069695955482642568148700562229176260251178583536419487980908091559857835435061107738342577721238867472906707137018972732922561558182733697896925585927432185838349248083245871485535732440027050682150220713528243639428317184 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 alpha beta)))
(if (<=.f64 beta #s(literal 101999999999999997001442069695955482642568148700562229176260251178583536419487980908091559857835435061107738342577721238867472906707137018972732922561558182733697896925585927432185838349248083245871485535732440027050682150220713528243639428317184 binary64)) #s(literal 1/16 binary64) (.f64 (+.f64 i alpha) (/.f64 i (.f64 beta beta))))
(if (<=.f64 beta #s(literal 101999999999999997001442069695955482642568148700562229176260251178583536419487980908091559857835435061107738342577721238867472906707137018972732922561558182733697896925585927432185838349248083245871485535732440027050682150220713528243639428317184 binary64)) #s(literal 1/16 binary64) (.f64 alpha (/.f64 i (.f64 beta beta))))
(if (<=.f64 beta #s(literal 379999999999999995012337857663000865769106016608875589804792548054115118771032580325078355635471327403336217223697703315247846080962848600165126504853288783951440258011789119863141691972397507482612125406031327652376006269913593831203941344346112 binary64)) #s(literal 1/16 binary64) (/.f64 (*.f64 alpha #s(literal 1/4 binary64)) beta))
#s(literal 1/16 binary64)

soundness1.4s (9.5%)

Memory

43.2MiB live, 947.6MiB allocated

Rules

9 164×	`lower-fma.f64`
9 164×	`lower-fma.f32`
7 648×	`lower-*.f64`
7 648×	`lower-*.f32`
6 888×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1778	18414
1	6032	18125
0	8189	16872
0	17	157
0	29	127
1	146	127
2	1503	127
0	8201	117
0	1089	12630
1	3841	11840
0	8260	10972
0	42	330
0	78	278
1	399	266
2	3879	266
0	10692	260
0	2159	22542
1	7405	22536
0	8794	20765
0	1836	21137
1	6244	20803
0	8239	19433
0	33	251
0	62	226
1	271	226
2	2609	226
0	9326	226

Stop Event

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

Compiler

Compiled 382 to 215 computations (43.7% saved)

preprocess117.0ms (0.8%)

Memory: -32.6MiB live, 230.4MiB allocated
Compiler: Compiled 426 to 172 computations (59.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze43.0ms (0.3%)

sample2.1s (14.5%)

preprocess563.0ms (3.8%)

explain440.0ms (3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify711.0ms (4.8%)

localize77.0ms (0.5%)

series88.0ms (0.6%)

rewrite511.0ms (3.5%)

simplify644.0ms (4.4%)

eval212.0ms (1.4%)

prune250.0ms (1.7%)

simplify322.0ms (2.2%)

localize163.0ms (1.1%)

series134.0ms (0.9%)

rewrite513.0ms (3.5%)

simplify558.0ms (3.8%)

eval555.0ms (3.8%)

prune276.0ms (1.9%)

simplify388.0ms (2.6%)

localize161.0ms (1.1%)

series119.0ms (0.8%)

rewrite382.0ms (2.6%)

simplify553.0ms (3.7%)

eval381.0ms (2.6%)

prune338.0ms (2.3%)

simplify430.0ms (2.9%)

localize103.0ms (0.7%)

series78.0ms (0.5%)

rewrite325.0ms (2.2%)

simplify494.0ms (3.3%)

eval682.0ms (4.6%)

prune316.0ms (2.1%)

regimes84.0ms (0.6%)

regimes40.0ms (0.3%)

regimes9.0ms (0.1%)

regimes32.0ms (0.2%)

regimes12.0ms (0.1%)

regimes5.0ms (0%)

regimes3.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

bsearch23.0ms (0.2%)

bsearch16.0ms (0.1%)

bsearch1.0ms (0%)

bsearch17.0ms (0.1%)

bsearch11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch30.0ms (0.2%)

simplify8.0ms (0.1%)

soundness1.4s (9.5%)

preprocess117.0ms (0.8%)

end0.0ms (0%)

Profiling