Metrics for Octave 3.8, jcobi/4

analyze16.0ms (0.1%)

Memory

-11.8MiB live, 25.9MiB 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)

sample2.4s (15.1%)

Memory

39.3MiB live, 2 200.3MiB allocated

Samples

2.0s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-mult: 606.0ms (37.5% of total)

ival-add: 597.0ms (36.9% of total)

ival-div: 178.0ms (11% of total)

ival->: 167.0ms (10.3% of total)

ival-sub: 36.0ms (2.2% of total)

ival-and: 15.0ms (0.9% of total)

exact: 14.0ms (0.9% of total)

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

Bogosity

preprocess881.0ms (5.5%)

Memory

-6.2MiB live, 807.2MiB allocated

Algorithm

2×	egg-herbie

Rules

12 470×	`accelerator-lowering-fma.f32`
12 470×	`accelerator-lowering-fma.f64`
3 894×	`+-lowering-+.f64`
3 894×	`+-lowering-+.f32`
3 870×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	561
1	431	535
2	2133	531
0	17	53
1	64	53
2	312	53
3	1998	53
4	6932	53
0	8038	47

Stop Event

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

Calls

Call 1

Inputs

(/ (/ (* (* 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))

Outputs

(/ (/ (* (* 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))

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

Call 2

Inputs
(/ (/ (* (* 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))
(/ (/ (* (* i (+ (+ (neg alpha) beta) i)) (+ (* beta (neg alpha)) (* i (+ (+ (neg alpha) beta) i)))) (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i)))) (- (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i))) 1))
(/ (/ (* (* i (+ (+ alpha (neg beta)) i)) (+ (* (neg beta) alpha) (* i (+ (+ alpha (neg beta)) i)))) (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i)))) (- (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i))) 1))
(/ (/ (* (* (neg i) (+ (+ alpha beta) (neg i))) (+ (* beta alpha) (* (neg i) (+ (+ alpha beta) (neg i))))) (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i))))) (- (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i)))) 1))
(neg (/ (/ (* (* i (+ (+ (neg alpha) beta) i)) (+ (* beta (neg alpha)) (* i (+ (+ (neg alpha) beta) i)))) (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i)))) (- (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i))) 1)))
(neg (/ (/ (* (* i (+ (+ alpha (neg beta)) i)) (+ (* (neg beta) alpha) (* i (+ (+ alpha (neg beta)) i)))) (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i)))) (- (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i))) 1)))
(neg (/ (/ (* (* (neg i) (+ (+ alpha beta) (neg i))) (+ (* beta alpha) (* (neg i) (+ (+ alpha beta) (neg i))))) (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i))))) (- (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i)))) 1)))
(/ (/ (* (* i (+ (+ beta alpha) i)) (+ (* alpha beta) (* i (+ (+ beta alpha) i)))) (* (+ (+ beta alpha) (* 2 i)) (+ (+ beta alpha) (* 2 i)))) (- (* (+ (+ beta alpha) (* 2 i)) (+ (+ beta alpha) (* 2 i))) 1))
(/ (/ (* (* alpha (+ (+ i beta) alpha)) (+ (* beta i) (* alpha (+ (+ i beta) alpha)))) (* (+ (+ i beta) (* 2 alpha)) (+ (+ i beta) (* 2 alpha)))) (- (* (+ (+ i beta) (* 2 alpha)) (+ (+ i beta) (* 2 alpha))) 1))
(/ (/ (* (* beta (+ (+ alpha i) beta)) (+ (* i alpha) (* beta (+ (+ alpha i) beta)))) (* (+ (+ alpha i) (* 2 beta)) (+ (+ alpha i) (* 2 beta)))) (- (* (+ (+ alpha i) (* 2 beta)) (+ (+ alpha i) (* 2 beta))) 1))

Outputs
(/ (/ (* (* 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))
(* (* (+ i (+ alpha beta)) (/ i (+ alpha (+ beta (* i 2))))) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (* i 2)))) (+ (* (+ alpha (+ beta (* i 2))) (+ alpha (+ beta (* i 2)))) -1)))
(/ (/ (* (* i (+ (+ (neg alpha) beta) i)) (+ (* beta (neg alpha)) (* i (+ (+ (neg alpha) beta) i)))) (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i)))) (- (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i))) 1))
(* (* i (+ i (- beta alpha))) (/ (/ (- (* i (+ i (- beta alpha))) (* alpha beta)) (* (+ beta (- (* i 2) alpha)) (+ beta (- (* i 2) alpha)))) (+ (* (+ beta (- (* i 2) alpha)) (+ beta (- (* i 2) alpha))) -1)))
(/ (/ (* (* i (+ (+ alpha (neg beta)) i)) (+ (* (neg beta) alpha) (* i (+ (+ alpha (neg beta)) i)))) (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i)))) (- (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i))) 1))
(/ (* (- (* i (- (+ i alpha) beta)) (* alpha beta)) (* (/ i (+ alpha (- (* i 2) beta))) (/ (- (+ i alpha) beta) (+ alpha (- (* i 2) beta))))) (+ (* (+ alpha (- (* i 2) beta)) (+ alpha (- (* i 2) beta))) -1))
(/ (/ (* (* (neg i) (+ (+ alpha beta) (neg i))) (+ (* beta alpha) (* (neg i) (+ (+ alpha beta) (neg i))))) (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i))))) (- (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i)))) 1))
(* (neg i) (* (+ alpha (- beta i)) (/ (- (* alpha beta) (* i (+ alpha (- beta i)))) (* (+ alpha (- beta (* i 2))) (* (+ alpha (- beta (* i 2))) (+ (* (+ alpha (- beta (* i 2))) (+ alpha (- beta (* i 2)))) -1))))))
(neg (/ (/ (* (* i (+ (+ (neg alpha) beta) i)) (+ (* beta (neg alpha)) (* i (+ (+ (neg alpha) beta) i)))) (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i)))) (- (* (+ (+ (neg alpha) beta) (* 2 i)) (+ (+ (neg alpha) beta) (* 2 i))) 1)))
(* (/ (* i (+ i (- beta alpha))) (+ (* (+ beta (- (* i 2) alpha)) (+ beta (- (* i 2) alpha))) -1)) (/ (- (* i (+ i (- beta alpha))) (* alpha beta)) (* (+ beta (- (* i 2) alpha)) (+ (- alpha beta) (* i -2)))))
(neg (/ (/ (* (* i (+ (+ alpha (neg beta)) i)) (+ (* (neg beta) alpha) (* i (+ (+ alpha (neg beta)) i)))) (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i)))) (- (* (+ (+ alpha (neg beta)) (* 2 i)) (+ (+ alpha (neg beta)) (* 2 i))) 1)))
(* (/ (* i (- (+ i alpha) beta)) (+ (- beta alpha) (* i -2))) (/ (/ (- (* i (- (+ i alpha) beta)) (* alpha beta)) (+ alpha (- (* i 2) beta))) (+ (* (+ alpha (- (* i 2) beta)) (+ alpha (- (* i 2) beta))) -1)))
(neg (/ (/ (* (* (neg i) (+ (+ alpha beta) (neg i))) (+ (* beta alpha) (* (neg i) (+ (+ alpha beta) (neg i))))) (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i))))) (- (* (+ (+ alpha beta) (* 2 (neg i))) (+ (+ alpha beta) (* 2 (neg i)))) 1)))
(* (* i (+ alpha (- beta i))) (/ (- (* alpha beta) (* i (+ alpha (- beta i)))) (* (+ alpha (- beta (* i 2))) (* (+ alpha (- beta (* i 2))) (+ (* (+ alpha (- beta (* i 2))) (+ alpha (- beta (* i 2)))) -1)))))
(/ (/ (* (* i (+ (+ beta alpha) i)) (+ (* alpha beta) (* i (+ (+ beta alpha) i)))) (* (+ (+ beta alpha) (* 2 i)) (+ (+ beta alpha) (* 2 i)))) (- (* (+ (+ beta alpha) (* 2 i)) (+ (+ beta alpha) (* 2 i))) 1))
(* (* (+ i (+ alpha beta)) (/ i (+ alpha (+ beta (* i 2))))) (/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (* i 2)))) (+ (* (+ alpha (+ beta (* i 2))) (+ alpha (+ beta (* i 2)))) -1)))
(/ (/ (* (* alpha (+ (+ i beta) alpha)) (+ (* beta i) (* alpha (+ (+ i beta) alpha)))) (* (+ (+ i beta) (* 2 alpha)) (+ (+ i beta) (* 2 alpha)))) (- (* (+ (+ i beta) (* 2 alpha)) (+ (+ i beta) (* 2 alpha))) 1))
(* (* alpha (+ i (+ alpha beta))) (/ (+ (* alpha (+ i (+ alpha beta))) (* i beta)) (* (+ i (+ beta (* alpha 2))) (* (+ i (+ beta (* alpha 2))) (+ (* (+ i (+ beta (* alpha 2))) (+ i (+ beta (* alpha 2)))) -1)))))
(/ (/ (* (* beta (+ (+ alpha i) beta)) (+ (* i alpha) (* beta (+ (+ alpha i) beta)))) (* (+ (+ alpha i) (* 2 beta)) (+ (+ alpha i) (* 2 beta)))) (- (* (+ (+ alpha i) (* 2 beta)) (+ (+ alpha i) (* 2 beta))) 1))
(* beta (* (/ (+ (* beta (+ i (+ alpha beta))) (* i alpha)) (* (+ i (+ alpha (* beta 2))) (+ i (+ alpha (* beta 2))))) (/ (+ i (+ alpha beta)) (+ (* (+ i (+ alpha (* beta 2))) (+ i (+ alpha (* beta 2)))) -1))))

Symmetry

(sort alpha beta)

explain456.0ms (2.8%)

Memory

-17.4MiB live, 477.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
207	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))))`
144	1	(-4.0031376872489894e-33 4.936064832438182e+212 1.1641122806729861e+51)	-	`(/.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	165	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	144
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	207
↳	`(*.f64 beta alpha)`	overflow	15
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	284
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	165
`/.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	128	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	144
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	207
↳	`(*.f64 beta alpha)`	overflow	15
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	284
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	165
↳	`(/.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	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))`	overflow	165
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	165
`/.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	42	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	144
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	207
↳	`(*.f64 beta alpha)`	overflow	15
↳	`(*.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	17	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))`	overflow	165
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	165

Confusion

	Predicted +	Predicted -
+	207	0
-	0	49

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	207	0	0
-	0	0	49

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	49
1	62
2	145

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

70.0ms	510×	0	valid
1.0ms	2×	2	valid

Compiler

Compiled 482 to 72 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 14.0ms (42.7% of total)

ival-add: 9.0ms (27.5% of total)

ival-div: 6.0ms (18.3% of total)

ival-sub: 2.0ms (6.1% of total)

exact: 1.0ms (3.1% of total)

adjust: 0.0ms (0% of total)

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

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

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	19.6%	(/.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

▶

19.6%

(/.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)

simplify363.0ms (2.3%)

Memory

24.7MiB live, 812.5MiB 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

12 470×	`accelerator-lowering-fma.f32`
12 470×	`accelerator-lowering-fma.f64`
3 894×	`+-lowering-+.f64`
3 894×	`+-lowering-+.f32`
3 870×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	183
1	64	183
2	312	183
3	1998	183
4	6932	183
0	8038	166

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (* (* 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))
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
(* i (+ (+ alpha beta) i))
i
(+ (+ alpha beta) i)
(+ alpha beta)
alpha
beta
(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
(* beta alpha)
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
(+ (+ alpha beta) (* 2 i))
(* 2 i)
2
(- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)
1

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

localize77.0ms (0.5%)

Memory

-25.7MiB live, 105.0MiB 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	45.8%	(/.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	31.0%	(/.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))))

Samples

52.0ms	255×	0	valid
0.0ms	1×	2	valid

Compiler

Compiled 185 to 19 computations (89.7% saved)

Precisions

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

ival-add: 27.0ms (69.7% of total)

ival-mult: 7.0ms (18.1% of total)

ival-div: 3.0ms (7.7% of total)

ival-sub: 1.0ms (2.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series62.0ms (0.4%)

Memory

1.6MiB live, 117.6MiB allocated

Counts

7 → 252

Calls

Call 1

Inputs
#<alt (/ (/ (* (* 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))>
#<alt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))>
#<alt (+ (+ alpha beta) (* 2 i))>
#<alt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)>
#<alt (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))>
#<alt (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))>
#<alt (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 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))>
#<alt (/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (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)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -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))>
#<alt (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))>
#<alt (+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))))>
#<alt (+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))))>
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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
6.0ms	i	@	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	alpha	@	-inf	(/ (/ (* (* 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))
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))
3.0ms	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))

rewrite443.0ms (2.8%)

Memory

50.5MiB live, 1 064.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 174×	`accelerator-lowering-fma.f32`
5 174×	`accelerator-lowering-fma.f64`
4 888×	`/-lowering-/.f32`
4 888×	`/-lowering-/.f64`
4 186×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	127
1	134	127
2	1498	127
0	8172	117

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 609

Calls

Call 1

Inputs
(/ (/ (* (* 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))
(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
(+ (+ alpha beta) (* 2 i))
(- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

Outputs
(exp.f64 (.f64 (log.f64 (.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 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (neg.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i 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)))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (neg.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (neg.f64 (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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 #s(literal 0 binary64) (.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 #s(literal 0 binary64) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))) (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha 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 #s(literal 0 binary64) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))))
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simplify793.0ms (4.9%)

Memory

-152.0MiB live, 909.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 164×	`accelerator-lowering-fma.f32`
9 164×	`accelerator-lowering-fma.f64`
5 962×	`+-lowering-+.f64`
5 962×	`+-lowering-+.f32`
4 964×	`-lowering-.f32`

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 → 252

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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(- (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2)) 1)
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(pow alpha 2)
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(* (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))))) (/ 1 (pow alpha 2))))
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(pow alpha 2)
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(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
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(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
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(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
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(- (pow (+ alpha (* 2 i)) 2) 1)
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(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)
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(- (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2)) 1)
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(pow beta 2)
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(* (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))))
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(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
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(pow beta 2)
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(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
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(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
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(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
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(- (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)
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(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
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(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
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(* 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))))
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(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
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(* 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))))
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(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
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(/ (* 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))))
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(* 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))))
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(* 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))))
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(* 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))))))))
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(* 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))))
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(/ (* (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)))
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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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(- (+ (* 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 (/ (+ (* (+ (* 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 (-.f64 #s(literal 0 binary64) i) (-.f64 (-.f64 #s(literal 0 binary64) i) beta))
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(+ (* -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)))
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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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(* i (+ alpha i))
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(* -1 (* i (+ (* -1 alpha) (* -1 i))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 i (+.f64 alpha 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)))
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(+ (* -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)))
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(* 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))))))
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(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ i (+ (* 2 alpha) (* 2 beta)))) (pow (+ alpha beta) 2))))))
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(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)))))))
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(* (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))))
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(* (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 (-.f64 #s(literal 0 binary64) i) (-.f64 (-.f64 #s(literal 0 binary64) 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 (-.f64 #s(literal 0 binary64) i) beta) (/.f64 (.f64 (+.f64 beta i) (fma.f64 i #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) 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 (-.f64 #s(literal 0 binary64) i) beta) (/.f64 (-.f64 (.f64 i (.f64 (+.f64 beta i) (fma.f64 i #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) i) beta)))) (/.f64 (.f64 (.f64 i i) (*.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 (-.f64 #s(literal 0 binary64) i) beta) (/.f64 (-.f64 (.f64 i (.f64 (+.f64 beta i) (fma.f64 i #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) i) beta)))) (/.f64 (.f64 (.f64 i i) (*.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) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 i (+.f64 alpha i)))))
(* (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 (-.f64 #s(literal 0 binary64) i) alpha) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 i #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) 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 (-.f64 #s(literal 0 binary64) i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (fma.f64 i #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) i) alpha))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (-.f64 #s(literal 0 binary64) 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 (-.f64 #s(literal 0 binary64) i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (fma.f64 i #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) i) alpha))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (-.f64 #s(literal 0 binary64) 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)) (-.f64 #s(literal 0 binary64) 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)) (-.f64 #s(literal 0 binary64) 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)))

eval220.0ms (1.4%)

Memory: 10.1MiB live, 433.8MiB allocated
Compiler: Compiled 120 771 to 4 630 computations (96.2% saved)

prune473.0ms (3%)

Memory

29.5MiB live, 425.5MiB allocated

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1 400	12	1 412
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1 401	12	1 413

Accuracy

89.0%

Counts

1 413 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	12.8%	(/.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))
	19.6%	(/.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)))) (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))))
	19.4%	(/.f64 (/.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))) (-.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)))
▶	18.7%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
	18.5%	(/.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))))
▶	39.7%	(/.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)))
	18.2%	(/.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 (+.f64 alpha i)) (.f64 beta beta))
	45.1%	(.f64 (pow.f64 (.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 alpha (+.f64 i beta))))) #s(literal -1 binary64)) (pow.f64 (.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))) #s(literal -1 binary64)))
	40.5%	(.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha 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 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
	45.2%	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64)))) (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
▶	72.3%	#s(literal 1/16 binary64)

Compiler

Compiled 898 to 380 computations (57.7% saved)

simplify378.0ms (2.4%)

Memory

1.1MiB live, 719.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 i (+.f64 alpha (+.f64 i beta)))
✓	cost-diff	0	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))
✓	cost-diff	0	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
✓	cost-diff	384	(fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.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	1280	(-.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 i i) #s(literal 1/4 binary64))
✓	cost-diff	0	(/.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)))
✓	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	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

10 000×	`accelerator-lowering-fma.f32`
10 000×	`accelerator-lowering-fma.f64`
4 504×	`-lowering-.f32`
4 504×	`-lowering-.f64`
3 976×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	477
1	168	461
2	756	439
3	4445	425
4	7179	425
0	8020	387

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
1/16
#s(literal 1/16 binary64)
(/ (* i (+ alpha i)) (* beta beta))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(* i (+ alpha i))
(*.f64 i (+.f64 i alpha))
i
(+ alpha i)
(+.f64 i alpha)
alpha
(* beta beta)
(*.f64 beta beta)
beta
(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
(.f64 i (.f64 #s(literal 1/4 binary64) (/.f64 i (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(* (* i i) 1/4)
(.f64 i (.f64 i #s(literal 1/4 binary64)))
(* i i)
(*.f64 i i)
i
1/4
#s(literal 1/4 binary64)
(- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)
(fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
(*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))
(+ (+ alpha beta) (* 2 i))
(+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))
(+ alpha beta)
(+.f64 alpha beta)
alpha
beta
(* 2 i)
(+.f64 i i)
2
#s(literal 2 binary64)
1
#s(literal 1 binary64)
(/ (+ (* i (+ alpha i)) (* i (- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta)))) (* beta beta))
(/.f64 (.f64 i (+.f64 i (fma.f64 (/.f64 (+.f64 i alpha) beta) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64)))) alpha))) (*.f64 beta beta))
(+ (* i (+ alpha i)) (* i (- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta))))
(.f64 i (+.f64 i (fma.f64 (/.f64 (+.f64 i alpha) beta) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64)))) alpha)))
i
(+ alpha i)
(+.f64 i alpha)
alpha
(* i (- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta)))
(.f64 i (/.f64 (.f64 (+.f64 i alpha) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 8 binary64) (*.f64 alpha #s(literal 4 binary64))))) beta))
(- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta))
(/.f64 (.f64 (+.f64 i alpha) (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64))))) beta)
(/ (* (+ alpha i) (+ (+ alpha i) i)) beta)
(fma.f64 (+.f64 i alpha) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 0 binary64))
(* (+ alpha i) (+ (+ alpha i) i))
(*.f64 (+.f64 i alpha) (fma.f64 i #s(literal 2 binary64) alpha))
(+ (+ alpha i) i)
(fma.f64 i #s(literal 2 binary64) alpha)
beta
(/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta)
(/.f64 (.f64 (+.f64 i alpha) (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64)))) beta)
(* (+ alpha i) (+ (* alpha 4) (* i 8)))
(.f64 (+.f64 i alpha) (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64))))
(+ (* alpha 4) (* i 8))
(fma.f64 i #s(literal 8 binary64) (*.f64 alpha #s(literal 4 binary64)))
4
#s(literal 4 binary64)
(* i 8)
(*.f64 i #s(literal 8 binary64))
8
#s(literal 8 binary64)
(* beta beta)
(*.f64 beta beta)
(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1)))
(/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (.f64 (+.f64 i beta) (+.f64 i alpha)))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta)))
(.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (*.f64 (+.f64 i beta) (+.f64 i alpha))))
(* i (+ alpha (+ i beta)))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
i
(+ alpha (+ i beta))
(+.f64 i (+.f64 alpha beta))
alpha
(+ i beta)
(+.f64 i beta)
beta
(+ (* i (+ alpha (+ i beta))) (* alpha beta))
(*.f64 (+.f64 i beta) (+.f64 i alpha))
(* alpha beta)
(*.f64 alpha beta)
(* (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
(.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))
(*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))
(+ alpha (+ (* i 2) beta))
(+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))
(+ (* i 2) beta)
(fma.f64 i #s(literal 2 binary64) beta)
2
#s(literal 2 binary64)
(+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1)
(fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))
-1
#s(literal -1 binary64)

localize139.0ms (0.9%)

Memory

-3.2MiB live, 293.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	99.9%	(.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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)))
✓	accuracy	99.9%	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))
✓	accuracy	21.0%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
✓	accuracy	84.8%	(/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)
✓	accuracy	84.8%	(/.f64 (*.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)
✓	accuracy	78.3%	(/.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	54.9%	(-.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 #s(literal 2 binary64) i)
✓	accuracy	100.0%	(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
✓	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	46.6%	(/.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)))
✓	accuracy	100.0%	(+.f64 alpha i)
✓	accuracy	100.0%	(*.f64 i (+.f64 alpha i))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	74.7%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))

Samples

79.0ms	255×	0	valid
1.0ms	1×	2	valid

Compiler

Compiled 454 to 49 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 23.0ms (40.4% of total)

ival-div: 17.0ms (29.8% of total)

ival-add: 14.0ms (24.6% of total)

ival-sub: 2.0ms (3.5% of total)

exact: 1.0ms (1.8% of total)

adjust: 0.0ms (0% of total)

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

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

series75.0ms (0.5%)

Memory

-12.2MiB live, 104.3MiB allocated

Counts

21 → 660

Calls

Call 1

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

165 calls:

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

rewrite913.0ms (5.7%)

Memory

32.5MiB live, 455.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 256×	`/-lowering-/.f32`
4 256×	`/-lowering-/.f64`
4 120×	`-lowering-.f32`
4 120×	`-lowering-.f64`
3 254×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	289
1	374	275
2	4134	275
0	8534	253

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 710

Calls

Call 1

Inputs
(/ (* i (+ alpha i)) (* beta beta))
(* i (+ alpha i))
(+ alpha i)
(* beta beta)
(- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1)
(* 2 i)
(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
(* (* i i) 1/4)
(- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta))
(+ (* i (+ alpha i)) (* i (- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta))))
(/ (+ (* i (+ alpha i)) (* i (- (/ (* (+ alpha i) (+ (+ alpha i) i)) beta) (/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta)))) (* beta beta))
(+ (* i (+ alpha (+ i beta))) (* alpha beta))
(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1)))
(* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta)))
(* i (+ alpha (+ i beta)))
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
(+ (+ alpha beta) (* 2 i))
(/ (* (+ alpha i) (+ (+ alpha i) i)) beta)
(/ (* (+ alpha i) (+ (* alpha 4) (* i 8))) beta)
(* (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
(* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) 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 (-.f64 #s(literal 0 binary64) beta))) (/.f64 (.f64 i (+.f64 i alpha)) (*.f64 beta (-.f64 #s(literal 0 binary64) beta))))
(neg.f64 (/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta (-.f64 #s(literal 0 binary64) beta))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.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 (*.f64 i (+.f64 i alpha)) beta)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 beta beta) (.f64 i (+.f64 i alpha)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i alpha))) (.f64 beta (-.f64 #s(literal 0 binary64) beta)))
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i alpha)))) (neg.f64 (.f64 beta (-.f64 #s(literal 0 binary64) beta))))
(/.f64 (neg.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta)) (-.f64 #s(literal 0 binary64) 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 (*.f64 i (+.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)))
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(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha beta) (*.f64 (+.f64 i i) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 i i) (*.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i #s(literal 2 binary64) alpha) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) beta))
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(fma.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal 2 binary64)) i (.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
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(/.f64 (fma.f64 (.f64 alpha (.f64 alpha alpha)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))) (fma.f64 (.f64 alpha (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 alpha (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (-.f64 (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (.f64 alpha (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (.f64 (+.f64 i i) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 i i) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))) (-.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 i i) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 (-.f64 (.f64 (.f64 alpha (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 alpha (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))) (-.f64 (.f64 alpha (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 #s(literal 8 binary64) (.f64 i (.f64 i i))))) (fma.f64 (+.f64 i i) (-.f64 (+.f64 i i) (+.f64 alpha beta)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))
(/.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha (.f64 alpha alpha)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (-.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) (*.f64 alpha alpha)))
(/.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (-.f64 beta (+.f64 i i))))) (+.f64 alpha (-.f64 beta (+.f64 i i))))
(/.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (-.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
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(/.f64 (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha (.f64 alpha alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (-.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) (*.f64 alpha alpha)))
(/.f64 (.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (-.f64 beta (+.f64 i i)))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (+.f64 alpha (-.f64 beta (+.f64 i i))))
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(pow.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal 2 binary64))
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(pow.f64 (exp.f64 (log.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) #s(literal 2 binary64))
(.f64 #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 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
(.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal 1 binary64)))
(.f64 (.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))
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(.f64 (.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (-.f64 beta (+.f64 i i)))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (-.f64 beta (+.f64 i i))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 alpha (-.f64 beta (+.f64 i i)))) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 2 binary64)))
(*.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)))))

simplify800.0ms (5%)

Memory

7.6MiB live, 998.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 144×	`accelerator-lowering-fma.f32`
7 144×	`accelerator-lowering-fma.f64`
6 726×	`-lowering-.f32`
6 726×	`-lowering-.f64`
4 978×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1723	19077
1	6091	18772
0	8464	17391

Stop Event

1×	iter limit
1×	node limit

Counts

660 → 660

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)
(- (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)
(* 1/4 (/ (pow i 2) (- (pow (+ alpha beta) 2) 1)))
(* (pow i 2) (+ (* -1 (/ (* i (+ alpha beta)) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* 1/4 (/ 1 (- (pow (+ alpha beta) 2) 1)))))
(* (pow i 2) (+ (* i (+ (* -1 (/ (+ alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* -1/4 (* i (+ (* -16 (/ (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* 4 (/ 1 (pow (- (pow (+ alpha beta) 2) 1) 2)))))))) (* 1/4 (/ 1 (- (pow (+ alpha beta) 2) 1)))))
(* (pow i 2) (+ (* i (+ (* -1 (/ (+ alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 2))) (* i (+ (* -1/4 (* i (+ (* -16 (/ (+ alpha beta) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* -4 (/ (* (+ alpha beta) (+ (* -16 (/ (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* 4 (/ 1 (pow (- (pow (+ alpha beta) 2) 1) 2))))) (- (pow (+ alpha beta) 2) 1)))))) (* -1/4 (+ (* -16 (/ (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 3))) (* 4 (/ 1 (pow (- (pow (+ alpha beta) 2) 1) 2))))))))) (* 1/4 (/ 1 (- (pow (+ alpha beta) 2) 1)))))
1/16
(+ 1/16 (* -1/16 (/ (+ alpha beta) i)))
(- (+ 1/16 (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/64 (- (pow (+ alpha beta) 2) 1))) (pow i 2)))) (* 1/16 (/ (+ alpha beta) i)))
(- (+ 1/16 (* -1 (/ (+ (* -1 (* (+ alpha beta) (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/64 (- (pow (+ alpha beta) 2) 1))))) (* -1/64 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))) (pow i 3)))) (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 1/64 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (* 1/16 (/ (+ alpha beta) i)))))
1/16
(+ 1/16 (* -1/16 (/ (+ alpha beta) i)))
(+ 1/16 (* -1 (/ (- (+ (* -1/16 (/ (pow (+ alpha beta) 2) i)) (* 1/64 (/ (- (pow (+ alpha beta) 2) 1) i))) (* -1/16 (+ alpha beta))) i)))
(+ 1/16 (* -1 (/ (- (* -1 (/ (- (+ (* 1/64 (/ (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)) i)) (/ (* (+ alpha beta) (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/64 (- (pow (+ alpha beta) 2) 1)))) i)) (+ (* -1/16 (pow (+ alpha beta) 2)) (* 1/64 (- (pow (+ alpha beta) 2) 1)))) i)) (* -1/16 (+ alpha beta))) i)))
(* 1/4 (/ (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* -1/4 (/ (* alpha (* (pow i 2) (+ (* 2 beta) (* 4 i)))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))) (* 1/4 (/ (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(+ (* 1/4 (/ (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))) (* alpha (+ (* -1/4 (* alpha (+ (* -1 (/ (* (pow i 2) (pow (+ (* 2 beta) (* 4 i)) 2)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3))) (/ (pow i 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* -1/4 (/ (* (pow i 2) (+ (* 2 beta) (* 4 i))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))))
(+ (* 1/4 (/ (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))) (* alpha (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 beta) (* 4 i))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))) (* alpha (+ (* -1/4 (* alpha (+ (* -1 (/ (* (+ (* -1 (/ (* (pow i 2) (pow (+ (* 2 beta) (* 4 i)) 2)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3))) (/ (pow i 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))) (+ (* 2 beta) (* 4 i))) (- (pow (+ beta (* 2 i)) 2) 1))) (* -1 (/ (* (pow i 2) (+ (* 2 beta) (* 4 i))) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3)))))) (* -1/4 (+ (* -1 (/ (* (pow i 2) (pow (+ (* 2 beta) (* 4 i)) 2)) (pow (- (pow (+ beta (* 2 i)) 2) 1) 3))) (/ (pow i 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2)))))))))
(* 1/4 (/ (pow i 2) (pow alpha 2)))
(/ (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 beta) (* 4 i))) alpha)) (* 1/4 (pow i 2))) (pow alpha 2))
(/ (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 beta) (* 4 i))) alpha)) (+ (* -1/4 (/ (+ (* -1 (* (pow i 2) (pow (+ (* 2 beta) (* 4 i)) 2))) (* (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))) (pow alpha 2))) (* 1/4 (pow i 2)))) (pow alpha 2))
(/ (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 beta) (* 4 i))) alpha)) (+ (* -1/4 (/ (+ (* -1 (* (+ (* -1 (* (pow i 2) (pow (+ (* 2 beta) (* 4 i)) 2))) (* (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (* 2 beta) (* 4 i)))) (* -1 (* (pow i 2) (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) (pow alpha 3))) (+ (* -1/4 (/ (+ (* -1 (* (pow i 2) (pow (+ (* 2 beta) (* 4 i)) 2))) (* (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))) (pow alpha 2))) (* 1/4 (pow i 2))))) (pow alpha 2))
(* 1/4 (/ (pow i 2) (pow alpha 2)))
(/ (+ (* -1/2 (/ (* (pow i 2) (+ beta (* 2 i))) alpha)) (* 1/4 (pow i 2))) (pow alpha 2))
(/ (+ (* -1 (/ (+ (* 1/4 (/ (+ (* -4 (* (pow i 2) (pow (+ beta (* 2 i)) 2))) (* (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))) alpha)) (* 1/2 (* (pow i 2) (+ beta (* 2 i))))) alpha)) (* 1/4 (pow i 2))) (pow alpha 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (+ (* -4 (* (pow i 2) (pow (+ beta (* 2 i)) 2))) (* (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* 1/4 (/ (+ (* 2 (* (+ beta (* 2 i)) (+ (* -4 (* (pow i 2) (pow (+ beta (* 2 i)) 2))) (* (pow i 2) (- (pow (+ beta (* 2 i)) 2) 1))))) (* 2 (* (pow i 2) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))))) alpha))) alpha)) (* 1/2 (* (pow i 2) (+ beta (* 2 i))))) alpha)) (* 1/4 (pow i 2))) (pow alpha 2))
(* 1/4 (/ (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* -1/4 (/ (* beta (* (pow i 2) (+ (* 2 alpha) (* 4 i)))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))) (* 1/4 (/ (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))))
(+ (* 1/4 (/ (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (* beta (+ (* -1/4 (* beta (+ (* -1 (/ (* (pow i 2) (pow (+ (* 2 alpha) (* 4 i)) 2)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3))) (/ (pow i 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* -1/4 (/ (* (pow i 2) (+ (* 2 alpha) (* 4 i))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))
(+ (* 1/4 (/ (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (* beta (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 alpha) (* 4 i))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))) (* beta (+ (* -1/4 (* beta (+ (* -1 (/ (* (+ (* -1 (/ (* (pow i 2) (pow (+ (* 2 alpha) (* 4 i)) 2)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3))) (/ (pow i 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))) (+ (* 2 alpha) (* 4 i))) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -1 (/ (* (pow i 2) (+ (* 2 alpha) (* 4 i))) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))))) (* -1/4 (+ (* -1 (/ (* (pow i 2) (pow (+ (* 2 alpha) (* 4 i)) 2)) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3))) (/ (pow i 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))))))
(* 1/4 (/ (pow i 2) (pow beta 2)))
(/ (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 alpha) (* 4 i))) beta)) (* 1/4 (pow i 2))) (pow beta 2))
(/ (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 alpha) (* 4 i))) beta)) (+ (* -1/4 (/ (+ (* -1 (* (pow i 2) (pow (+ (* 2 alpha) (* 4 i)) 2))) (* (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 2))) (* 1/4 (pow i 2)))) (pow beta 2))
(/ (+ (* -1/4 (/ (* (pow i 2) (+ (* 2 alpha) (* 4 i))) beta)) (+ (* -1/4 (/ (+ (* -1 (* (+ (* -1 (* (pow i 2) (pow (+ (* 2 alpha) (* 4 i)) 2))) (* (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (* 2 alpha) (* 4 i)))) (* -1 (* (pow i 2) (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) (pow beta 3))) (+ (* -1/4 (/ (+ (* -1 (* (pow i 2) (pow (+ (* 2 alpha) (* 4 i)) 2))) (* (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 2))) (* 1/4 (pow i 2))))) (pow beta 2))
(* 1/4 (/ (pow i 2) (pow beta 2)))
(/ (+ (* -1/2 (/ (* (pow i 2) (+ alpha (* 2 i))) beta)) (* 1/4 (pow i 2))) (pow beta 2))
(/ (+ (* -1 (/ (+ (* 1/4 (/ (+ (* -4 (* (pow i 2) (pow (+ alpha (* 2 i)) 2))) (* (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))) beta)) (* 1/2 (* (pow i 2) (+ alpha (* 2 i))))) beta)) (* 1/4 (pow i 2))) (pow beta 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (+ (* -4 (* (pow i 2) (pow (+ alpha (* 2 i)) 2))) (* (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (* 1/4 (/ (+ (* 2 (* (+ alpha (* 2 i)) (+ (* -4 (* (pow i 2) (pow (+ alpha (* 2 i)) 2))) (* (pow i 2) (- (pow (+ alpha (* 2 i)) 2) 1))))) (* 2 (* (pow i 2) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) beta))) beta)) (* 1/2 (* (pow i 2) (+ alpha (* 2 i))))) beta)) (* 1/4 (pow i 2))) (pow beta 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(- (* 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)
(+ (* 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 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))))
(+ (* 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))))
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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)))
(/ (+ (* -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))
(/ (+ (* -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))
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (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)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -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))
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))))
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(+ (* beta (- (+ (* beta (- (+ (* -1 (* beta (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (+ (/ (* (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 4 alpha) (* 8 i)))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (/ (* (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))))
(/ (* 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 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)) (- (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))
(* 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))))
(* i (+ alpha beta))
(* i (+ alpha (+ beta i)))
(* i (+ alpha (+ beta i)))
(* i (+ alpha (+ beta i)))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* i (+ beta i))
(+ (* alpha i) (* i (+ beta i)))
(+ (* alpha i) (* i (+ beta i)))
(+ (* alpha i) (* i (+ beta i)))
(* alpha i)
(* alpha (+ i (/ (* i (+ beta i)) alpha)))
(* alpha (+ i (/ (* i (+ beta i)) alpha)))
(* alpha (+ i (/ (* i (+ beta i)) alpha)))
(* alpha i)
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))
(* i (+ alpha i))
(+ (* beta i) (* i (+ alpha i)))
(+ (* beta i) (* i (+ alpha i)))
(+ (* beta i) (* i (+ alpha i)))
(* beta i)
(* beta (+ i (/ (* i (+ alpha i)) beta)))
(* beta (+ i (/ (* i (+ alpha i)) beta)))
(* beta (+ i (/ (* i (+ alpha i)) beta)))
(* beta i)
(* -1 (* beta (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))
(* -1 (* beta (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))
(* -1 (* beta (+ (* -1 i) (* -1 (/ (* i (+ alpha 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))))
(+ 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)))
(* 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)
(* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))
(+ (* alpha (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (+ (* alpha (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (+ (* alpha (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (+ (* alpha (+ (* 4 beta) (* 8 i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(pow alpha 4)
(* (pow alpha 4) (+ 1 (+ (* 4 (/ beta alpha)) (* 8 (/ i alpha)))))
(* (pow alpha 4) (- (+ 1 (+ (* 2 (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))) (+ (* 4 (/ beta alpha)) (+ (* 8 (/ i alpha)) (/ (pow (+ (* 2 beta) (* 4 i)) 2) (pow alpha 2)))))) (/ 1 (pow alpha 2))))
(* (pow alpha 4) (- (+ 1 (+ (* 2 (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))) (+ (* 4 (/ beta alpha)) (+ (* 8 (/ i alpha)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 3)) (+ (/ (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i))) (pow alpha 3)) (/ (pow (+ (* 2 beta) (* 4 i)) 2) (pow alpha 2)))))))) (/ 1 (pow alpha 2))))
(pow alpha 4)
(* (pow alpha 4) (+ 1 (* 4 (/ (+ beta (* 2 i)) alpha))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ (* -4 (+ beta (* 2 i))) (* -1 (/ (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1) alpha))) alpha))))
(* (pow alpha 4) (+ 1 (* -1 (/ (+ (* -4 (+ beta (* 2 i))) (* -1 (/ (- (+ (* -1 (/ (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) alpha)) (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2)))) 1) alpha))) alpha))))
(* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))
(+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3)))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (pow (+ alpha beta) 3)) (* i (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (pow (+ alpha beta) 3)) (* i (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (+ (* 16 (pow (+ alpha beta) 2)) (* 32 (* i (+ alpha beta)))))))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))
(* 16 (pow i 4))
(* (pow i 4) (+ 16 (* 32 (/ (+ alpha beta) i))))
(* (pow i 4) (+ 16 (+ (* 4 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 32 (/ (+ alpha beta) i)))))))
(* (pow i 4) (+ 16 (+ (* 4 (/ (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)) (pow i 3))) (+ (* 4 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 3) (pow i 3))) (+ (* 16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 32 (/ (+ alpha beta) i)))))))))
(* 16 (pow i 4))
(* (pow i 4) (+ 16 (* 32 (/ (+ alpha beta) i))))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 (+ alpha beta)) (* -1 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i))) i))))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 (+ alpha beta)) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) i))) i))))
(* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))
(+ (* beta (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (+ (* beta (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (+ (* beta (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (+ (* beta (+ (* 4 alpha) (* 8 i))) (pow (+ (* 2 alpha) (* 4 i)) 2))) 1)) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
(pow beta 4)
(* (pow beta 4) (+ 1 (+ (* 4 (/ alpha beta)) (* 8 (/ i beta)))))
(* (pow beta 4) (- (+ 1 (+ (* 2 (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))) (+ (* 4 (/ alpha beta)) (+ (* 8 (/ i beta)) (/ (pow (+ (* 2 alpha) (* 4 i)) 2) (pow beta 2)))))) (/ 1 (pow beta 2))))
(* (pow beta 4) (- (+ 1 (+ (* 2 (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))) (+ (* 4 (/ alpha beta)) (+ (* 8 (/ i beta)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 3)) (+ (/ (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i))) (pow beta 3)) (/ (pow (+ (* 2 alpha) (* 4 i)) 2) (pow beta 2)))))))) (/ 1 (pow beta 2))))
(pow beta 4)
(* (pow beta 4) (+ 1 (* 4 (/ (+ alpha (* 2 i)) beta))))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -4 (+ alpha (* 2 i))) (* -1 (/ (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1) beta))) beta))))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -4 (+ alpha (* 2 i))) (* -1 (/ (- (+ (* -1 (/ (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) beta)) (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2)))) 1) beta))) 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 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 (+ 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)))))))
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(* (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 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (/.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 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (/.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)
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(/.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))
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(* -1 (/ (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.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))
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(* 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))))
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(* 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))))
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(* 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))))
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(* -6 (/ (pow i 3) beta))
(.f64 #s(literal -6 binary64) (/.f64 (.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)))))))
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(* (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 (/.f64 alpha (.f64 i beta)) (/.f64 alpha (.f64 i i))) (/.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 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 (/.f64 alpha (.f64 i beta)) (/.f64 alpha (.f64 i i))) (/.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 3) beta))
(.f64 #s(literal -6 binary64) (/.f64 (.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)))))
(.f64 (neg.f64 (.f64 i (.f64 i i))) (-.f64 (/.f64 #s(literal 6 binary64) beta) (/.f64 (-.f64 #s(literal 1 binary64) (-.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)))))
(.f64 (neg.f64 (.f64 i (.f64 i i))) (-.f64 (/.f64 #s(literal 6 binary64) beta) (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64)))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) alpha) (+.f64 (/.f64 (.f64 alpha alpha) beta) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha alpha) beta)))) i)) 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)))))
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(+ (* 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 #s(literal -3 binary64) (/.f64 (.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))))
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(* (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 #s(literal -3 binary64) (/.f64 (.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) (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (/.f64 (fma.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (*.f64 (/.f64 i beta) #s(literal -12 binary64))) (-.f64 #s(literal 0 binary64) 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) (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (/.f64 (-.f64 (-.f64 (.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64)))) (/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i)) alpha)) 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) (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (/.f64 (-.f64 (-.f64 (.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64)))) (/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (*.f64 i i)) alpha)) i) 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 (.f64 i beta) (+.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 (.f64 i beta) (+.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 (.f64 i beta) (+.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)))
(-.f64 (.f64 i (+.f64 alpha i)) (/.f64 (.f64 i (neg.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 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(-.f64 (.f64 i (+.f64 alpha i)) (/.f64 (.f64 i (neg.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 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i)))
(-.f64 (.f64 i (+.f64 alpha i)) (/.f64 (.f64 i (neg.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))
(/ (* i (- (+ alpha (/ (pow alpha 2) beta)) (* 4 (/ (pow alpha 2) beta)))) (pow beta 2))
(.f64 i (/.f64 (+.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 #s(literal -4 binary64) (/.f64 (.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 (+.f64 (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 alpha (.f64 beta beta)) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 beta beta))))) (.f64 #s(literal -4 binary64) (/.f64 (.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 (+.f64 (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 alpha (.f64 beta beta)) (/.f64 (.f64 alpha alpha) (.f64 beta (.f64 beta beta))))) (.f64 #s(literal -4 binary64) (/.f64 (.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))))))
(.f64 (neg.f64 (.f64 i (.f64 i i))) (-.f64 (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.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))))))
(.f64 (neg.f64 (.f64 i (.f64 i i))) (-.f64 (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) (.f64 beta beta))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 alpha (.f64 beta beta))) (/.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))))))
(.f64 (neg.f64 (.f64 i (.f64 i i))) (-.f64 (/.f64 #s(literal 6 binary64) (.f64 beta (.f64 beta beta))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 (-.f64 (.f64 (/.f64 alpha beta) #s(literal -3 binary64)) (.f64 (/.f64 alpha beta) #s(literal -12 binary64))) (.f64 beta beta))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 alpha (.f64 beta beta))) (/.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 #s(literal -3 binary64) (.f64 alpha (/.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 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 #s(literal -3 binary64) (.f64 alpha (/.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 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) (-.f64 (.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta)))) (/.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)) (-.f64 #s(literal 0 binary64) (/.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) (-.f64 (.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64)))) (.f64 beta beta)) (/.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)) (/.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) (-.f64 (.f64 #s(literal -3 binary64) (/.f64 i (.f64 beta (.f64 beta beta)))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 i (-.f64 (.f64 (/.f64 i beta) #s(literal -3 binary64)) (.f64 (/.f64 i beta) #s(literal -12 binary64)))) (.f64 beta beta)) (/.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)) (/.f64 i (*.f64 beta beta))) alpha)))
(/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) (pow beta 3))
(/.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)))))) (.f64 beta (*.f64 beta beta)))
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))
(/.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 (.f64 i beta) (+.f64 alpha i))) (.f64 beta (.f64 beta beta)))
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))
(/.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 (.f64 i beta) (+.f64 alpha i))) (.f64 beta (.f64 beta beta)))
(/ (+ (* beta (* i (+ alpha i))) (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) (pow beta 3))
(/.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 (.f64 i beta) (+.f64 alpha i))) (.f64 beta (.f64 beta beta)))
(/ (* i (+ alpha i)) (pow beta 2))
(/.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))
(/.f64 (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))) (.f64 beta beta))
(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
(/.f64 (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))) (.f64 beta beta))
(/ (+ (* i (+ alpha i)) (/ (* i (- (* (+ alpha i) (+ alpha (* 2 i))) (* (+ alpha i) (+ (* 4 alpha) (* 8 i))))) beta)) (pow beta 2))
(/.f64 (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))) (.f64 beta beta))
(/ (* 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))
(/.f64 (-.f64 (.f64 i (+.f64 alpha i)) (/.f64 (.f64 i (neg.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 beta beta))
(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/.f64 (-.f64 (.f64 i (+.f64 alpha i)) (/.f64 (.f64 i (neg.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 beta beta))
(/ (+ (* -1 (/ (* i (- (* -1 (* (+ alpha i) (+ alpha (* 2 i)))) (* -1 (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/.f64 (-.f64 (.f64 i (+.f64 alpha i)) (/.f64 (.f64 i (neg.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 beta beta))
(* alpha beta)
(*.f64 alpha beta)
(+ (* alpha beta) (* i (+ alpha beta)))
(fma.f64 alpha beta (*.f64 i (+.f64 alpha beta)))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))
(pow i 2)
(*.f64 i i)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(.f64 (.f64 i i) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 alpha i)) (/.f64 beta i)))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 alpha i) (fma.f64 alpha (/.f64 beta (*.f64 i i)) (/.f64 beta i)))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(.f64 (.f64 i i) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 alpha i) (fma.f64 alpha (/.f64 beta (*.f64 i i)) (/.f64 beta i)))))
(pow i 2)
(*.f64 i i)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(.f64 (.f64 i i) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 alpha i)) (/.f64 beta i)))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 (-.f64 #s(literal 0 binary64) alpha) beta) (/.f64 (*.f64 alpha beta) i)) i)))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 (-.f64 #s(literal 0 binary64) alpha) beta) (/.f64 (*.f64 alpha beta) i)) i)))
(* i (+ beta i))
(*.f64 i (+.f64 i beta))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(*.f64 (+.f64 i beta) (+.f64 alpha i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(*.f64 (+.f64 i beta) (+.f64 alpha i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(*.f64 (+.f64 i beta) (+.f64 alpha i))
(* alpha (+ beta i))
(*.f64 alpha (+.f64 i beta))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)))
(* -1 (* alpha (+ (* -1 beta) (* -1 i))))
(-.f64 #s(literal 0 binary64) (*.f64 alpha (-.f64 (-.f64 #s(literal 0 binary64) i) beta)))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(*.f64 (-.f64 #s(literal 0 binary64) alpha) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)) beta))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(*.f64 (-.f64 #s(literal 0 binary64) alpha) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)) beta))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(*.f64 (-.f64 #s(literal 0 binary64) alpha) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)) beta))
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(*.f64 (+.f64 alpha i) (+.f64 i beta))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(*.f64 (+.f64 alpha i) (+.f64 i beta))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
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(* beta (+ alpha i))
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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
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1/16
#s(literal 1/16 binary64)
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(* (pow alpha 4) (+ 1 (* -1 (/ (+ (* -4 (+ beta (* 2 i))) (* -1 (/ (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1) alpha))) alpha))))
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(* (pow alpha 4) (+ 1 (* -1 (/ (+ (* -4 (+ beta (* 2 i))) (* -1 (/ (- (+ (* -1 (/ (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) alpha)) (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2)))) 1) alpha))) alpha))))
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(* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))
(.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3)))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))
(fma.f64 i (.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 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (pow (+ alpha beta) 3)) (* i (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))
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(+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (pow (+ alpha beta) 3)) (* i (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (+ (* 16 (pow (+ alpha beta) 2)) (* 32 (* i (+ alpha beta)))))))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))
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(* 16 (pow i 4))
(*.f64 #s(literal 16 binary64) (pow.f64 i #s(literal 4 binary64)))
(* (pow i 4) (+ 16 (* 32 (/ (+ alpha beta) i))))
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 (/.f64 (+.f64 alpha beta) i) #s(literal 32 binary64) #s(literal 16 binary64)))
(* (pow i 4) (+ 16 (+ (* 4 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 32 (/ (+ alpha beta) i)))))))
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(* (pow i 4) (+ 16 (+ (* 4 (/ (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)) (pow i 3))) (+ (* 4 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 3) (pow i 3))) (+ (* 16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 32 (/ (+ alpha beta) i)))))))))
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(* 16 (pow i 4))
(*.f64 #s(literal 16 binary64) (pow.f64 i #s(literal 4 binary64)))
(* (pow i 4) (+ 16 (* 32 (/ (+ alpha beta) i))))
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 (/.f64 (+.f64 alpha beta) i) #s(literal 32 binary64) #s(literal 16 binary64)))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 (+ alpha beta)) (* -1 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i))) i))))
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(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 (+ alpha beta)) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) i))) i))))
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(* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))
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(+ (* beta (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
(fma.f64 beta (fma.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))))) (.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))))
(+ (* beta (+ (* beta (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
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(+ (* beta (+ (* beta (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (+ (* beta (+ (* 4 alpha) (* 8 i))) (pow (+ (* 2 alpha) (* 4 i)) 2))) 1)) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
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(pow beta 4)
(pow.f64 beta #s(literal 4 binary64))
(* (pow beta 4) (+ 1 (+ (* 4 (/ alpha beta)) (* 8 (/ i beta)))))
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(* (pow beta 4) (- (+ 1 (+ (* 2 (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))) (+ (* 4 (/ alpha beta)) (+ (* 8 (/ i beta)) (/ (pow (+ (* 2 alpha) (* 4 i)) 2) (pow beta 2)))))) (/ 1 (pow beta 2))))
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(* (pow beta 4) (- (+ 1 (+ (* 2 (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))) (+ (* 4 (/ alpha beta)) (+ (* 8 (/ i beta)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 3)) (+ (/ (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i))) (pow beta 3)) (/ (pow (+ (* 2 alpha) (* 4 i)) 2) (pow beta 2)))))))) (/ 1 (pow beta 2))))
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(pow beta 4)
(pow.f64 beta #s(literal 4 binary64))
(* (pow beta 4) (+ 1 (* 4 (/ (+ alpha (* 2 i)) beta))))
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal 4 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64)))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -4 (+ alpha (* 2 i))) (* -1 (/ (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1) beta))) beta))))
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(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -4 (+ alpha (* 2 i))) (* -1 (/ (- (+ (* -1 (/ (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) beta)) (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2)))) 1) beta))) beta))))
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(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))
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(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
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(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
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(pow alpha 2)
(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
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(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
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(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
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(pow alpha 2)
(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
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(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
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(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
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(pow (+ alpha beta) 2)
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))
(fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha beta)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
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(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(* 4 (pow i 2))
(.f64 (.f64 i i) #s(literal 4 binary64))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
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(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
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(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
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(* 4 (pow i 2))
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(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
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(* (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 (fma.f64 (+.f64 alpha beta) #s(literal -4 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.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 (fma.f64 (+.f64 alpha beta) #s(literal -4 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) i)) i)))
(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 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))))))
(.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) (/.f64 (-.f64 (.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)) 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 (-.f64 (.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)) beta)) beta)))

eval261.0ms (1.6%)

Memory: -39.7MiB live, 541.4MiB allocated
Compiler: Compiled 76 447 to 5 008 computations (93.4% saved)

prune297.0ms (1.9%)

Memory

4.5MiB live, 498.5MiB allocated

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	1 635	20	1 655
Fresh	6	1	7
Picked	3	2	5
Done	0	0	0
Total	1 644	23	1 667

Accuracy

99.0%

Counts

1 667 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	12.8%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 #s(literal 8 binary64) (.f64 i i)) beta)))) (*.f64 beta beta))
▶	13.8%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)))) (.f64 beta beta))
	13.6%	(/.f64 (fma.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)) (.f64 i i)) (.f64 beta beta))
	19.4%	(/.f64 (/.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))) (-.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)))
▶	21.3%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
▶	40.5%	(/.f64 (.f64 (/.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)))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha 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)))
	28.9%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	18.8%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 alpha beta) (+.f64 alpha 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))))
▶	18.6%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.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))))
✓	18.7%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
	18.7%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 i beta) (+.f64 alpha i))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
	18.5%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 i beta) (+.f64 i beta))) (.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))))
	34.4%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (*.f64 i #s(literal 2 binary64))) #s(literal 1 binary64)))
	31.2%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) #s(literal 1 binary64)))
	11.9%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (*.f64 beta beta))
	15.3%	(/.f64 (.f64 i i) (.f64 beta beta))
	28.9%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	21.3%	(.f64 (/.f64 (.f64 i (+.f64 i alpha)) beta) (/.f64 #s(literal 1 binary64) beta))
	27.5%	(.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 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64)))) beta) (+.f64 i alpha))) #s(literal -1 binary64)))
	27.5%	(.f64 (/.f64 i beta) (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 8 binary64) (.f64 alpha #s(literal 4 binary64)))) beta) (+.f64 i alpha)) beta))
	27.4%	(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 8 binary64) (*.f64 alpha #s(literal 4 binary64)))) beta) (+.f64 i alpha)) beta)))
▶	11.2%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	72.3%	#s(literal 1/16 binary64)

Compiler

Compiled 1 160 to 561 computations (51.6% saved)

simplify361.0ms (2.3%)

Memory

-15.4MiB live, 690.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 i (+.f64 alpha (+.f64 i beta)))
✓	cost-diff	0	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))
✓	cost-diff	0	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.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))))
✓	cost-diff	384	(fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))
✓	cost-diff	0	(.f64 i (.f64 (/.f64 (*.f64 i i) beta) #s(literal -6 binary64)))
✓	cost-diff	0	(+.f64 alpha i)
✓	cost-diff	0	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)))) (.f64 beta beta))
✓	cost-diff	448	(fma.f64 i (+.f64 alpha i) (.f64 i (.f64 (/.f64 (*.f64 i i) beta) #s(literal -6 binary64))))
✓	cost-diff	0	(+.f64 i alpha)
✓	cost-diff	0	(*.f64 i (+.f64 i alpha))
✓	cost-diff	0	(/.f64 (*.f64 i (+.f64 i alpha)) beta)
✓	cost-diff	384	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) 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 (.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))))
✓	cost-diff	0	(.f64 (/.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)))) (fma.f64 i (+.f64 i (+.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 (/.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)))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha 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)))

Rules

10 352×	`accelerator-lowering-fma.f32`
10 352×	`accelerator-lowering-fma.f64`
5 786×	`-lowering-.f32`
5 786×	`-lowering-.f64`
3 208×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	450
1	167	450
2	732	438
3	3817	412
4	7154	412
0	8077	380

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (* (/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
(* (/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
(/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))))
(* i (+ i (+ alpha beta)))
i
(+ i (+ alpha beta))
(+ alpha beta)
alpha
beta
(* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))
(+ alpha (+ (* i 2) beta))
(+ (* i 2) beta)
2
(+ (* i (+ i (+ alpha beta))) (* alpha beta))
(* alpha beta)
(+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1)
-1
(* alpha (/ i (* beta beta)))
alpha
(/ i (* beta beta))
i
(* beta beta)
beta
(/ (/ (* i (+ i alpha)) beta) beta)
(/ (* i (+ i alpha)) beta)
(* i (+ i alpha))
i
(+ i alpha)
alpha
beta
(/ (+ (* i (+ alpha i)) (* i (* (/ (* i i) beta) -6))) (* beta beta))
(+ (* i (+ alpha i)) (* i (* (/ (* i i) beta) -6)))
i
(+ alpha i)
alpha
(* i (* (/ (* i i) beta) -6))
(* (/ (* i i) beta) -6)
(/ (* i i) beta)
(* i i)
beta
-6
(* beta beta)
(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
(* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta)))
(* i (+ alpha (+ i beta)))
i
(+ alpha (+ i beta))
alpha
(+ i beta)
beta
(+ (* i (+ alpha (+ i beta))) (* alpha beta))
(* alpha beta)
(* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(* (+ (* i 2) beta) (+ (* i 2) beta))
(+ (* i 2) beta)
2
(+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)
-1

Outputs
(/ (* (/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
(/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (.f64 (+.f64 i alpha) (+.f64 i beta)))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
(* (/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
(/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (.f64 (+.f64 i alpha) (+.f64 i beta)))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) 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))))
(* i (+ i (+ alpha beta)))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
i
(+ i (+ alpha beta))
(+.f64 i (+.f64 alpha beta))
(+ alpha beta)
(+.f64 alpha beta)
alpha
beta
(* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))
(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
(+ alpha (+ (* i 2) beta))
(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))
(+ (* i 2) beta)
(fma.f64 i #s(literal 2 binary64) beta)
2
#s(literal 2 binary64)
(+ (* i (+ i (+ alpha beta))) (* alpha beta))
(*.f64 (+.f64 i alpha) (+.f64 i beta))
(* alpha beta)
(*.f64 alpha beta)
(+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1)
(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))
-1
#s(literal -1 binary64)
(* alpha (/ i (* beta beta)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
alpha
(/ i (* beta beta))
(/.f64 i (*.f64 beta beta))
i
(* beta beta)
(*.f64 beta beta)
beta
(/ (/ (* i (+ i alpha)) beta) beta)
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ i alpha)) beta)
(/.f64 (*.f64 i (+.f64 i alpha)) beta)
(* i (+ i alpha))
(*.f64 i (+.f64 i alpha))
i
(+ i alpha)
(+.f64 i alpha)
alpha
beta
(/ (+ (* i (+ alpha i)) (* i (* (/ (* i i) beta) -6))) (* beta beta))
(.f64 (fma.f64 (fma.f64 i (/.f64 #s(literal -6 binary64) beta) #s(literal 1 binary64)) i alpha) (/.f64 i (.f64 beta beta)))
(+ (* i (+ alpha i)) (* i (* (/ (* i i) beta) -6)))
(*.f64 i (fma.f64 (fma.f64 i (/.f64 #s(literal -6 binary64) beta) #s(literal 1 binary64)) i alpha))
i
(+ alpha i)
(+.f64 i alpha)
alpha
(* i (* (/ (* i i) beta) -6))
(/.f64 (.f64 i (.f64 i (*.f64 i #s(literal -6 binary64)))) beta)
(* (/ (* i i) beta) -6)
(/.f64 (.f64 i (.f64 i #s(literal -6 binary64))) beta)
(/ (* i i) beta)
(/.f64 (*.f64 i i) beta)
(* i i)
(*.f64 i i)
beta
-6
#s(literal -6 binary64)
(* beta beta)
(*.f64 beta beta)
(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
(/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (.f64 (+.f64 i alpha) (+.f64 i beta)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (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)))))
(* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta)))
(.f64 (+.f64 i (+.f64 alpha beta)) (.f64 i (*.f64 (+.f64 i alpha) (+.f64 i beta))))
(* i (+ alpha (+ i beta)))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
i
(+ alpha (+ i beta))
(+.f64 i (+.f64 alpha beta))
alpha
(+ i beta)
(+.f64 i beta)
beta
(+ (* i (+ alpha (+ i beta))) (* alpha beta))
(*.f64 (+.f64 i alpha) (+.f64 i beta))
(* alpha beta)
(*.f64 alpha beta)
(* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(.f64 (fma.f64 i #s(literal 2 binary64) beta) (.f64 (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))))
(* (+ (* i 2) beta) (+ (* i 2) beta))
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
(+ (* i 2) beta)
(fma.f64 i #s(literal 2 binary64) beta)
2
#s(literal 2 binary64)
(+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)
(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))
-1
#s(literal -1 binary64)

localize191.0ms (1.2%)

Memory

35.5MiB live, 228.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
✓	accuracy	99.9%	(.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)))
✓	accuracy	99.9%	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))
✓	accuracy	21.0%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.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))))
✓	accuracy	99.8%	(.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64))
✓	accuracy	93.3%	(fma.f64 i (+.f64 alpha i) (.f64 i (.f64 (/.f64 (*.f64 i i) beta) #s(literal -6 binary64))))
✓	accuracy	86.3%	(/.f64 (*.f64 i i) beta)
✓	accuracy	78.3%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (.f64 (/.f64 (.f64 i i) beta) #s(literal -6 binary64)))) (.f64 beta beta))
✓	accuracy	100.0%	(+.f64 i alpha)
✓	accuracy	100.0%	(*.f64 i (+.f64 i alpha))
✓	accuracy	94.4%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
✓	accuracy	86.3%	(/.f64 (*.f64 i (+.f64 i alpha)) beta)
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	88.3%	(/.f64 i (*.f64 beta beta))
✓	accuracy	82.9%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	accuracy	100.0%	(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	94.1%	(.f64 (/.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)))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))
✓	accuracy	45.8%	(/.f64 (.f64 (/.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)))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha 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)))
✓	accuracy	37.6%	(/.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))))

Samples

98.0ms	255×	0	valid
1.0ms	1×	2	valid

Compiler

Compiled 416 to 45 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-div: 32.0ms (46.6% of total)

ival-mult: 22.0ms (32% of total)

ival-add: 14.0ms (20.4% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series90.0ms (0.6%)

Memory

-2.3MiB live, 149.8MiB allocated

Counts

24 → 732

Calls

Call 1

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

Calls

183 calls:

Time	Variable		Point	Expression
16.0ms	i	@	0	(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
6.0ms	i	@	inf	(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
6.0ms	beta	@	-inf	(/ (* (/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
4.0ms	beta	@	0	(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
1.0ms	beta	@	-inf	(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))

rewrite517.0ms (3.2%)

Memory

-14.9MiB live, 757.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 120×	`-lowering-.f32`
5 120×	`-lowering-.f64`
4 244×	`/-lowering-/.f32`
4 244×	`/-lowering-/.f64`
3 550×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	298
1	352	294
2	3546	294
0	8722	276

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 1 046

Calls

Call 1

Inputs
(/ (* (/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
(+ (* i (+ i (+ alpha beta))) (* alpha beta))
(* (/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
(/ (* i (+ i (+ alpha beta))) (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))))
(* alpha (/ i (* beta beta)))
(/ i (* beta beta))
(* beta beta)
(/ (/ (* i (+ i alpha)) beta) beta)
(/ (* i (+ i alpha)) beta)
(* i (+ i alpha))
(+ i alpha)
(+ (* i (+ alpha i)) (* i (* (/ (* i i) beta) -6)))
(/ (+ (* i (+ alpha i)) (* i (* (/ (* i i) beta) -6))) (* beta beta))
(+ alpha i)
(* i (* (/ (* i i) beta) -6))
(+ (* i (+ alpha (+ i beta))) (* alpha beta))
(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
(* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta)))
(* i (+ alpha (+ i beta)))
(* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta)))
(/ (* i i) beta)
(* (/ (* i i) beta) -6)
(* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(* (+ (* i 2) beta) (+ (* i 2) beta))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)) (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(neg.f64 (/.f64 (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (/.f64 (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)) (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(/.f64 (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)) (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)) (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (/.f64 (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) #s(literal 1 binary64)) (.f64 (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(/.f64 (.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) #s(literal 1 binary64)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))) (/.f64 (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (.f64 i (+.f64 i (+.f64 alpha beta)))))
(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))
(/.f64 (.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))
(/.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (+.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal 1 binary64))) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
(pow.f64 (.f64 (/.f64 (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)) (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (/.f64 (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)) (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 i (.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(.f64 (/.f64 i (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (*.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha))))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))))
(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)))) (+.f64 (+.f64 beta (fma.f64 i #s(literal 2 binary64) alpha)) #s(literal 1 binary64))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
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(pow.f64 (exp.f64 (log.f64 (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 2 binary64))
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
(.f64 (.f64 (fma.f64 (.f64 i (.f64 i i)) #s(literal 8 binary64) (.f64 beta (.f64 beta beta))) (fma.f64 (.f64 i (.f64 i i)) #s(literal 8 binary64) (.f64 beta (.f64 beta beta)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 beta (-.f64 beta (.f64 i #s(literal 2 binary64))) (.f64 (*.f64 i i) #s(literal 4 binary64)))) #s(literal 2 binary64)))
(.f64 (.f64 (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) (.f64 beta beta)) (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) (.f64 beta beta))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 i #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) beta))) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 (fma.f64 i #s(literal 2 binary64) beta))) (exp.f64 (log.f64 (fma.f64 i #s(literal 2 binary64) beta))))

simplify1.1s (7.1%)

Memory

4.1MiB live, 1 104.2MiB allocated

Algorithm

1×	egg-herbie

Rules

6 998×	`-lowering-.f32`
6 998×	`-lowering-.f64`
6 676×	`accelerator-lowering-fma.f32`
6 676×	`accelerator-lowering-fma.f64`
4 528×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1881	22224
1	6557	22208
0	8345	20468

Stop Event

1×	iter limit
1×	node limit

Counts

732 → 732

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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(/ (* (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))
(/ (- (+ (* 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))
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(* -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))))) (* 4 (* i (* (+ 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)) (+ (* -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))
(/ (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ beta (* 2 i)) (- (* (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)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) (+ (* -1 beta) (* -1 i)))) alpha)) (+ (* (pow i 2) (pow (+ beta i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* 4 (* i (* (+ beta (* 2 i)) (+ (* -1 beta) (* -1 i)))))) (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1)) alpha)))) (+ (* -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))
(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 4) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* (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))
(/ (- (+ (* 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 (* (+ 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))
(* 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 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))))
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(* 1/4 (pow i 2))
(* (pow i 2) (- (+ 1/4 (* 1/4 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/4 (/ (+ alpha beta) i))))
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(* (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))
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(* i (+ 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 (* i (+ (* -1 beta) (* -1 i))))
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))
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(* i (+ alpha i))
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(- (+ (* -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)))
(/ 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)))
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(+ (* 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)
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(/ (- (+ 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))
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(* -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))
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(+ (* 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))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
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(+ (* -6 (/ (pow i 3) (pow beta 3))) (+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
(+ (* -6 (/ (pow i 3) (pow beta 3))) (+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2))))
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(* -6 (/ (pow i 3) (pow beta 3)))
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(/ (* alpha (* i (+ alpha beta))) (* beta (- (pow beta 2) 1)))
(* i (+ (* i (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (/ (* alpha (+ alpha beta)) (* beta (- (pow beta 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1))))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (/ (* alpha (+ alpha beta)) (* beta (- (pow beta 2) 1)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (+ (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1)))) (* i (- (/ 1 (* (pow beta 2) (- (pow beta 2) 1))) (+ (* 32 (/ (* alpha (+ alpha beta)) (* (pow beta 2) (pow (- (pow beta 2) 1) 2)))) (+ (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1))) (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1))))))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1))))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (/ (* alpha (+ alpha beta)) (* beta (- (pow beta 2) 1)))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ 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 beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/8 (/ beta i)) (* 2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 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 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 3))) (+ (* 1/8 (/ beta i)) (+ (* 2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 2))) (* 2 (/ (* beta (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) (* 2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))))))) (pow i 3)))))))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ beta i)))
(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) i)) (* -1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i)))) i)))
(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta)))) (* -1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* beta (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta)))) (* -1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(+ (* alpha (+ (/ (* alpha (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(+ (* alpha (+ (/ (* alpha (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(/ (* (pow alpha 2) (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))))
(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
(* -1 (/ (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha))))
(* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1)))
(+ (* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1))) (* beta (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))))
(+ (* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* beta (- (* 1/4 (/ (+ alpha i) (* i (- (* 4 (pow i 2)) 1)))) (+ (* 1/16 (/ (* (pow (+ alpha i) 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))))
(+ (* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* beta (- (+ (* -1 (* beta (+ (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ (+ alpha i) (* i (- (* 4 (pow i 2)) 1)))) (+ (* 1/16 (/ (* (pow (+ alpha i) 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))) (* (pow i 2) (- (* 4 (pow i 2)) 1))))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))) (+ (* 1/4 (/ (* (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2))))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (- (* 4 (pow i 2)) 1)))) (* 1/2 (/ (pow (+ alpha i) 2) (* i (pow (- (* 4 (pow i 2)) 1) 2)))))))) (* 1/4 (/ (+ alpha i) (* i (- (* 4 (pow i 2)) 1))))) (+ (* 1/16 (/ (* (pow (+ alpha i) 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (* 8 (/ (* (pow i 2) (+ alpha 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)))) (+ (* 8 (/ (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i))))) (pow beta 2))) (+ (* 8 (/ (* (pow i 2) (+ alpha i)) beta)) (/ (* i (* (+ alpha i) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))) (pow beta 2))))) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* 8 (* i (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* 8 (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i)))))) (* i (* (+ alpha i) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))) (+ (* i (* (+ alpha i) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i)))) (- (+ (* 8 (pow i 2)) (* 16 (pow 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))))) (+ (* 8 (/ (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i))))) (pow beta 2))) (+ (* 8 (/ (* (pow i 2) (+ alpha i)) beta)) (/ (* i (* (+ alpha i) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))) (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))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -8 (* i (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -8 (/ (* i (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -8 (* i (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) beta)))) (+ (* -8 (* i (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta))) (pow beta 2))
(* 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))))
(* i (+ alpha beta))
(* i (+ alpha (+ beta i)))
(* i (+ alpha (+ beta i)))
(* i (+ alpha (+ beta i)))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(pow i 2)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(* i (+ beta i))
(+ (* alpha i) (* i (+ beta i)))
(+ (* alpha i) (* i (+ beta i)))
(+ (* alpha i) (* i (+ beta i)))
(* alpha i)
(* alpha (+ i (/ (* i (+ beta i)) alpha)))
(* alpha (+ i (/ (* i (+ beta i)) alpha)))
(* alpha (+ i (/ (* i (+ beta i)) alpha)))
(* alpha i)
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))
(* -1 (* alpha (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha)))))
(* i (+ alpha i))
(+ (* beta i) (* i (+ alpha i)))
(+ (* beta i) (* i (+ alpha i)))
(+ (* beta i) (* i (+ alpha i)))
(* beta i)
(* beta (+ i (/ (* i (+ alpha i)) beta)))
(* beta (+ i (/ (* i (+ alpha i)) beta)))
(* beta (+ i (/ (* i (+ alpha i)) beta)))
(* beta i)
(* -1 (* beta (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))
(* -1 (* beta (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta)))))
(* -1 (* beta (+ (* -1 i) (* -1 (/ (* i (+ alpha 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 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 (+ 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 i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(/ (pow i 2) beta)
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* -6 (/ (pow i 2) beta))
(* (pow beta 2) (- (pow beta 2) 1))
(+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1)))
(+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (+ (* 4 (pow beta 3)) (* i (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* (pow beta 2) (- (pow beta 2) 1)))
(+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (+ (* 4 (pow beta 3)) (* i (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (+ (* 16 (pow beta 2)) (* 32 (* beta i))))))))) (* (pow beta 2) (- (pow beta 2) 1)))
(* 16 (pow i 4))
(* (pow i 4) (+ 16 (* 32 (/ beta i))))
(* (pow i 4) (+ 16 (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i)))))))
(* (pow i 4) (+ 16 (+ (* 4 (/ (* beta (- (pow beta 2) 1)) (pow i 3))) (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 4 (/ (pow beta 3) (pow i 3))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i)))))))))
(* 16 (pow i 4))
(* (pow i 4) (+ 16 (* 32 (/ beta i))))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i))) i))))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) i))) i))))
(* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1)))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (* beta i)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1))))))
(pow beta 4)
(* (pow beta 4) (+ 1 (* 8 (/ i beta))))
(* (pow beta 4) (- (+ 1 (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 2) (pow beta 2)))))) (/ 1 (pow beta 2))))
(* (pow beta 4) (- (+ 1 (+ (* 4 (/ (* i (- (* 4 (pow i 2)) 1)) (pow beta 3))) (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (+ (* 16 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 3) (pow beta 3)))))))) (/ 1 (pow beta 2))))
(pow beta 4)
(* (pow beta 4) (+ 1 (* 8 (/ i beta))))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) beta))) beta))))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* -1 (/ (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) beta)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1) beta))) beta))))
(pow beta 2)
(+ (* 4 (* beta i)) (pow beta 2))
(+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2))
(+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ beta i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))))
(* (pow i 2) (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ beta i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (pow beta 2) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (pow beta 2) i))) i))))
(* 4 (pow i 2))
(+ (* 4 (* beta i)) (* 4 (pow i 2)))
(+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i))))
(+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 4 (/ i beta))))
(* (pow beta 2) (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))))
(* (pow beta 2) (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))))
(pow beta 2)
(* (pow beta 2) (+ 1 (* 4 (/ i beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -4 (/ (pow i 2) beta))) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -4 (/ (pow i 2) beta))) 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 alpha (.f64 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 alpha (/.f64 beta (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (.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 alpha (.f64 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 alpha (.f64 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))))))))))
(* 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 alpha (.f64 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 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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 alpha (.f64 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))))))) (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 alpha (.f64 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))))))
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))
(- (+ 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))))))
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(- (+ 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)))))))))
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1/16
#s(literal 1/16 binary64)
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
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(* 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 #s(literal 1 binary64) (-.f64 (fma.f64 i (-.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 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 (-.f64 (.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))))) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (/.f64 (.f64 #s(literal 4 binary64) (.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 (+.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (.f64 alpha (.f64 beta (+.f64 alpha beta))) (.f64 i (.f64 i i))) #s(literal 1/4 binary64) (.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)))))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i)) (fma.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)))) (.f64 i (.f64 i i))) (fma.f64 (/.f64 (+.f64 alpha beta) i) #s(literal 1/4 binary64) (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta)) #s(literal 1/4 binary64)) (fma.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)))) (.f64 i (.f64 i i))) (.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)))))))))
(* 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) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) i) #s(literal 1/4 binary64) (neg.f64 (.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 (neg.f64 (+.f64 alpha beta)) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))) i))) i) #s(literal 1/4 binary64)))
(* (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) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)) (/.f64 (-.f64 (fma.f64 (.f64 alpha (/.f64 (.f64 beta (+.f64 alpha beta)) i)) #s(literal 1/4 binary64) (neg.f64 (-.f64 (.f64 (.f64 #s(literal -1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal -1/16 binary64) (.f64 (neg.f64 (+.f64 alpha beta)) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta)))))))) (fma.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) (neg.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 (.f64 (.f64 #s(literal -1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal -1/16 binary64) (.f64 (neg.f64 (+.f64 alpha beta)) (.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (+.f64 alpha beta))))))) i)))) i))) i) #s(literal 1/4 binary64)))
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))
(.f64 (.f64 i i) (/.f64 (.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 (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.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 i i) (/.f64 (.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)))
(fma.f64 alpha (fma.f64 alpha (-.f64 (/.f64 (.f64 i (+.f64 beta i)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (/.f64 (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.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 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.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 i i) (/.f64 (.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 (- (+ (* 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)))
(fma.f64 alpha (fma.f64 alpha (fma.f64 alpha (-.f64 (/.f64 (.f64 (.f64 i i) (.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 6 binary64))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (/.f64 (-.f64 (/.f64 (.f64 i (+.f64 beta i)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (/.f64 (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.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 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i)))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64))))) (-.f64 (/.f64 (.f64 i (+.f64 beta i)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (/.f64 (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.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 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (pow.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 4 binary64)))))) (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i i) (.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 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))))
(* 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))
(-.f64 (fma.f64 i (/.f64 (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i))) alpha) (.f64 i (+.f64 beta i))) (/.f64 (.f64 (.f64 i (+.f64 beta i)) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) 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)))))
(-.f64 (fma.f64 i (+.f64 beta i) (fma.f64 i (/.f64 (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i))) alpha) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 alpha alpha)))) (fma.f64 i (/.f64 (.f64 (+.f64 beta i) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (/.f64 (.f64 i (-.f64 (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 i (+.f64 beta i))) (.f64 (+.f64 beta i) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))))) (.f64 alpha alpha)) (/.f64 (.f64 (.f64 i (+.f64 beta i)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 alpha alpha)))))
(- (+ (* -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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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (+ (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1)))) (* i (- (/ 1 (* (pow beta 2) (- (pow beta 2) 1))) (+ (* 32 (/ (* alpha (+ alpha beta)) (* (pow beta 2) (pow (- (pow beta 2) 1) 2)))) (+ (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1))) (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1))))))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1))))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (/ (* alpha (+ alpha beta)) (* beta (- (pow beta 2) 1)))))
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1/16
#s(literal 1/16 binary64)
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ beta i)))
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(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/8 (/ beta i)) (* 2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 2))))))
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(- (+ 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 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 3))) (+ (* 1/8 (/ beta i)) (+ (* 2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 2))) (* 2 (/ (* beta (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) (* 2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))))))) (pow i 3)))))))))
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1/16
#s(literal 1/16 binary64)
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ beta i)))
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(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) i)) (* -1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i)))) i)))
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(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta)))) (* -1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* beta (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta)))) (* -1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) i))))) i))) i)))
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
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(+ (/ (* 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (/.f64 (.f64 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 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 i i) (/.f64 (.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))))))
(+ (* alpha (+ (/ (* alpha (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (fma.f64 alpha (/.f64 (.f64 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 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 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 i i) (/.f64 (.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))))))
(+ (* alpha (+ (/ (* alpha (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (fma.f64 alpha (/.f64 (.f64 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 i (fma.f64 (+.f64 beta i) (+.f64 beta i) (.f64 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 i i) (/.f64 (.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))))))
(/ (* (pow alpha 2) (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
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(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))))
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(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
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(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
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(* -1 (/ (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(/.f64 (neg.f64 (.f64 (.f64 alpha alpha) (.f64 i (fma.f64 beta #s(literal -1 binary64) (neg.f64 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))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
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(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha))))
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(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha))))
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(* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1)))
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(+ (* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* beta (- (* 1/4 (/ (+ alpha i) (* i (- (* 4 (pow i 2)) 1)))) (+ (* 1/16 (/ (* (pow (+ alpha i) 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))))
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(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 #s(literal 32 binary64) (/.f64 beta i) #s(literal 16 binary64)))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i))) i))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (+.f64 #s(literal 16 binary64) (neg.f64 (/.f64 (fma.f64 beta #s(literal -32 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)) (.f64 (*.f64 beta beta) #s(literal 20 binary64))) i))) i))))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) i))) i))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (+.f64 #s(literal 16 binary64) (neg.f64 (/.f64 (fma.f64 beta #s(literal -32 binary64) (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)) (.f64 (.f64 beta beta) #s(literal 20 binary64))) (neg.f64 (/.f64 (.f64 #s(literal -4 binary64) (fma.f64 beta (fma.f64 beta beta #s(literal -1 binary64)) (.f64 beta (.f64 beta beta)))) i))) i))) i))))
(* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1)))
(.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64)))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))))
(fma.f64 beta (fma.f64 #s(literal 4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i)))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))
(fma.f64 beta (fma.f64 #s(literal 4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (fma.f64 beta (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)) (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i))))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (* beta i)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1))))))
(fma.f64 beta (fma.f64 #s(literal 4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (fma.f64 beta (fma.f64 (.f64 beta i) #s(literal 8 binary64) (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64))) (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i))))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))
(pow beta 4)
(pow.f64 beta #s(literal 4 binary64))
(* (pow beta 4) (+ 1 (* 8 (/ i beta))))
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 4) (- (+ 1 (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 2) (pow beta 2)))))) (/ 1 (pow beta 2))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 (.f64 i i) (.f64 beta beta)) #s(literal 24 binary64) (/.f64 (.f64 i #s(literal 8 binary64)) beta)) (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))))
(* (pow beta 4) (- (+ 1 (+ (* 4 (/ (* i (- (* 4 (pow i 2)) 1)) (pow beta 3))) (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (+ (* 16 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 3) (pow beta 3)))))))) (/ 1 (pow beta 2))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (.f64 beta (.f64 beta beta))) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) (fma.f64 (/.f64 (.f64 i i) (.f64 beta beta)) #s(literal 24 binary64) (/.f64 (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i))) (.f64 beta (.f64 beta beta)))))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))))
(pow beta 4)
(pow.f64 beta #s(literal 4 binary64))
(* (pow beta 4) (+ 1 (* 8 (/ i beta))))
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) beta))) beta))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (fma.f64 i #s(literal -8 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)) beta))) beta))))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* -1 (/ (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) beta)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1) beta))) beta))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 i #s(literal -8 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 i (.f64 i i)) #s(literal -16 binary64) (.f64 #s(literal -4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))))) beta) (fma.f64 (*.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64))) beta))) beta) #s(literal 1 binary64)))
(pow beta 2)
(*.f64 beta beta)
(+ (* 4 (* beta i)) (pow beta 2))
(fma.f64 beta beta (.f64 (.f64 beta i) #s(literal 4 binary64)))
(+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 beta i)) (.f64 beta beta))
(+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 beta i)) (.f64 beta beta))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ beta i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 beta i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta i) #s(literal 4 binary64)) (/.f64 (.f64 beta beta) (.f64 i i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta i) #s(literal 4 binary64)) (/.f64 (.f64 beta beta) (.f64 i i))))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ beta i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 beta i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (pow beta 2) i))) i))))
(.f64 (.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 beta #s(literal -4 binary64) (neg.f64 (/.f64 (*.f64 beta beta) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (pow beta 2) i))) i))))
(.f64 (.f64 i i) (+.f64 #s(literal 4 binary64) (neg.f64 (/.f64 (fma.f64 beta #s(literal -4 binary64) (neg.f64 (/.f64 (*.f64 beta beta) i))) i))))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(+ (* 4 (* beta i)) (* 4 (pow i 2)))
(.f64 #s(literal 4 binary64) (.f64 i (+.f64 beta i)))
(+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i))))
(fma.f64 beta (fma.f64 i #s(literal 4 binary64) beta) (.f64 #s(literal 4 binary64) (.f64 i i)))
(+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i))))
(fma.f64 beta (fma.f64 i #s(literal 4 binary64) beta) (.f64 #s(literal 4 binary64) (.f64 i i)))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 4 (/ i beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 4 binary64) (+.f64 (/.f64 i beta) (/.f64 (.f64 i i) (.f64 beta beta))) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 4 binary64) (+.f64 (/.f64 i beta) (/.f64 (.f64 i i) (.f64 beta beta))) #s(literal 1 binary64)))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 4 (/ i beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -4 (/ (pow i 2) beta))) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal -4 binary64) (+.f64 i (/.f64 (.f64 i i) beta))) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -4 (/ (pow i 2) beta))) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal -4 binary64) (+.f64 i (/.f64 (.f64 i i) beta))) beta) #s(literal 1 binary64)))

eval278.0ms (1.7%)

Memory: 32.3MiB live, 528.9MiB allocated
Compiler: Compiled 99 282 to 5 772 computations (94.2% saved)

prune334.0ms (2.1%)

Memory

13.8MiB live, 572.7MiB allocated

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	1 778	18	1 796
Fresh	8	8	16
Picked	4	1	5
Done	0	2	2
Total	1 790	29	1 819

Accuracy

99.0%

Counts

1 819 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	20.1%	(/.f64 (/.f64 (*.f64 i i) beta) beta)
	28.9%	(/.f64 (*.f64 (/.f64 (+.f64 i alpha) beta) i) beta)
▶	40.4%	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	13.2%	(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
	18.6%	(/.f64 (.f64 (.f64 i (+.f64 beta i)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.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))))
	18.6%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 beta 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))))
✓	18.7%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
	18.7%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 i beta) (+.f64 alpha i))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
	18.6%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 beta i) (+.f64 alpha 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))))
▶	18.5%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 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))))
	35.3%	(/.f64 (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (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)))
	18.5%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 i beta) (+.f64 i beta))) (.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))))
	34.4%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (*.f64 i #s(literal 2 binary64))) #s(literal 1 binary64)))
	31.2%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) #s(literal 1 binary64)))
	11.9%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (*.f64 beta beta))
▶	13.8%	(/.f64 (.f64 i (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha)) (.f64 beta beta))
	18.2%	(/.f64 (*.f64 i (+.f64 alpha i)) (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)))
▶	15.3%	(/.f64 (.f64 i i) (.f64 beta beta))
	35.8%	(/.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha 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)))
	21.0%	(/.f64 #s(literal 1 binary64) (.f64 beta (/.f64 beta (.f64 i (+.f64 i alpha)))))
▶	28.9%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	27.5%	(.f64 (/.f64 i beta) (pow.f64 (/.f64 beta (fma.f64 i (.f64 (/.f64 i beta) #s(literal -6 binary64)) (+.f64 i alpha))) #s(literal -1 binary64)))
	27.5%	(.f64 (/.f64 i beta) (/.f64 (fma.f64 i (.f64 (/.f64 i beta) #s(literal -6 binary64)) (+.f64 i alpha)) beta))
	13.2%	(*.f64 (/.f64 alpha beta) (/.f64 i beta))
	27.4%	(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (fma.f64 (+.f64 i alpha) (/.f64 (-.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 8 binary64) (*.f64 alpha #s(literal 4 binary64)))) beta) (+.f64 i alpha)) beta)))
	28.8%	(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (+.f64 i alpha) beta)))
	23.6%	(*.f64 i (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
✓	11.2%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	72.3%	#s(literal 1/16 binary64)

Compiler

Compiled 1 300 to 639 computations (50.8% saved)

simplify642.0ms (4%)

Memory

-15.7MiB live, 1 128.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 alpha (+.f64 i beta))
✓	cost-diff	0	(*.f64 i (+.f64 alpha (+.f64 i beta)))
✓	cost-diff	0	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (*.f64 i (+.f64 beta i)))
✓	cost-diff	0	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 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))))
✓	cost-diff	0	(fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha)
✓	cost-diff	0	(*.f64 i (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha))
✓	cost-diff	0	(/.f64 (.f64 i (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha)) (.f64 beta beta))
✓	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 i)
✓	cost-diff	0	(/.f64 (.f64 i i) (.f64 beta beta))
✓	cost-diff	0	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
✓	cost-diff	0	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 i (+.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 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))

Rules

19 056×	`accelerator-lowering-fma.f32`
19 056×	`accelerator-lowering-fma.f64`
5 892×	`+-lowering-+.f64`
5 892×	`+-lowering-+.f32`
4 458×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	389
1	159	389
2	643	374
3	3507	359
4	6715	359
0	8416	327

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
(/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta)))
(* i (+ i (+ alpha beta)))
i
(+ i (+ alpha beta))
(+ alpha beta)
alpha
beta
(* (+ (* i 2) beta) (+ (* i 2) beta))
(+ (* i 2) beta)
2
(+ (* i (+ i (+ alpha beta))) (* alpha beta))
(* alpha beta)
(+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)
-1
(/ (* i i) (* beta beta))
(* i i)
i
(* beta beta)
beta
(* (/ (+ i alpha) beta) (/ i beta))
(/ (+ i alpha) beta)
(+ i alpha)
i
alpha
beta
(/ i beta)
(/ (* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha)) (* beta beta))
(* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha))
i
(+ (* i (+ (* (/ i beta) -6) 1)) alpha)
(+ (* (/ i beta) -6) 1)
(/ i beta)
beta
-6
1
alpha
(* beta beta)
(/ (* (* i (+ alpha (+ i beta))) (* i (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
(* (* i (+ alpha (+ i beta))) (* i (+ beta i)))
(* i (+ alpha (+ i beta)))
i
(+ alpha (+ i beta))
alpha
(+ i beta)
beta
(* i (+ beta i))
(+ beta i)
(* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(* (+ (* i 2) beta) (+ (* i 2) beta))
(+ (* i 2) beta)
2
(+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)
-1

Outputs
(/ (* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(/.f64 (.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 (+.f64 i alpha) (+.f64 i beta)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (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)))))
(* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
(/.f64 (.f64 i (.f64 (+.f64 i (+.f64 alpha beta)) (.f64 (+.f64 i alpha) (+.f64 i beta)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta)))
(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(* i (+ i (+ alpha beta)))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
i
(+ i (+ alpha beta))
(+.f64 i (+.f64 alpha beta))
(+ alpha beta)
(+.f64 alpha beta)
alpha
beta
(* (+ (* i 2) beta) (+ (* i 2) beta))
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
(+ (* i 2) beta)
(fma.f64 i #s(literal 2 binary64) beta)
2
#s(literal 2 binary64)
(+ (* i (+ i (+ alpha beta))) (* alpha beta))
(*.f64 (+.f64 i alpha) (+.f64 i beta))
(* alpha beta)
(*.f64 alpha beta)
(+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)
(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(/ (* i i) (* beta beta))
(.f64 i (/.f64 i (.f64 beta beta)))
(* i i)
(*.f64 i i)
i
(* beta beta)
(*.f64 beta beta)
beta
(* (/ (+ i alpha) beta) (/ i beta))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (+ i alpha) beta)
(/.f64 (+.f64 i alpha) beta)
(+ i alpha)
(+.f64 i alpha)
i
alpha
beta
(/ i beta)
(/.f64 i beta)
(/ (* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha)) (* beta beta))
(.f64 (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha) (/.f64 i (.f64 beta beta)))
(* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha))
(*.f64 i (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha))
i
(+ (* i (+ (* (/ i beta) -6) 1)) alpha)
(fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha)
(+ (* (/ i beta) -6) 1)
(fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64))
(/ i beta)
(/.f64 i beta)
beta
-6
#s(literal -6 binary64)
1
#s(literal 1 binary64)
alpha
(* beta beta)
(*.f64 beta beta)
(/ (* (* i (+ alpha (+ i beta))) (* i (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (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)))))
(* (* i (+ alpha (+ i beta))) (* i (+ beta i)))
(.f64 (.f64 i i) (*.f64 (+.f64 i (+.f64 alpha beta)) (+.f64 i beta)))
(* i (+ alpha (+ i beta)))
(*.f64 i (+.f64 i (+.f64 alpha beta)))
i
(+ alpha (+ i beta))
(+.f64 i (+.f64 alpha beta))
alpha
(+ i beta)
(+.f64 i beta)
beta
(* i (+ beta i))
(*.f64 i (+.f64 i beta))
(+ beta i)
(+.f64 i beta)
(* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(.f64 (fma.f64 i #s(literal 2 binary64) beta) (.f64 (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))))
(* (+ (* i 2) beta) (+ (* i 2) beta))
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
(+ (* i 2) beta)
(fma.f64 i #s(literal 2 binary64) beta)
2
#s(literal 2 binary64)
(+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)
(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))
-1
#s(literal -1 binary64)

localize172.0ms (1.1%)

Memory

8.2MiB live, 240.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
✓	accuracy	99.9%	(.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)))
✓	accuracy	99.9%	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (*.f64 i (+.f64 beta i)))
✓	accuracy	21.0%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 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))))
✓	accuracy	100.0%	(*.f64 i (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha))
✓	accuracy	99.9%	(fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha)
✓	accuracy	99.8%	(fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64))
✓	accuracy	78.3%	(/.f64 (.f64 i (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha)) (.f64 beta beta))
✓	accuracy	100.0%	(/.f64 (+.f64 i alpha) beta)
✓	accuracy	100.0%	(/.f64 i beta)
✓	accuracy	100.0%	(+.f64 i alpha)
✓	accuracy	99.7%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	75.5%	(/.f64 (.f64 i i) (.f64 beta beta))
✓	accuracy	100.0%	(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
✓	accuracy	94.1%	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))
✓	accuracy	45.8%	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
✓	accuracy	37.6%	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))

Samples

90.0ms	255×	0	valid
1.0ms	1×	2	valid

Compiler

Compiled 350 to 42 computations (88% saved)

Precisions

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

ival-mult: 23.0ms (50% of total)

ival-add: 12.0ms (26.1% of total)

ival-div: 10.0ms (21.8% of total)

exact: 1.0ms (2.2% of total)

adjust: 0.0ms (0% of total)

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

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

series58.0ms (0.4%)

Memory

-23.4MiB live, 131.2MiB allocated

Counts

21 → 636

Calls

Call 1

Inputs
#<alt (/ (* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))>
#<alt (+ (* i (+ i (+ alpha beta))) (* alpha beta))>
#<alt (* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))>
#<alt (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta)))>
#<alt (/ (* i i) (* beta beta))>
#<alt (* i i)>
#<alt (* beta beta)>
#<alt (* (/ (+ i alpha) beta) (/ i beta))>
#<alt (/ (+ i alpha) beta)>
#<alt (+ i alpha)>
#<alt (/ i beta)>
#<alt (/ (* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha)) (* beta beta))>
#<alt (* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha))>
#<alt (+ (* i (+ (* (/ i beta) -6) 1)) alpha)>
#<alt (+ (* (/ i beta) -6) 1)>
#<alt (/ (* (* i (+ alpha (+ i beta))) (* i (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))>
#<alt (* (* i (+ alpha (+ i beta))) (* i (+ beta i)))>
#<alt (* i (+ alpha (+ i beta)))>
#<alt (+ alpha (+ i beta))>
#<alt (* (+ (* i 2) beta) (+ (* i 2) beta))>
#<alt (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))>

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

Calls

159 calls:

Time	Variable		Point	Expression
4.0ms	i	@	inf	(* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
3.0ms	alpha	@	0	(/ (* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha)) (* beta beta))
2.0ms	i	@	0	(/ (* (* i (+ alpha (+ i beta))) (* i (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
2.0ms	beta	@	0	(/ (* (* i (+ alpha (+ i beta))) (* i (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
1.0ms	i	@	-inf	(/ (* (* i (+ alpha (+ i beta))) (* i (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))

rewrite522.0ms (3.3%)

Memory

38.4MiB live, 873.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 190×	`/-lowering-/.f32`
5 190×	`/-lowering-/.f64`
4 314×	`-lowering-.f32`
4 314×	`-lowering-.f64`
3 052×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	251
1	315	246
2	3262	246
0	8870	227

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1 109

Calls

Call 1

Inputs
(/ (* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
(+ (* i (+ i (+ alpha beta))) (* alpha beta))
(* (/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta))) (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
(/ (* i (+ i (+ alpha beta))) (* (+ (* i 2) beta) (+ (* i 2) beta)))
(/ (* i i) (* beta beta))
(* i i)
(* beta beta)
(* (/ (+ i alpha) beta) (/ i beta))
(/ (+ i alpha) beta)
(+ i alpha)
(/ i beta)
(/ (* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha)) (* beta beta))
(* i (+ (* i (+ (* (/ i beta) -6) 1)) alpha))
(+ (* i (+ (* (/ i beta) -6) 1)) alpha)
(+ (* (/ i beta) -6) 1)
(/ (* (* i (+ alpha (+ i beta))) (* i (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
(* (* i (+ alpha (+ i beta))) (* i (+ beta i)))
(* i (+ alpha (+ i beta)))
(+ alpha (+ i beta))
(* (+ (* i 2) beta) (+ (* i 2) beta))
(* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (.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 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (-.f64 #s(literal 0 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 #s(literal 0 binary64) (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha 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 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) (-.f64 #s(literal 0 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 i (.f64 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) (.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 #s(literal 1 binary64) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 i (+.f64 alpha (+.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 (.f64 (+.f64 alpha (+.f64 i beta)) (-.f64 #s(literal 0 binary64) i)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 #s(literal 0 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 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (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 (.f64 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) #s(literal 1 binary64)) (.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 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (.f64 i (.f64 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 #s(literal 0 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 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha 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 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (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 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha 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 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 alpha (+.f64 i beta)))))
(/.f64 (.f64 (.f64 (+.f64 alpha (+.f64 i beta)) (-.f64 #s(literal 0 binary64) i)) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (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 i #s(literal 2 binary64) beta) (neg.f64 (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (fma.f64 i #s(literal 2 binary64) beta))
(/.f64 (.f64 (.f64 i (.f64 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) (/.f64 #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 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(/.f64 (/.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) (neg.f64 (.f64 (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 i (+.f64 alpha (+.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 (neg.f64 (.f64 (.f64 (+.f64 alpha (+.f64 i beta)) (-.f64 #s(literal 0 binary64) i)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) (neg.f64 (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) (neg.f64 (.f64 (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 (neg.f64 (.f64 (.f64 i (.f64 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) #s(literal 1 binary64))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (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 i #s(literal 2 binary64) beta) (neg.f64 (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (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 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 alpha (+.f64 i beta))))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 alpha (+.f64 i beta)) (-.f64 #s(literal 0 binary64) i)) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (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 (fma.f64 i #s(literal 2 binary64) beta) (neg.f64 (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 (neg.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) (neg.f64 (fma.f64 i #s(literal 2 binary64) beta)))
(/.f64 (neg.f64 (.f64 (.f64 i (.f64 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))) (/.f64 #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 (fma.f64 i #s(literal 2 binary64) beta) (neg.f64 (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (neg.f64 (/.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64)))) (neg.f64 (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
(pow.f64 (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (/.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 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 i (.f64 (/.f64 (+.f64 alpha (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha 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 alpha (+.f64 i beta))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha 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 (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (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 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 #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 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.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 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))) (/.f64 #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))))
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simplify601.0ms (3.7%)

Memory

-23.0MiB live, 981.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 666×	`-lowering-.f32`
6 666×	`-lowering-.f64`
6 332×	`accelerator-lowering-fma.f32`
6 332×	`accelerator-lowering-fma.f64`
3 984×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1531	15732
1	5321	15502
0	8195	14385

Stop Event

1×	iter limit
1×	node limit

Counts

636 → 636

Calls

Call 1

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

Outputs
(/ (* alpha (* i (+ alpha beta))) (* beta (- (pow beta 2) 1)))
(/.f64 (.f64 alpha (.f64 i (+.f64 alpha beta))) (*.f64 beta (fma.f64 beta beta #s(literal -1 binary64))))
(* i (+ (* i (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (/ (* alpha (+ alpha beta)) (* beta (- (pow beta 2) 1)))))
(.f64 i (fma.f64 i (+.f64 (/.f64 alpha (.f64 beta (fma.f64 beta beta #s(literal -1 binary64)))) (-.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 (.f64 beta beta) (fma.f64 beta beta #s(literal -1 binary64)))) (/.f64 (.f64 (.f64 alpha (+.f64 alpha beta)) (.f64 #s(literal 4 binary64) (fma.f64 beta (fma.f64 beta beta #s(literal -1 binary64)) (.f64 beta (.f64 beta beta))))) (.f64 (.f64 beta (.f64 beta beta)) (.f64 (fma.f64 beta beta #s(literal -1 binary64)) (fma.f64 beta beta #s(literal -1 binary64))))))) (/.f64 (.f64 alpha (+.f64 alpha beta)) (.f64 beta (fma.f64 beta beta #s(literal -1 binary64))))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1))))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (/ (* alpha (+ alpha beta)) (* beta (- (pow beta 2) 1)))))
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (+ (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1)))) (* i (- (/ 1 (* (pow beta 2) (- (pow beta 2) 1))) (+ (* 32 (/ (* alpha (+ alpha beta)) (* (pow beta 2) (pow (- (pow beta 2) 1) 2)))) (+ (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 2 (/ alpha (* (pow beta 2) (- (pow beta 2) 1))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1))) (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1))))))))) (+ (/ (* alpha (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (+ (/ alpha (* beta (- (pow beta 2) 1))) (/ (pow (+ alpha beta) 2) (* (pow beta 2) (- (pow beta 2) 1))))) (/ (* alpha (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (/ (* alpha (+ alpha beta)) (* beta (- (pow beta 2) 1)))))
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1/16
#s(literal 1/16 binary64)
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ beta i)))
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(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/8 (/ beta i)) (* 2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 2))))))
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(- (+ 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 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 3))) (+ (* 1/8 (/ beta i)) (+ (* 2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (pow i 2))) (* 2 (/ (* beta (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) (* 2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))))))) (pow i 3)))))))))
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1/16
#s(literal 1/16 binary64)
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ beta i)))
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(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) i)) (* -1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i)))) i)))
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(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta)))) (* -1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* beta (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* beta (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta)))) (* -1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 beta))) i))))) i))) i)))
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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))))
(+ (/ (* 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 (.f64 i i) (/.f64 (.f64 (+.f64 i beta) (+.f64 i beta)) (.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 alpha i) (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta)))) (.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)))))
(+ (* alpha (+ (/ (* alpha (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (fma.f64 alpha (/.f64 (.f64 i (+.f64 i beta)) (.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 i (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta)))) (.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 (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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)))))
(+ (* alpha (+ (/ (* alpha (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 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)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (fma.f64 alpha (/.f64 (.f64 i (+.f64 i beta)) (.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 i (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta)))) (.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 (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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)))))
(/ (* (pow alpha 2) (* i (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 alpha alpha)) (.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))))
(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))))
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(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
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(* (pow alpha 2) (+ (/ (* i (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
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(* -1 (/ (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(-.f64 #s(literal 0 binary64) (/.f64 (.f64 (.f64 alpha alpha) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) 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)))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) 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 i (fma.f64 (+.f64 i beta) (-.f64 (-.f64 #s(literal 0 binary64) beta) i) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) beta) i)))) (.f64 alpha (.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))))))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha))))
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(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha))))
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(* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1)))
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(+ (* 1/4 (/ (pow (+ alpha i) 2) (- (* 4 (pow i 2)) 1))) (* beta (- (+ (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* beta (- (* 1/4 (/ (+ alpha i) (* i (- (* 4 (pow i 2)) 1)))) (+ (* 1/16 (/ (* (pow (+ alpha i) 2) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))) (* 1/4 (/ (* (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))) (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (* i (- (* 4 (pow i 2)) 1)))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))) (* (pow i 2) (- (* 4 (pow i 2)) 1)))))))) (* 1/16 (/ (* (pow (+ alpha i) 2) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))) (* (pow i 2) (pow (- (* 4 (pow i 2)) 1) 2)))))))
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(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (* 8 (/ (* (pow i 2) (+ alpha i)) beta))) (pow beta 2))
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(/ (- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (* 8 (/ (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i))))) (pow beta 2))) (+ (* 8 (/ (* (pow i 2) (+ alpha i)) beta)) (/ (* i (* (+ alpha i) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))) (pow beta 2))))) (pow beta 2))
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(/ (- (+ (* -1 (/ (+ (* 8 (* i (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* 8 (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i)))))) (* i (* (+ alpha i) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))) (+ (* i (* (+ alpha i) (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3))))) (* (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i)))) (- (+ (* 8 (pow i 2)) (* 16 (pow 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))))) (+ (* 8 (/ (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 8 (* (pow i 2) (+ alpha i))))) (pow beta 2))) (+ (* 8 (/ (* (pow i 2) (+ alpha i)) beta)) (/ (* i (* (+ alpha i) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))) (pow beta 2))))) (pow beta 2))
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(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha))) (.f64 beta beta))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta))) (pow beta 2))
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(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -8 (* i (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta))) (pow beta 2))
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(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -8 (/ (* i (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -8 (* i (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)) beta)))) (+ (* -8 (* i (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 8 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta))) (pow beta 2))
(/.f64 (neg.f64 (fma.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (/.f64 (-.f64 (-.f64 (.f64 i (fma.f64 (+.f64 alpha i) (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)))) (/.f64 (fma.f64 #s(literal -8 binary64) (/.f64 (.f64 i (+.f64 (fma.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 #s(literal 8 binary64) (.f64 i (-.f64 (.f64 i (fma.f64 (+.f64 alpha i) (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)))) (.f64 (.f64 (.f64 i i) (+.f64 alpha i)) #s(literal -8 binary64)))))) (.f64 (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)) (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64))))) beta) (-.f64 (-.f64 (fma.f64 (-.f64 (.f64 i (fma.f64 (+.f64 alpha i) (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)))) (.f64 (.f64 (.f64 i i) (+.f64 alpha i)) #s(literal -8 binary64))) (/.f64 (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)) beta) (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)))) (/.f64 (.f64 i (.f64 (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (fma.f64 (.f64 i (.f64 i i)) #s(literal -16 binary64) (.f64 #s(literal -4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))))))) beta)) (-.f64 (.f64 (.f64 i #s(literal -8 binary64)) (-.f64 (.f64 i (fma.f64 (+.f64 alpha i) (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)))) (.f64 (.f64 (.f64 i i) (+.f64 alpha i)) #s(literal -8 binary64)))) (.f64 (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)) (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)))))) beta)) (.f64 (.f64 (.f64 i i) (+.f64 alpha i)) #s(literal -8 binary64))) beta))) (*.f64 beta beta))
(* alpha beta)
(*.f64 alpha beta)
(+ (* alpha beta) (* i (+ alpha beta)))
(fma.f64 alpha beta (*.f64 i (+.f64 alpha beta)))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))
(+ (* alpha beta) (* i (+ alpha (+ beta i))))
(fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))
(pow i 2)
(*.f64 i i)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(.f64 (.f64 i i) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 alpha i)) (/.f64 beta i)))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(.f64 (.f64 i i) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 alpha i)) (fma.f64 alpha (/.f64 beta (*.f64 i i)) (/.f64 beta i))))
(* (pow i 2) (+ 1 (+ (/ alpha i) (+ (/ beta i) (/ (* alpha beta) (pow i 2))))))
(.f64 (.f64 i i) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 alpha i)) (fma.f64 alpha (/.f64 beta (*.f64 i i)) (/.f64 beta i))))
(pow i 2)
(*.f64 i i)
(* (pow i 2) (+ 1 (+ (/ alpha i) (/ beta i))))
(.f64 (.f64 i i) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 alpha i)) (/.f64 beta i)))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 (-.f64 #s(literal 0 binary64) alpha) beta) (/.f64 (*.f64 alpha beta) i)) i)))
(* (pow i 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha beta)) (* -1 (/ (* alpha beta) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 (-.f64 #s(literal 0 binary64) alpha) beta) (/.f64 (*.f64 alpha beta) i)) i)))
(* i (+ beta i))
(*.f64 i (+.f64 i beta))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(*.f64 (+.f64 i beta) (+.f64 alpha i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(*.f64 (+.f64 i beta) (+.f64 alpha i))
(+ (* alpha (+ beta i)) (* i (+ beta i)))
(*.f64 (+.f64 i beta) (+.f64 alpha i))
(* alpha (+ beta i))
(*.f64 alpha (+.f64 i beta))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)))
(* alpha (+ beta (+ i (/ (* i (+ beta i)) alpha))))
(*.f64 alpha (+.f64 beta (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)))
(* -1 (* alpha (+ (* -1 beta) (* -1 i))))
(-.f64 #s(literal 0 binary64) (*.f64 alpha (-.f64 (-.f64 #s(literal 0 binary64) beta) i)))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(*.f64 (-.f64 #s(literal 0 binary64) alpha) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)) beta))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(*.f64 (-.f64 #s(literal 0 binary64) alpha) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)) beta))
(* -1 (* alpha (+ (* -1 beta) (+ (* -1 i) (* -1 (/ (* i (+ beta i)) alpha))))))
(*.f64 (-.f64 #s(literal 0 binary64) alpha) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 i beta) alpha) i)) beta))
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(*.f64 (+.f64 alpha i) (+.f64 i beta))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(*.f64 (+.f64 alpha i) (+.f64 i beta))
(+ (* beta (+ alpha i)) (* i (+ alpha i)))
(*.f64 (+.f64 alpha i) (+.f64 i beta))
(* beta (+ alpha i))
(*.f64 beta (+.f64 alpha i))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(*.f64 beta (+.f64 alpha (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(*.f64 beta (+.f64 alpha (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)))
(* beta (+ alpha (+ i (/ (* i (+ alpha i)) beta))))
(*.f64 beta (+.f64 alpha (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)))
(* -1 (* beta (+ (* -1 alpha) (* -1 i))))
(-.f64 #s(literal 0 binary64) (*.f64 beta (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(*.f64 (-.f64 #s(literal 0 binary64) beta) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)) alpha))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(*.f64 (-.f64 #s(literal 0 binary64) beta) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)) alpha))
(* -1 (* beta (+ (* -1 alpha) (+ (* -1 i) (* -1 (/ (* i (+ alpha i)) beta))))))
(*.f64 (-.f64 #s(literal 0 binary64) beta) (-.f64 (neg.f64 (fma.f64 i (/.f64 (+.f64 alpha i) beta) i)) alpha))
(/ (* alpha (* i (+ alpha beta))) beta)
(/.f64 (.f64 alpha (.f64 i (+.f64 alpha beta))) beta)
(* i (+ (* i (- (+ (/ alpha beta) (/ (pow (+ alpha beta) 2) (pow beta 2))) (* 4 (/ (* alpha (+ alpha beta)) (pow beta 2))))) (/ (* alpha (+ alpha beta)) beta)))
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ 1 beta)) (* 2 (/ alpha (pow beta 2)))) (+ (* 4 (/ (* alpha (+ alpha beta)) (pow beta 3))) (* 4 (/ (- (+ (/ alpha beta) (/ (pow (+ alpha beta) 2) (pow beta 2))) (* 4 (/ (* alpha (+ alpha beta)) (pow beta 2)))) beta))))) (+ (/ alpha beta) (/ (pow (+ alpha beta) 2) (pow beta 2)))) (* 4 (/ (* alpha (+ alpha beta)) (pow beta 2))))) (/ (* alpha (+ alpha beta)) beta)))
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(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ 1 beta)) (+ (* 2 (/ alpha (pow beta 2))) (* i (- (/ 1 (pow beta 2)) (+ (* 4 (/ (- (+ (* 2 (/ 1 beta)) (* 2 (/ alpha (pow beta 2)))) (+ (* 4 (/ (* alpha (+ alpha beta)) (pow beta 3))) (* 4 (/ (- (+ (/ alpha beta) (/ (pow (+ alpha beta) 2) (pow beta 2))) (* 4 (/ (* alpha (+ alpha beta)) (pow beta 2)))) beta)))) beta)) (* 4 (/ (- (+ (/ alpha beta) (/ (pow (+ alpha beta) 2) (pow beta 2))) (* 4 (/ (* alpha (+ alpha beta)) (pow beta 2)))) (pow beta 2)))))))) (+ (* 4 (/ (* alpha (+ alpha beta)) (pow beta 3))) (* 4 (/ (- (+ (/ alpha beta) (/ (pow (+ alpha beta) 2) (pow beta 2))) (* 4 (/ (* alpha (+ alpha beta)) (pow beta 2)))) beta))))) (+ (/ alpha beta) (/ (pow (+ alpha beta) 2) (pow beta 2)))) (* 4 (/ (* alpha (+ alpha beta)) (pow beta 2))))) (/ (* alpha (+ alpha beta)) beta)))
(.f64 i (fma.f64 i (fma.f64 i (+.f64 (/.f64 #s(literal 2 binary64) beta) (+.f64 (fma.f64 i (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (.f64 #s(literal -4 binary64) (+.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 beta beta)) (/.f64 #s(literal 2 binary64) beta)) (.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 (+.f64 alpha beta) (.f64 beta (.f64 beta beta))) (/.f64 (+.f64 (/.f64 alpha beta) (+.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 beta beta)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha (+.f64 alpha beta)) (.f64 beta beta))))) beta)))) beta) (/.f64 (+.f64 (/.f64 alpha beta) (+.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 beta beta)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha (+.f64 alpha beta)) (.f64 beta beta))))) (.f64 beta beta))))) (.f64 #s(literal 2 binary64) (/.f64 alpha (.f64 beta beta)))) (.f64 #s(literal -4 binary64) (fma.f64 alpha (/.f64 (+.f64 alpha beta) (.f64 beta (.f64 beta beta))) (/.f64 (+.f64 (/.f64 alpha beta) (+.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 beta beta)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha (+.f64 alpha beta)) (.f64 beta beta))))) beta))))) (+.f64 (/.f64 alpha beta) (+.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 beta beta)) (.f64 #s(literal -4 binary64) (/.f64 (.f64 alpha (+.f64 alpha beta)) (.f64 beta beta)))))) (/.f64 (.f64 alpha (+.f64 alpha beta)) 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 (/ 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)) 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 beta 2) (pow i 2))) (+ (* 1/4 (/ beta i)) (/ (* beta (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 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 alpha beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 i i))) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (fma.f64 beta (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) beta)) (.f64 i i)) (/.f64 (*.f64 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 beta 2) (pow i 2))) (+ (* 1/4 (/ beta i)) (+ (* 1/4 (/ (* (pow beta 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta))) (pow i 3))) (+ (/ (* beta (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta))) (pow i 2)) (/ (* beta (- (* 1/4 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/16 (pow beta 2)) (* beta (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta)))))) (pow i 3))))))))
(.f64 (.f64 i i) (-.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (.f64 alpha (.f64 beta (+.f64 alpha beta))) (.f64 i (.f64 i i))) #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) i) (/.f64 (fma.f64 alpha beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 i i)))))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (fma.f64 (/.f64 beta i) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 beta beta) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) beta))) (.f64 i (.f64 i i))) (fma.f64 beta (/.f64 (+.f64 (fma.f64 (fma.f64 alpha beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) #s(literal 1/4 binary64) (.f64 (.f64 beta beta) #s(literal -1/16 binary64))) (.f64 beta (.f64 #s(literal -1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) beta)))) (.f64 i (.f64 i i))) (.f64 beta (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) 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 (/ 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)) beta)) i)))
(* (pow i 2) (+ 1/4 (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta))) (* 1/4 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -1 (/ (* beta (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta))) i)) (* -1/16 (/ (pow beta 2) i)))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (fma.f64 (/.f64 (neg.f64 (fma.f64 alpha beta (.f64 (+.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)) beta))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 beta beta) i) (/.f64 (.f64 beta (.f64 #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (+.f64 alpha beta)) beta))) i))) i)))
(* (pow i 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta))) (* -1 (/ (- (+ (* -1 (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* beta (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta)))) (* -1/16 (pow beta 2))))) (* 1/4 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -1 (/ (* beta (- (* 1/4 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -1 (* beta (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 beta)))) (* -1/16 (pow beta 2))))) i)) (* 1/4 (/ (* (pow beta 2) (- (* 1/4 (+ (* 2 alpha) (* 2 beta))) (* 1/4 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)) 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 alpha beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) #s(literal 1/4 binary64) (.f64 beta (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) beta)))) (.f64 (.f64 beta beta) #s(literal 1/16 binary64)))) (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 beta beta) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) beta)))) i) (/.f64 (.f64 beta (+.f64 (fma.f64 (neg.f64 (fma.f64 alpha beta (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) #s(literal 1/4 binary64) (.f64 beta (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) beta)))) (.f64 (*.f64 beta beta) #s(literal 1/16 binary64)))) i))) i)) i)))
(/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2))
(/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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)) (pow (+ beta (* 2 i)) 2)))
(fma.f64 alpha (/.f64 (.f64 i (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (*.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)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)))
(fma.f64 alpha (fma.f64 i (/.f64 (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 alpha (.f64 i (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) (/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (*.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)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (pow (+ beta (* 2 i)) 2)))) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow (+ beta (* 2 i)) 2)))
(fma.f64 alpha (fma.f64 i (/.f64 (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 alpha (.f64 i (+.f64 i beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) (/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))
(/ (* (pow alpha 2) (* i (+ beta i))) (pow (+ beta (* 2 i)) 2))
(.f64 (.f64 alpha alpha) (/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))
(* (pow alpha 2) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (pow (+ beta (* 2 i)) 2)))))
(.f64 (.f64 alpha alpha) (fma.f64 i (/.f64 (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta))) (.f64 alpha (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) (/.f64 (.f64 i (+.f64 i beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))))
(* (pow alpha 2) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (pow (+ beta (* 2 i)) 2))))))
(.f64 (.f64 alpha alpha) (fma.f64 i (/.f64 (+.f64 i beta) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (/.f64 (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta))) (.f64 alpha (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) (/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))))))
(* (pow alpha 2) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* alpha (pow (+ beta (* 2 i)) 2))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow alpha 2) (pow (+ beta (* 2 i)) 2))))))
(.f64 (.f64 alpha alpha) (fma.f64 i (/.f64 (+.f64 i beta) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 i (/.f64 (fma.f64 (+.f64 i beta) (+.f64 i beta) (.f64 i (+.f64 i beta))) (.f64 alpha (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))) (/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))))))
(* -1 (/ (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))) (pow (+ beta (* 2 i)) 2)))
(.f64 (neg.f64 (.f64 alpha alpha)) (/.f64 (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) beta) i)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow (+ beta (* 2 i)) 2))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (* alpha (pow (+ beta (* 2 i)) 2))))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) beta) i) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 i (fma.f64 (+.f64 i beta) (-.f64 (-.f64 #s(literal 0 binary64) beta) i) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) beta) i)))) (.f64 alpha (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow (+ beta (* 2 i)) 2))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (pow (+ beta (* 2 i)) 2))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) beta) i) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 i beta) (-.f64 (-.f64 #s(literal 0 binary64) beta) i) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) beta) i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.f64 alpha (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))) alpha))))
(* (pow alpha 2) (+ (* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow (+ beta (* 2 i)) 2))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (pow (+ beta (* 2 i)) 2)))) (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) (pow (+ beta (* 2 i)) 2))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) beta) i) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (-.f64 (/.f64 (.f64 i (fma.f64 (+.f64 i beta) (-.f64 (-.f64 #s(literal 0 binary64) beta) i) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) beta) i)))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.f64 alpha (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))))) alpha))))
(* 1/4 (pow (+ alpha i) 2))
(.f64 #s(literal 1/4 binary64) (.f64 (+.f64 alpha i) (+.f64 alpha i)))
(+ (* 1/4 (pow (+ alpha i) 2)) (* beta (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) i)) (* 1/4 (/ (pow (+ alpha i) 2) i)))))
(fma.f64 beta (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) i))) (.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 alpha i) (+.f64 alpha i))))
(+ (* 1/4 (pow (+ alpha i) 2)) (* beta (- (+ (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) i)) (* beta (- (+ (* 1/4 (/ (+ alpha i) i)) (* 1/4 (/ (pow (+ alpha i) 2) (pow i 2)))) (+ (* 1/16 (/ (pow (+ alpha i) 2) (pow i 2))) (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (pow i 2))))))) (* 1/4 (/ (pow (+ alpha i) 2) i)))))
(fma.f64 beta (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) i) (fma.f64 beta (+.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 alpha i) i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 i i))) (.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 i i)))) (.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 i i)))) (.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) i) #s(literal -1/4 binary64)))) (.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 alpha i) (+.f64 alpha i))))
(+ (* 1/4 (pow (+ alpha i) 2)) (* beta (- (+ (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) i)) (* beta (- (+ (* 1/4 (/ (+ alpha i) i)) (+ (* 1/4 (/ (pow (+ alpha i) 2) (pow i 2))) (* beta (- (+ (* 1/16 (/ (pow (+ alpha i) 2) (pow i 3))) (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (pow i 3)))) (+ (* 1/4 (/ (+ alpha i) (pow i 2))) (+ (* 1/4 (/ (- (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) i)) (* 1/4 (/ (pow (+ alpha i) 2) i))) (pow i 2))) (* 1/4 (/ (pow (+ alpha i) 2) (pow i 3))))))))) (+ (* 1/16 (/ (pow (+ alpha i) 2) (pow i 2))) (* 1/4 (/ (+ (* i (+ alpha i)) (pow (+ alpha i) 2)) (pow i 2))))))) (* 1/4 (/ (pow (+ alpha i) 2) i)))))
(fma.f64 beta (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) i) (fma.f64 beta (-.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 alpha i) i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 i i))) (.f64 beta (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 i (.f64 i i))) (.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 i (.f64 i i))))) (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) i))) (.f64 i i)) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 i (.f64 i i)))) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 alpha i)) (.f64 i i)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 i i)) (.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 i i))))) (.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 alpha i)) i) #s(literal -1/4 binary64)))) (.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 alpha i) (+.f64 alpha i))))
(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (* 4 (/ (* (pow i 2) (+ alpha i)) beta)))
(fma.f64 i (+.f64 alpha i) (fma.f64 i (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) beta) (.f64 #s(literal -4 binary64) (.f64 (.f64 i i) (/.f64 (+.f64 alpha i) beta)))))
(- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (* 4 (/ (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 4 (* (pow i 2) (+ alpha i))))) (pow beta 2))) (+ (* 4 (/ (* (pow i 2) (+ alpha i)) beta)) (* 4 (/ (* (pow i 3) (+ alpha i)) (pow beta 2))))))
(-.f64 (fma.f64 i (+.f64 alpha i) (fma.f64 i (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) beta) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 beta beta)))) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 i (fma.f64 i (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (.f64 (.f64 i i) #s(literal -4 binary64)) (+.f64 alpha i)))) (.f64 beta beta)) (.f64 #s(literal 4 binary64) (fma.f64 (.f64 i i) (/.f64 (+.f64 alpha i) beta) (/.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 alpha i)) (*.f64 beta beta))))))
(- (+ (* -1 (/ (+ (* 4 (* i (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* 4 (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 4 (* (pow i 2) (+ alpha i)))))) (* 4 (* (pow i 3) (+ alpha i))))))) (* 4 (* (pow i 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 4 (* (pow i 2) (+ alpha 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))))) (+ (* 4 (/ (* i (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* 4 (* (pow i 2) (+ alpha i))))) (pow beta 2))) (+ (* 4 (/ (* (pow i 2) (+ alpha i)) beta)) (* 4 (/ (* (pow i 3) (+ alpha i)) (pow beta 2))))))
(-.f64 (-.f64 (fma.f64 i (+.f64 alpha i) (fma.f64 i (/.f64 (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) beta) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 beta beta)))) (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 i (fma.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 #s(literal -4 binary64) (fma.f64 i (fma.f64 i (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (.f64 (.f64 i i) #s(literal -4 binary64)) (+.f64 alpha i))) (.f64 (.f64 i (.f64 i i)) (+.f64 alpha i))))) (.f64 (.f64 i i) (fma.f64 i (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (.f64 (.f64 i i) #s(literal -4 binary64)) (+.f64 alpha i)))))) (.f64 beta (.f64 beta beta)))) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 i (fma.f64 i (fma.f64 i (+.f64 alpha i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 (.f64 (.f64 i i) #s(literal -4 binary64)) (+.f64 alpha i)))) (.f64 beta beta)) (.f64 #s(literal 4 binary64) (fma.f64 (.f64 i i) (/.f64 (+.f64 alpha i) beta) (/.f64 (.f64 (.f64 i (.f64 i i)) (+.f64 alpha i)) (.f64 beta beta))))))
(* -1 (* i (+ (* -1 alpha) (* -1 i))))
(-.f64 #s(literal 0 binary64) (*.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta)))
(neg.f64 (fma.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (/.f64 (-.f64 (.f64 i (fma.f64 (+.f64 alpha i) (-.f64 (-.f64 #s(literal 0 binary64) i) alpha) (.f64 i (-.f64 (-.f64 #s(literal 0 binary64) i) alpha)))) (.f64 (.f64 (*.f64 i i) #s(literal -4 binary64)) (+.f64 alpha i))) beta)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* i (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))))) (* -4 (* (pow i 3) (+ (* -1 alpha) (* -1 i)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* (pow i 2) (+ (* -1 alpha) (* -1 i))))) beta)))
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(* (pow i 2) (+ (* i (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (+ (* i (- (+ (* -1 (* i (+ (* 32 (/ (+ alpha beta) (* (pow beta 2) (pow (- (pow beta 2) 1) 2)))) (+ (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (/ 1 (* (pow beta 2) (- (pow beta 2) 1))) (+ (/ (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (/ alpha (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1))) (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (/ alpha (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1))))))) (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (+ (/ (* (+ alpha beta) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))) (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (- (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (/ alpha (* (pow beta 2) (- (pow beta 2) 1)))) (/ (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (* (pow beta 2) (- (pow beta 2) 1)))))) (/ alpha (* (pow beta 2) (- (pow beta 2) 1))))) (/ (* (+ alpha beta) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 3) (pow (- (pow beta 2) 1) 2))))) (+ (/ 1 (- (pow beta 2) 1)) (/ alpha (* beta (- (pow beta 2) 1))))))
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1/16
#s(literal 1/16 binary64)
(- (+ 1/16 (* 1/16 (/ (+ alpha (* 2 beta)) i))) (* 1/8 (/ beta i)))
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(- (+ 1/16 (+ (* 1/16 (/ (* beta (+ alpha beta)) (pow i 2))) (* 1/16 (/ (+ alpha (* 2 beta)) i)))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/8 (/ beta i)) (* 2 (/ (* beta (- (* 1/16 (+ alpha (* 2 beta))) (* 1/8 beta))) (pow i 2))))))
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(- (+ 1/16 (+ (* -1 (/ (+ (* 1/256 (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (+ (* 1/16 (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ alpha (* 2 beta))) (* 1/8 beta)))) (* 2 (* beta (- (* 1/16 (* beta (+ alpha beta))) (+ (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) (* 2 (* beta (- (* 1/16 (+ alpha (* 2 beta))) (* 1/8 beta)))))))))) (pow i 3))) (+ (* 1/16 (/ (* beta (+ alpha beta)) (pow i 2))) (* 1/16 (/ (+ alpha (* 2 beta)) i))))) (+ (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))) (+ (* 1/8 (/ beta i)) (* 2 (/ (* beta (- (* 1/16 (+ alpha (* 2 beta))) (* 1/8 beta))) (pow i 2))))))
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1/16
#s(literal 1/16 binary64)
(+ 1/16 (* -1 (/ (- (* 1/16 (+ (* -1 beta) (* -1 (+ alpha beta)))) (* -1/8 beta)) i)))
(-.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal 1/16 binary64) (-.f64 (-.f64 #s(literal 0 binary64) beta) (+.f64 alpha beta)) (*.f64 beta #s(literal 1/8 binary64))) i))
(+ 1/16 (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (* beta (+ alpha beta))) (+ (* -2 (* beta (- (* 1/16 (+ (* -1 beta) (* -1 (+ alpha beta)))) (* -1/8 beta)))) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) i)) (* 1/16 (+ (* -1 beta) (* -1 (+ alpha beta))))) (* -1/8 beta)) i)))
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(+ 1/16 (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* beta (- (* 1/16 (* beta (+ alpha beta))) (+ (* -2 (* beta (- (* 1/16 (+ (* -1 beta) (* -1 (+ alpha beta)))) (* -1/8 beta)))) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) i)) (+ (* 1/256 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (+ (* 1/16 (* beta (+ alpha beta))) (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (+ (* -1 beta) (* -1 (+ alpha beta)))) (* -1/8 beta))) i))))) (+ (* -2 (* beta (- (* 1/16 (+ (* -1 beta) (* -1 (+ alpha beta)))) (* -1/8 beta)))) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) i)) (* 1/16 (+ (* -1 beta) (* -1 (+ alpha beta))))) (* -1/8 beta)) i)))
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(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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))))
(+ (/ (* alpha (* (pow i 2) (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (/.f64 (.f64 (.f64 i i) (+.f64 i beta)) (.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 (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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)))))
(+ (/ (* alpha (* (pow i 2) (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (/.f64 (.f64 (.f64 i i) (+.f64 i beta)) (.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 (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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)))))
(+ (/ (* alpha (* (pow i 2) (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
(fma.f64 alpha (/.f64 (.f64 (.f64 i i) (+.f64 i beta)) (.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 (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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)))))
(/ (* alpha (* (pow i 2) (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(/.f64 (.f64 alpha (.f64 (.f64 i i) (+.f64 i beta))) (.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))))
(* alpha (+ (/ (* (pow i 2) (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))))
(.f64 alpha (fma.f64 (.f64 i i) (/.f64 (.f64 (+.f64 i beta) (+.f64 i beta)) (.f64 alpha (.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 i beta)) (.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))))))
(* alpha (+ (/ (* (pow i 2) (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))))
(.f64 alpha (fma.f64 (.f64 i i) (/.f64 (.f64 (+.f64 i beta) (+.f64 i beta)) (.f64 alpha (.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 i beta)) (.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))))))
(* alpha (+ (/ (* (pow i 2) (+ beta i)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* alpha (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))))
(.f64 alpha (fma.f64 (.f64 i i) (/.f64 (.f64 (+.f64 i beta) (+.f64 i beta)) (.f64 alpha (.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 i beta)) (.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))))))
(/ (* alpha (* (pow i 2) (+ beta i))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
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(* (pow i 4) (+ 16 (* 32 (/ beta i))))
(.f64 (.f64 (.f64 i (.f64 i i)) i) (fma.f64 #s(literal 32 binary64) (/.f64 beta i) #s(literal 16 binary64)))
(* (pow i 4) (+ 16 (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i)))))))
(.f64 (.f64 (.f64 i (.f64 i i)) i) (+.f64 #s(literal 16 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (fma.f64 #s(literal 16 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (.f64 #s(literal 32 binary64) (/.f64 beta i)))))))
(* (pow i 4) (+ 16 (+ (* 4 (/ (* beta (- (pow beta 2) 1)) (pow i 3))) (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 4 (/ (pow beta 3) (pow i 3))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i)))))))))
(.f64 (.f64 (.f64 i (.f64 i i)) i) (+.f64 #s(literal 16 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 beta (fma.f64 beta beta #s(literal -1 binary64))) (.f64 i (.f64 i i))) (fma.f64 #s(literal 4 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 beta (.f64 beta beta)) (.f64 i (.f64 i i))) (fma.f64 #s(literal 16 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (*.f64 #s(literal 32 binary64) (/.f64 beta i)))))))))
(* 16 (pow i 4))
(.f64 #s(literal 16 binary64) (.f64 (.f64 i (.f64 i i)) i))
(* (pow i 4) (+ 16 (* 32 (/ beta i))))
(.f64 (.f64 (.f64 i (.f64 i i)) i) (fma.f64 #s(literal 32 binary64) (/.f64 beta i) #s(literal 16 binary64)))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i))) i))))
(.f64 (.f64 (.f64 i (.f64 i i)) i) (-.f64 #s(literal 16 binary64) (/.f64 (-.f64 (.f64 beta #s(literal -32 binary64)) (/.f64 (fma.f64 (.f64 beta beta) #s(literal 20 binary64) (*.f64 (fma.f64 beta beta #s(literal -1 binary64)) #s(literal 4 binary64))) i)) i)))
(* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) i))) i))))
(.f64 (.f64 (.f64 i (.f64 i i)) i) (-.f64 #s(literal 16 binary64) (/.f64 (-.f64 (.f64 beta #s(literal -32 binary64)) (/.f64 (-.f64 (fma.f64 (.f64 beta beta) #s(literal 20 binary64) (.f64 (fma.f64 beta beta #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -4 binary64) (fma.f64 beta (fma.f64 beta beta #s(literal -1 binary64)) (.f64 beta (.f64 beta beta)))) i)) i)) i)))
(* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1)))
(.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64)))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))))
(fma.f64 beta (fma.f64 #s(literal 4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i)))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))
(fma.f64 beta (fma.f64 #s(literal 4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (fma.f64 beta (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)) (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i))))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))))
(+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (* beta i)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1))))))
(fma.f64 beta (fma.f64 #s(literal 4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (fma.f64 beta (fma.f64 #s(literal 8 binary64) (.f64 i beta) (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64))) (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i))))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i i)) (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))))
(pow beta 4)
(pow.f64 beta #s(literal 4 binary64))
(* (pow beta 4) (+ 1 (* 8 (/ i beta))))
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 4) (- (+ 1 (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 2) (pow beta 2)))))) (/ 1 (pow beta 2))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 (.f64 i i) (.f64 beta beta)) #s(literal 24 binary64) (/.f64 (.f64 #s(literal 8 binary64) i) beta)) (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))))
(* (pow beta 4) (- (+ 1 (+ (* 4 (/ (* i (- (* 4 (pow i 2)) 1)) (pow beta 3))) (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (+ (* 16 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 3) (pow beta 3)))))))) (/ 1 (pow beta 2))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (.f64 beta (.f64 beta beta))) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) (fma.f64 (/.f64 (.f64 i i) (.f64 beta beta)) #s(literal 24 binary64) (/.f64 (.f64 #s(literal 16 binary64) (.f64 i (.f64 i i))) (.f64 beta (.f64 beta beta)))))) (/.f64 #s(literal 1 binary64) (*.f64 beta beta)))))
(pow beta 4)
(pow.f64 beta #s(literal 4 binary64))
(* (pow beta 4) (+ 1 (* 8 (/ i beta))))
(*.f64 (pow.f64 beta #s(literal 4 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) beta))) beta))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 i #s(literal -8 binary64)) (/.f64 (fma.f64 (*.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64)) beta)) beta)))
(* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* -1 (/ (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) beta)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1) beta))) beta))))
(.f64 (pow.f64 beta #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 i #s(literal -8 binary64)) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 i (.f64 i i)) #s(literal -16 binary64) (.f64 #s(literal -4 binary64) (.f64 i (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))))) beta) (fma.f64 (.f64 i i) #s(literal 24 binary64) #s(literal -1 binary64))) beta)) beta)))

eval315.0ms (2%)

Memory: 20.1MiB live, 589.5MiB allocated
Compiler: Compiled 82 130 to 5 584 computations (93.2% saved)

prune355.0ms (2.2%)

Memory

15.1MiB live, 775.8MiB allocated

Pruning

30 alts after pruning (24 fresh and 6 done)

	Pruned	Kept	Total
New	1 888	14	1 902
Fresh	11	10	21
Picked	2	3	5
Done	0	3	3
Total	1 901	30	1 931

Accuracy

99.0%

Counts

1 931 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	20.1%	(/.f64 (/.f64 (*.f64 i i) beta) beta)
	40.7%	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (.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)))
	27.5%	(/.f64 (*.f64 (/.f64 i beta) (fma.f64 i (fma.f64 i (/.f64 #s(literal -6 binary64) beta) #s(literal 1 binary64)) alpha)) beta)
	26.7%	(/.f64 (*.f64 (/.f64 i beta) i) beta)
	13.2%	(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
	18.5%	(/.f64 (.f64 (.f64 i (+.f64 i beta)) (.f64 i (+.f64 i beta))) (.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))))
	18.6%	(/.f64 (.f64 (.f64 i (+.f64 beta i)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.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))))
✓	18.7%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
	18.7%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 i beta) (+.f64 alpha i))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.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))))
	18.6%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 beta i) (+.f64 alpha 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))))
	18.5%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 i (+.f64 beta i))) (.f64 (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i beta)) (.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))))
	34.4%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (*.f64 i #s(literal 2 binary64))) #s(literal 1 binary64)))
	31.2%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) #s(literal 1 binary64)))
	11.9%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (*.f64 beta beta))
✓	13.8%	(/.f64 (.f64 i (fma.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)) alpha)) (.f64 beta beta))
	18.2%	(/.f64 (*.f64 i (+.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)))
	13.8%	(/.f64 (.f64 i (.f64 i (fma.f64 (/.f64 i beta) #s(literal -6 binary64) #s(literal 1 binary64)))) (*.f64 beta beta))
✓	15.3%	(/.f64 (.f64 i i) (.f64 beta beta))
	35.8%	(/.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	21.2%	(/.f64 i (*.f64 (/.f64 beta i) beta))
	28.6%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 beta (+.f64 i alpha)) (/.f64 beta i)))
	19.8%	(/.f64 #s(literal 1 binary64) (.f64 beta (/.f64 beta (.f64 i i))))
✓	28.9%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	24.5%	(.f64 (/.f64 (.f64 i (+.f64 i beta)) (.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 i (+.f64 alpha (+.f64 i beta))))
	26.8%	(*.f64 (/.f64 i beta) (/.f64 i beta))
	13.2%	(*.f64 (/.f64 alpha beta) (/.f64 i beta))
	27.4%	(.f64 (/.f64 #s(literal 1 binary64) beta) (.f64 i (/.f64 (fma.f64 i (fma.f64 i (/.f64 #s(literal -6 binary64) beta) #s(literal 1 binary64)) alpha) beta)))
	23.6%	(*.f64 i (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
✓	11.2%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	72.3%	#s(literal 1/16 binary64)

Compiler

Compiled 2 185 to 551 computations (74.8% saved)

regimes153.0ms (1%)

Memory

-23.1MiB live, 105.8MiB allocated

Counts

65 → 2

Calls

Call 1

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

Outputs
#s(literal 1/16 binary64)
(/.f64 (*.f64 (/.f64 i beta) (fma.f64 i (fma.f64 i (/.f64 #s(literal -6 binary64) beta) #s(literal 1 binary64)) alpha)) beta)

Calls

4 calls:

59.0ms	beta
53.0ms	(/.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)))
17.0ms	i
17.0ms	alpha

Results

Accuracy	Segments	Branch
76.7%	2	`alpha`
91.1%	2	`beta`
85.3%	2	`i`
77.6%	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)

regimes10.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

29 → 2

Calls

Call 1

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

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
91.0%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes6.0ms (0%)

Memory

-25.2MiB live, 12.9MiB allocated

Counts

12 → 2

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

beta

Results

Accuracy	Segments	Branch
88.9%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes5.0ms (0%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	beta
2.0ms	i

Results

Accuracy	Segments	Branch
72.3%	1	`i`
78.8%	2	`beta`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0%)

Memory

13.8MiB live, 13.8MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

2.0ms

beta

2.0ms

(/.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
72.3%	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)))`
77.4%	2	`beta`

Compiler

Compiled 60 to 20 computations (66.7% saved)

regimes2.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

beta

Results

Accuracy	Segments	Branch
76.9%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes7.0ms (0%)

Memory

-34.5MiB live, 9.7MiB 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:

4.0ms	beta
1.0ms	alpha
1.0ms	i

Results

Accuracy	Segments	Branch
72.3%	1	`i`
72.3%	1	`alpha`
72.3%	1	`beta`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch16.0ms (0.1%)

Memory

21.3MiB live, 21.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.0888881764889414e+121	2.2142268082591589e+123

Samples

10.0ms

112×

valid

Compiler

Compiled 83 to 40 computations (51.8% saved)

Precisions

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

ival-mult: 3.0ms (44% of total)

ival-add: 2.0ms (29.3% of total)

ival-div: 1.0ms (14.7% 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)

bsearch19.0ms (0.1%)

Memory

-5.4MiB live, 33.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	1.0888881764889414e+121	2.2142268082591589e+123

Samples

13.0ms

112×

valid

Compiler

Compiled 77 to 36 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-div: 5.0ms (47.4% of total)

ival-mult: 3.0ms (28.4% of total)

ival-add: 2.0ms (19% of total)

ival-sub: 1.0ms (9.5% 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

-5.0MiB live, 32.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	1.0888881764889414e+121	2.2142268082591589e+123

Samples

11.0ms

112×

valid

Compiler

Compiled 75 to 34 computations (54.7% saved)

Precisions

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

ival-mult: 3.0ms (42.9% of total)

ival-add: 2.0ms (28.6% of total)

ival-sub: 1.0ms (14.3% of total)

ival-div: 1.0ms (14.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch21.0ms (0.1%)

Memory

2.6MiB live, 35.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	1.1256727753456965e+199	7.225526828201189e+202

Samples

15.0ms

128×

valid

Compiler

Compiled 75 to 35 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 3.0ms (37.9% of total)

ival-add: 2.0ms (25.2% of total)

ival-sub: 1.0ms (12.6% of total)

ival-div: 1.0ms (12.6% of total)

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

exact: 0.0ms (0% of total)

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

bsearch19.0ms (0.1%)

Memory

-2.9MiB live, 41.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	1.0888881764889414e+121	2.2142268082591589e+123

Samples

13.0ms

112×

valid

Compiler

Compiled 75 to 35 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (57.7% of total)

ival-add: 2.0ms (19.2% of total)

ival-sub: 1.0ms (9.6% of total)

ival-div: 1.0ms (9.6% of total)

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

exact: 0.0ms (0% of total)

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

bsearch18.0ms (0.1%)

Memory

8.3MiB live, 47.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.1256727753456965e+199	7.225526828201189e+202

Samples

12.0ms

128×

valid

Compiler

Compiled 75 to 35 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 4.0ms (44.3% of total)

ival-add: 2.0ms (22.1% of total)

ival-sub: 1.0ms (11.1% of total)

ival-div: 1.0ms (11.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Memory

-15.5MiB live, 24.1MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	83
1	43	83

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 beta #s(literal 11000000000000000066725478820095151949709469034627961299645755076173637028100320903478043295290517846054855965757558226944 binary64)) #s(literal 1/16 binary64) (/.f64 (*.f64 (/.f64 i beta) (fma.f64 i (fma.f64 i (/.f64 #s(literal -6 binary64) beta) #s(literal 1 binary64)) alpha)) beta))
(if (<=.f64 beta #s(literal 2199999999999999921605151124416169925509057994842114628066551448503482456116510605218693615518711246410229068746484183203840 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 11000000000000000066725478820095151949709469034627961299645755076173637028100320903478043295290517846054855965757558226944 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 72000000000000001627981931811332602889132500400856821805257528551614556367214517005114080733977377299296625176664715008489851486160079786944637921848618204154576193366986925637433454928538926794946904064 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 2199999999999999921605151124416169925509057994842114628066551448503482456116510605218693615518711246410229068746484183203840 binary64)) #s(literal 1/16 binary64) (/.f64 (.f64 i i) (.f64 beta beta)))
(if (<=.f64 beta #s(literal 72000000000000001627981931811332602889132500400856821805257528551614556367214517005114080733977377299296625176664715008489851486160079786944637921848618204154576193366986925637433454928538926794946904064 binary64)) #s(literal 1/16 binary64) (.f64 alpha (/.f64 i (.f64 beta beta))))
#s(literal 1/16 binary64)

Outputs
(if (<=.f64 beta #s(literal 11000000000000000066725478820095151949709469034627961299645755076173637028100320903478043295290517846054855965757558226944 binary64)) #s(literal 1/16 binary64) (/.f64 (*.f64 (/.f64 i beta) (fma.f64 i (fma.f64 i (/.f64 #s(literal -6 binary64) beta) #s(literal 1 binary64)) alpha)) beta))
(if (<=.f64 beta #s(literal 2199999999999999921605151124416169925509057994842114628066551448503482456116510605218693615518711246410229068746484183203840 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 2199999999999999921605151124416169925509057994842114628066551448503482456116510605218693615518711246410229068746484183203840 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 (+.f64 i alpha) beta)))
(if (<=.f64 beta #s(literal 11000000000000000066725478820095151949709469034627961299645755076173637028100320903478043295290517846054855965757558226944 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 72000000000000001627981931811332602889132500400856821805257528551614556367214517005114080733977377299296625176664715008489851486160079786944637921848618204154576193366986925637433454928538926794946904064 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 alpha beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 72000000000000001627981931811332602889132500400856821805257528551614556367214517005114080733977377299296625176664715008489851486160079786944637921848618204154576193366986925637433454928538926794946904064 binary64)) #s(literal 1/16 binary64) (*.f64 (/.f64 i beta) (/.f64 alpha beta)))
(if (<=.f64 beta #s(literal 2199999999999999921605151124416169925509057994842114628066551448503482456116510605218693615518711246410229068746484183203840 binary64)) #s(literal 1/16 binary64) (/.f64 (.f64 i i) (.f64 beta beta)))
(if (<=.f64 beta #s(literal 72000000000000001627981931811332602889132500400856821805257528551614556367214517005114080733977377299296625176664715008489851486160079786944637921848618204154576193366986925637433454928538926794946904064 binary64)) #s(literal 1/16 binary64) (.f64 alpha (/.f64 i (.f64 beta beta))))
#s(literal 1/16 binary64)

soundness1.0s (6.3%)

Memory

-1.7MiB live, 1 129.7MiB allocated

Rules

9 164×	`accelerator-lowering-fma.f32`
9 164×	`accelerator-lowering-fma.f64`
7 144×	`accelerator-lowering-fma.f32`
7 144×	`accelerator-lowering-fma.f64`
6 998×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	251
1	315	246
2	3262	246
0	8870	227
0	1089	12630
1	3841	11840
0	8260	10972
0	1881	22224
1	6557	22208
0	8345	20468
0	1723	19077
1	6091	18772
0	8464	17391
0	43	298
1	352	294
2	3546	294
0	8722	276
0	46	289
1	374	275
2	4134	275
0	8534	253

Stop Event

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

Compiler

Compiled 306 to 177 computations (42.2% saved)

preprocess84.0ms (0.5%)

Memory: 18.3MiB live, 174.8MiB allocated
Compiler: Compiled 330 to 134 computations (59.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze16.0ms (0.1%)

sample2.4s (15.1%)

preprocess881.0ms (5.5%)

explain456.0ms (2.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify363.0ms (2.3%)

localize77.0ms (0.5%)

series62.0ms (0.4%)

rewrite443.0ms (2.8%)

simplify793.0ms (4.9%)

eval220.0ms (1.4%)

prune473.0ms (3%)

simplify378.0ms (2.4%)

localize139.0ms (0.9%)

series75.0ms (0.5%)

rewrite913.0ms (5.7%)

simplify800.0ms (5%)

eval261.0ms (1.6%)

prune297.0ms (1.9%)

simplify361.0ms (2.3%)

localize191.0ms (1.2%)

series90.0ms (0.6%)

rewrite517.0ms (3.2%)

simplify1.1s (7.1%)

eval278.0ms (1.7%)

prune334.0ms (2.1%)

simplify642.0ms (4%)

localize172.0ms (1.1%)

series58.0ms (0.4%)

rewrite522.0ms (3.3%)

simplify601.0ms (3.7%)

eval315.0ms (2%)

prune355.0ms (2.2%)

regimes153.0ms (1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes7.0ms (0%)

bsearch16.0ms (0.1%)

bsearch19.0ms (0.1%)

bsearch16.0ms (0.1%)

bsearch21.0ms (0.1%)

bsearch19.0ms (0.1%)

bsearch18.0ms (0.1%)

simplify9.0ms (0.1%)

soundness1.0s (6.3%)

preprocess84.0ms (0.5%)

end0.0ms (0%)

Profiling