Metrics for Octave 3.8, jcobi/4

analyze15.0ms (0.1%)

Memory

-0.4MiB live, 42.3MiB 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 (16.7%)

Memory

4.8MiB live, 2 305.3MiB allocated

Samples

1.7s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-mult: 408.0ms (33.9% of total)

ival-add: 335.0ms (27.8% of total)

ival-div: 197.0ms (16.4% of total)

ival->: 151.0ms (12.6% of total)

ival-sub: 81.0ms (6.7% of total)

ival-and: 15.0ms (1.2% of total)

exact: 13.0ms (1.1% of total)

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

Bogosity

preprocess363.0ms (2.6%)

Memory

-1.9MiB live, 665.0MiB allocated

Algorithm

1×	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	81	508
1	377	482
2	2068	478
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))))

Symmetry

(sort alpha beta)

explain344.0ms (2.4%)

Memory

4.3MiB live, 598.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
227	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))))`
166	1	(-2.58840791909527e-89 1.4493890744421105e+297 2.902413100137247e+135)	-	`(/.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	184	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	169
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	227
↳	`(*.f64 beta alpha)`	overflow	15
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	336
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	184
`/.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	144	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	169
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	227
↳	`(*.f64 beta alpha)`	overflow	15
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	336
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	184
↳	`(/.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	144
↳	`(-.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	184
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	184
`/.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	43	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	169
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	227
↳	`(*.f64 beta alpha)`	overflow	15
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	336
`/.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	23	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	184
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	184

Confusion

	Predicted +	Predicted -
+	227	0
-	0	29

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	227	0	0
-	0	0	29

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	29
1	60
2	167

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

60.0ms

512×

valid

Compiler

Compiled 482 to 72 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 14.0ms (38% of total)

ival-add: 9.0ms (24.4% of total)

ival-sub: 7.0ms (19% of total)

ival-div: 6.0ms (16.3% of total)

exact: 1.0ms (2.7% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	11.8%	(/.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)))

Status

Accuracy

Program

▶

11.8%

(/.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)))

Compiler

Compiled 56 to 17 computations (69.6% saved)

simplify350.0ms (2.5%)

Memory

-9.3MiB live, 711.7MiB 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)

localize51.0ms (0.4%)

Memory

18.7MiB live, 97.6MiB 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	37.7%	(/.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	24.7%	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))

Samples

27.0ms

256×

valid

Compiler

Compiled 185 to 19 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 6.0ms (39.1% of total)

ival-add: 5.0ms (32.6% of total)

ival-div: 3.0ms (19.6% of total)

ival-sub: 1.0ms (6.5% of total)

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

exact: 0.0ms (0% of total)

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

series91.0ms (0.6%)

Memory

4.9MiB live, 83.2MiB 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)))))>
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#<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
27.0ms	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))
15.0ms	i	@	0	(/ (* (* 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))
3.0ms	i	@	inf	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
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))

rewrite725.0ms (5.1%)

Memory

-6.1MiB live, 701.4MiB 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)) (neg.f64 (.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)) (neg.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))))
(neg.f64 (/.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 (.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 (.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)) (+.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)))) (neg.f64 (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 #s(literal 1 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 (.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))))))
(/.f64 #s(literal 1 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 i (+.f64 alpha (+.f64 i beta))) (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 #s(literal 1 binary64) (neg.f64 (neg.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))))))))
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simplify477.0ms (3.4%)

Memory

-8.3MiB live, 756.3MiB 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)))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (+ (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* i (- (/ 1 (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (+ (* 32 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (+ (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))) (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
(- (+ 1/16 (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2))))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/8 (/ (+ alpha beta) i)) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))))))
(- (+ 1/16 (+ (* 1/16 (/ (* alpha (* beta (+ alpha beta))) (pow i 3))) (+ (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i)) (* 1/16 (/ (+ (* alpha beta) (pow (+ alpha beta) 2)) (pow i 2)))))) (+ (* 1/256 (/ (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (pow i 3))) (+ (* 1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 3))) (+ (* 1/8 (/ (+ alpha beta) i)) (+ (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (pow i 2))) (* 2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* alpha beta) (pow (+ alpha beta) 2))) (+ (* 1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) (* 2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))))))) (pow i 3)))))))))
1/16
(- (+ 1/16 (* 1/16 (/ (+ (* 2 alpha) (* 2 beta)) i))) (* 1/8 (/ (+ alpha beta) i)))
(+ 1/16 (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* 1/16 (/ (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i)) (* -1/256 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i)))) i)))
(+ 1/16 (* -1 (/ (+ (* -1 (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) (* -1 (/ (- (+ (* -1 (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* 1/16 (/ (* alpha (* beta (+ alpha beta))) i))) (+ (* -2 (/ (* (+ alpha beta) (- (* 1/16 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (+ (* -2 (* (+ alpha beta) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta))))) (* -1/256 (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) i)) (+ (* -1/256 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (* 1/16 (/ (* (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) (- (* 1/16 (+ (* 2 alpha) (* 2 beta))) (* 1/8 (+ alpha beta)))) i))))) i))) i)))
(/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* (pow i 2) (* (pow (+ beta i) 2) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 4) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* (pow i 2) (pow (+ beta i) 2)) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))))
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(/ (* i (+ beta i)) (pow alpha 2))
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(* -1 (/ (* i (+ (* -1 beta) (* -1 i))) (pow alpha 2)))
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))
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(/ (* i (+ alpha i)) (pow beta 2))
(/ (- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 4 alpha) (* 8 i)))) beta)) (pow beta 2))
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(* -1 (/ (* i (+ (* -1 alpha) (* -1 i))) (pow beta 2)))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(/ (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -4 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1))))))) beta)) (+ (* -1 (/ (* i (* (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) (+ (* -1 alpha) (* -1 i)))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)) beta)))) (+ (* -4 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (+ (* -1 alpha) (* -1 i)) (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1)))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 4 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta))) (pow beta 2))
(* 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)))))
(.f64 i (fma.f64 i (+.f64 (fma.f64 i (-.f64 (fma.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 (.f64 #s(literal 4 binary64) (.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.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) (.f64 (+.f64 alpha beta) (+.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) 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-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 (+.f64 alpha beta) #s(literal -1/8 binary64))) 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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(- (+ (* 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) (- (+ 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))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (- (pow (+ beta (* 2 i)) 2) 1) alpha))) alpha))))
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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)
(fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))
(- (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)
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(- (+ (* beta (+ 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)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta)))))
(* (pow beta 2) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta)))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (- (pow (+ alpha (* 2 i)) 2) 1) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64)) beta)) beta)))
(- (pow (+ alpha beta) 2) 1)
(fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1)
(fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
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(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (+.f64 (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i)) (/.f64 #s(literal -1 binary64) (*.f64 i i)))))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
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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))))))
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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))))))))
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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))))
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(* (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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(- (+ (* -1 (/ (+ (* (+ (* 2 beta) (* 4 i)) (- (* (pow i 2) (pow (+ beta i) 2)) (+ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i))))))) (pow alpha 3))) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2))))) (+ (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) alpha) (+ (/ (* i (* (+ beta i) (pow (+ beta (* 2 i)) 2))) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))))) (pow alpha 2)))))
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(* -1 (* i (+ (* -1 beta) (* -1 i))))
(*.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))
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(/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2))
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(+ (* beta (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))
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(+ (* beta (- (+ (* beta (- (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 4))))) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (pow (+ alpha (* 2 i)) 2))) (/ (* (pow i 2) (* (pow (+ alpha i) 2) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow (+ alpha (* 2 i)) 2)))
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(+ (* 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)))
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(* i (+ alpha i))
(*.f64 i (+.f64 alpha i))
(- (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta))
(fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) beta))))
(- (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))
(-.f64 (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 beta beta))) (fma.f64 i (+.f64 (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) beta) (/.f64 (.f64 (+.f64 alpha i) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) (.f64 beta beta))) (/.f64 (.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))))))) (*.f64 beta beta))))
(- (+ (* -1 (/ (+ (* (+ (* 2 alpha) (* 4 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i))))))) (pow beta 3))) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2))))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (+ (/ (* i (* (+ alpha i) (pow (+ alpha (* 2 i)) 2))) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))))) (pow beta 2)))))
(-.f64 (-.f64 (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (.f64 beta beta))) (/.f64 (fma.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (-.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (fma.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))))) (.f64 (.f64 i (+.f64 alpha i)) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))))))) (.f64 beta (.f64 beta beta)))) (fma.f64 i (+.f64 (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) beta) (/.f64 (.f64 (+.f64 alpha i) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))) (.f64 beta beta))) (/.f64 (.f64 (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 i (-.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))))))) (*.f64 beta beta))))
(* -1 (* i (+ (* -1 alpha) (* -1 i))))
(neg.f64 (*.f64 i (-.f64 (neg.f64 i) alpha)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))) beta)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (+.f64 (/.f64 (+.f64 (fma.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))))) (.f64 i (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))) (neg.f64 beta)) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (*.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) beta)))
(+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* (pow i 2) (pow (+ alpha i) 2)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i)))))))) beta)) (+ (* (pow i 2) (pow (+ alpha i) 2)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i))))))) beta))) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))))) (* -1 (* i (* (pow (+ alpha (* 2 i)) 2) (+ (* -1 alpha) (* -1 i))))))) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) (* 2 (* i (* (+ alpha (* 2 i)) (+ (* -1 alpha) (* -1 i)))))) beta)))
(neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (+.f64 (fma.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)) (.f64 #s(literal 2 binary64) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))))) (.f64 i (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) beta) (-.f64 (fma.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))) beta) (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i)))) (-.f64 (.f64 (.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha)) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) (.f64 i (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha)))))) (neg.f64 beta)) (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (.f64 #s(literal -2 binary64) (.f64 (*.f64 i (fma.f64 i #s(literal 2 binary64) alpha)) (-.f64 (neg.f64 i) alpha))))) beta)))
(* alpha (* beta (* i (+ alpha beta))))
(.f64 (.f64 alpha beta) (*.f64 i (+.f64 alpha beta)))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (pow (+ alpha beta) 2)))))
(.f64 i (fma.f64 i (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta)) (.f64 alpha (.f64 beta (+.f64 alpha beta)))))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ (* 2 alpha) (* 2 beta))) (pow (+ alpha beta) 2))))))
(.f64 i (fma.f64 i (fma.f64 i (.f64 #s(literal 2 binary64) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) (.f64 alpha (*.f64 beta (+.f64 alpha beta)))))
(* i (+ (* alpha (* beta (+ alpha beta))) (* i (+ (* alpha beta) (+ (* i (+ i (+ (* 2 alpha) (* 2 beta)))) (pow (+ alpha beta) 2))))))
(.f64 i (fma.f64 i (fma.f64 i (fma.f64 #s(literal 2 binary64) (+.f64 alpha beta) i) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 alpha beta))) (.f64 alpha (.f64 beta (+.f64 alpha beta)))))
(pow i 4)
(pow.f64 i #s(literal 4 binary64))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (/ (pow (+ alpha beta) 2) (pow i 2)))))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)) (fma.f64 alpha (/.f64 beta (.f64 i i)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i)))))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (+ (* 2 (/ beta i)) (+ (/ (* alpha beta) (pow i 2)) (+ (/ (* alpha (* beta (+ alpha beta))) (pow i 3)) (/ (pow (+ alpha beta) 2) (pow i 2))))))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)) (fma.f64 alpha (+.f64 (/.f64 beta (.f64 i i)) (/.f64 (.f64 beta (+.f64 alpha beta)) (.f64 i (.f64 i i)))) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (*.f64 i i)))))
(pow i 4)
(pow.f64 i #s(literal 4 binary64))
(* (pow i 4) (+ 1 (+ (* 2 (/ alpha i)) (* 2 (/ beta i)))))
(*.f64 (pow.f64 i #s(literal 4 binary64)) (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 alpha i) (/.f64 beta i)) #s(literal 1 binary64)))
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (+ (* -1 (/ (* alpha beta) i)) (* -1 (/ (pow (+ alpha beta) 2) i)))) i))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 alpha beta) (neg.f64 (fma.f64 alpha (/.f64 beta i) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)))) i)))
(* (pow i 4) (+ 1 (* -1 (/ (+ (* -1 (+ (* 2 alpha) (* 2 beta))) (* -1 (/ (+ (* -1 (+ (* -1 (* alpha beta)) (* -1 (pow (+ alpha beta) 2)))) (/ (* alpha (* beta (+ alpha beta))) i)) i))) i))))
(.f64 (pow.f64 i #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) (+.f64 alpha beta)) (/.f64 (-.f64 (/.f64 (.f64 alpha (.f64 beta (+.f64 alpha beta))) i) (neg.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (*.f64 alpha beta)))) i)) i)))
(* (pow i 2) (pow (+ beta i) 2))
(.f64 (.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)))
(+ (* alpha (* i (+ (* i (+ beta i)) (pow (+ beta i) 2)))) (* (pow i 2) (pow (+ beta i) 2)))
(fma.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i)) (.f64 alpha (.f64 i (*.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))))
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))
(fma.f64 alpha (fma.f64 alpha (.f64 i (+.f64 beta i)) (.f64 i (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))) (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))))
(+ (* alpha (+ (* alpha (* i (+ beta i))) (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))))) (* (pow i 2) (pow (+ beta i) 2)))
(fma.f64 alpha (fma.f64 alpha (.f64 i (+.f64 beta i)) (.f64 i (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)))) (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))))
(* (pow alpha 2) (* i (+ beta i)))
(.f64 (.f64 i (+.f64 beta i)) (*.f64 alpha alpha))
(* (pow alpha 2) (+ (* i (+ beta i)) (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha)))
(.f64 (.f64 alpha alpha) (.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha))))
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))
(.f64 (.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 alpha alpha)))))
(* (pow alpha 2) (+ (* i (+ beta i)) (+ (/ (* i (+ (* i (+ beta i)) (pow (+ beta i) 2))) alpha) (/ (* (pow i 2) (pow (+ beta i) 2)) (pow alpha 2)))))
(.f64 (.f64 alpha alpha) (fma.f64 i (+.f64 (+.f64 beta i) (/.f64 (.f64 (+.f64 beta i) (+.f64 (+.f64 beta i) i)) alpha)) (.f64 (.f64 i i) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) (*.f64 alpha alpha)))))
(* -1 (* (pow alpha 2) (* i (+ (* -1 beta) (* -1 i)))))
(.f64 (.f64 alpha alpha) (*.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta)))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i))))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (.f64 i (+.f64 (-.f64 (neg.f64 i) beta) (/.f64 (.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) alpha)))))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) beta) (/.f64 (fma.f64 i (.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) (.f64 (.f64 i (neg.f64 i)) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) alpha))) alpha))))
(* (pow alpha 2) (+ (* -1 (* i (+ (* -1 beta) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ beta i) 2)) alpha)) (* i (+ (* -1 (* i (+ beta i))) (* (+ beta i) (+ (* -1 beta) (* -1 i)))))) alpha))))
(.f64 (.f64 alpha alpha) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) beta) (/.f64 (fma.f64 i (.f64 (+.f64 beta i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) beta))) (.f64 (.f64 i (neg.f64 i)) (/.f64 (.f64 (+.f64 beta i) (+.f64 beta i)) alpha))) alpha))))
(* (pow i 2) (pow (+ alpha i) 2))
(.f64 (.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i)))
(+ (* beta (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2)))) (* (pow i 2) (pow (+ alpha i) 2)))
(fma.f64 (.f64 beta i) (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 (.f64 i i) (*.f64 (+.f64 alpha i) (+.f64 alpha i))))
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))
(fma.f64 beta (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 beta (.f64 i (+.f64 alpha i)))) (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))))
(+ (* beta (+ (* beta (* i (+ alpha i))) (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))))) (* (pow i 2) (pow (+ alpha i) 2)))
(fma.f64 beta (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) (.f64 beta (.f64 i (+.f64 alpha i)))) (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))))
(* (pow beta 2) (* i (+ alpha i)))
(.f64 (.f64 i (+.f64 alpha i)) (*.f64 beta beta))
(* (pow beta 2) (+ (* i (+ alpha i)) (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta)))
(.f64 (.f64 beta beta) (.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta))))
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))
(.f64 (.f64 beta beta) (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (*.f64 beta beta))))
(* (pow beta 2) (+ (* i (+ alpha i)) (+ (/ (* i (+ (* i (+ alpha i)) (pow (+ alpha i) 2))) beta) (/ (* (pow i 2) (pow (+ alpha i) 2)) (pow beta 2)))))
(.f64 (.f64 beta beta) (fma.f64 i (+.f64 (+.f64 alpha i) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta)) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (*.f64 beta beta))))
(* -1 (* (pow beta 2) (* i (+ (* -1 alpha) (* -1 i)))))
(.f64 (.f64 beta beta) (neg.f64 (*.f64 i (-.f64 (neg.f64 i) alpha))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i))))) beta))))
(.f64 (.f64 beta beta) (neg.f64 (.f64 i (+.f64 (-.f64 (neg.f64 i) alpha) (/.f64 (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) beta)))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))
(.f64 (.f64 beta beta) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (neg.f64 beta))) beta))))
(* (pow beta 2) (+ (* -1 (* i (+ (* -1 alpha) (* -1 i)))) (* -1 (/ (+ (* -1 (/ (* (pow i 2) (pow (+ alpha i) 2)) beta)) (* i (+ (* -1 (* i (+ alpha i))) (* (+ alpha i) (+ (* -1 alpha) (* -1 i)))))) beta))))
(.f64 (.f64 beta beta) (neg.f64 (fma.f64 i (-.f64 (neg.f64 i) alpha) (/.f64 (fma.f64 i (.f64 (+.f64 alpha i) (+.f64 (neg.f64 i) (-.f64 (neg.f64 i) alpha))) (/.f64 (.f64 (.f64 i i) (.f64 (+.f64 alpha i) (+.f64 alpha i))) (neg.f64 beta))) beta))))
(pow (+ beta (* 2 i)) 2)
(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
(+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))
(fma.f64 alpha (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) alpha)) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(pow alpha 2)
(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))))
(* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))
(.f64 (.f64 alpha alpha) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 beta alpha) (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (.f64 alpha alpha))))
(pow alpha 2)
(*.f64 alpha alpha)
(* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))
(.f64 (.f64 alpha alpha) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) beta) alpha) #s(literal 1 binary64)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha)) alpha)))
(* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))
(.f64 (.f64 alpha alpha) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) alpha)) alpha)))
(pow (+ alpha (* 2 i)) 2)
(*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha))
(+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))
(fma.f64 beta (fma.f64 alpha #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) beta)) (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta))))
(* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))
(.f64 (.f64 beta beta) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 alpha beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64))) (/.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (.f64 beta beta))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 2 binary64) alpha) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (neg.f64 beta))) beta)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))
(.f64 (.f64 beta beta) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) (fma.f64 i #s(literal 2 binary64) alpha) (/.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha)) (neg.f64 beta))) beta)))
(pow (+ alpha beta) 2)
(*.f64 (+.f64 alpha beta) (+.f64 alpha beta))
(+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))
(*.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))
(fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 alpha (+.f64 beta i))) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i))))
(* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))
(.f64 (.f64 i i) (+.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (.f64 i i))))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 (+.f64 alpha beta) i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)) i)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))
(.f64 (.f64 i i) (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 (.f64 (+.f64 alpha beta) #s(literal -4 binary64)) (/.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) i)) i)))

eval581.0ms (4.1%)

Memory: -87.5MiB live, 284.2MiB allocated
Compiler: Compiled 120 552 to 4 628 computations (96.2% saved)

prune366.0ms (2.6%)

Memory

15.0MiB live, 328.1MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	1 398	14	1 412
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1 399	14	1 413

Accuracy

86.1%

Counts

1 413 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	13.2%	(/.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))
▶	11.4%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
▶	10.9%	(/.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))))
	10.6%	(/.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))))
▶	31.0%	(/.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)))
	2.9%	(/.f64 (.f64 i (+.f64 beta i)) (.f64 alpha alpha))
	16.9%	(/.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)))
▶	15.2%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
	35.7%	(.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)))
	31.4%	(.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)))))
	35.7%	(.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)))))
	11.4%	(.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 #s(literal 1 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 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
	30.3%	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (/.f64 (/.f64 (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)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
▶	70.7%	#s(literal 1/16 binary64)

Compiler

Compiled 1 030 to 420 computations (59.2% saved)

simplify530.0ms (3.7%)

Memory

-14.5MiB live, 543.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

11 758×	`accelerator-lowering-fma.f32`
11 758×	`accelerator-lowering-fma.f64`
5 050×	`-lowering-.f32`
5 050×	`-lowering-.f64`
4 668×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	476
1	141	476
2	703	448
3	4980	416
4	7461	416
0	8552	383

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

localize127.0ms (0.9%)

Memory

9.8MiB live, 292.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	99.9%	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))
✓	accuracy	92.8%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	18.9%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
✓	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 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha 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	13.4%	(/.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	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	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)))
✓	accuracy	100.0%	(+.f64 alpha i)
✓	accuracy	100.0%	(*.f64 i (+.f64 alpha i))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	68.1%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))

Samples

65.0ms

256×

valid

Compiler

Compiled 439 to 38 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 24.0ms (56.8% of total)

ival-add: 10.0ms (23.7% of total)

ival-div: 7.0ms (16.6% of total)

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

exact: 1.0ms (2.4% of total)

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

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

series68.0ms (0.5%)

Memory

-4.3MiB live, 152.8MiB allocated

Counts

19 → 588

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

Calls

147 calls:

Time	Variable		Point	Expression
7.0ms	i	@	0	(/ (* (* i (+ alpha (+ i beta))) (+ (* i (+ alpha (+ i beta))) (* alpha beta))) (+ alpha (+ (* i 2) beta)))
4.0ms	alpha	@	0	(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
3.0ms	i	@	0	(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
1.0ms	beta	@	-inf	(* (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
1.0ms	beta	@	0	(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))

rewrite586.0ms (4.1%)

Memory

9.2MiB live, 720.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 092×	`/-lowering-/.f32`
5 092×	`/-lowering-/.f64`
4 962×	`-lowering-.f32`
4 962×	`-lowering-.f64`
2 062×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	267
1	292	264
2	3225	263
0	9240	244

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 1 002

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

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

simplify544.0ms (3.8%)

Memory

14.8MiB live, 902.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 560×	`accelerator-lowering-fma.f32`
6 560×	`accelerator-lowering-fma.f64`
6 532×	`-lowering-.f32`
6 532×	`-lowering-.f64`
4 514×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1773	24272
1	6259	23842
0	8116	21887

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 588

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

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

eval265.0ms (1.9%)

Memory: 18.3MiB live, 422.5MiB allocated
Compiler: Compiled 109 974 to 5 020 computations (95.4% saved)

prune284.0ms (2%)

Memory

4.9MiB live, 486.2MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	1 892	14	1 906
Fresh	8	1	9
Picked	3	2	5
Done	0	0	0
Total	1 903	17	1 920

Accuracy

98.5%

Counts

1 920 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.4%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
	31.3%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	10.9%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (.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 alpha (fma.f64 i #s(literal 2 binary64) beta))))))
	10.6%	(/.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))))
✓	10.9%	(/.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))))
	10.9%	(/.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))))
	10.6%	(/.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))))
▶	23.3%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) #s(literal 1 binary64)))
▶	2.9%	(/.f64 (.f64 i (+.f64 i beta)) (.f64 alpha alpha))
	16.9%	(/.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)))
	15.2%	(/.f64 (.f64 i i) (.f64 beta beta))
▶	10.1%	(/.f64 (.f64 i alpha) (.f64 beta beta))
▶	5.0%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
	23.0%	(/.f64 #s(literal 1 binary64) (.f64 beta (/.f64 beta (.f64 i (+.f64 i alpha)))))
	16.0%	(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
▶	31.3%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
✓	70.7%	#s(literal 1/16 binary64)

Compiler

Compiled 744 to 343 computations (53.9% saved)

simplify570.0ms (4%)

Memory

-27.3MiB live, 515.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

11 038×	`accelerator-lowering-fma.f32`
11 038×	`accelerator-lowering-fma.f64`
3 508×	`--lowering--.f32`
3 508×	`--lowering--.f64`
3 418×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	206
1	107	206
2	339	192
3	1507	190
4	2634	190
5	4083	190
6	6477	190
7	7924	190
0	8464	179

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize181.0ms (1.3%)

Memory

16.0MiB live, 213.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(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	100.0%	(*.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	87.9%	(.f64 beta (.f64 i (+.f64 alpha i)))
✓	accuracy	32.8%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
✓	accuracy	100.0%	(.f64 (.f64 i i) #s(literal 4 binary64))
✓	accuracy	100.0%	(.f64 (.f64 i i) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	45.9%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 i beta)
✓	accuracy	100.0%	(*.f64 alpha alpha)
✓	accuracy	100.0%	(*.f64 i (+.f64 i beta))
✓	accuracy	93.6%	(/.f64 (.f64 i (+.f64 i beta)) (.f64 alpha alpha))
✓	accuracy	100.0%	(*.f64 i alpha)
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	84.5%	(/.f64 (.f64 i 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	99.6%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))

Samples

85.0ms

256×

valid

Compiler

Compiled 195 to 36 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 20.0ms (54% of total)

ival-div: 9.0ms (24.3% of total)

ival-add: 7.0ms (18.9% of total)

ival-sub: 1.0ms (2.7% of total)

exact: 1.0ms (2.7% of total)

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

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

series59.0ms (0.4%)

Memory

14.3MiB live, 89.0MiB allocated

Counts

22 → 540

Calls

Call 1

Inputs
#<alt (* (/ (+ i alpha) beta) (/ i beta))>
#<alt (/ (+ i alpha) beta)>
#<alt (+ i alpha)>
#<alt (/ i beta)>
#<alt (/ (* i alpha) (* beta beta))>
#<alt (* i alpha)>
#<alt (* beta beta)>
#<alt (/ (* i (+ i beta)) (* alpha alpha))>
#<alt (* i (+ i beta))>
#<alt (+ i beta)>
#<alt (* alpha alpha)>
#<alt (- (* (* i i) 4) 1)>
#<alt (/ (* (* i i) 1/4) (- (* (* i i) 4) 1))>
#<alt (* (* i i) 1/4)>
#<alt (* i i)>
#<alt (/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1) (+ alpha (+ (* i 2) beta))))>
#<alt (* beta (* i (+ alpha i)))>
#<alt (* i (+ alpha i))>
#<alt (+ alpha i)>
#<alt (* (* i i) 4)>
#<alt (* (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1) (+ alpha (+ (* i 2) beta)))>
#<alt (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1)>

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

Calls

135 calls:

Time	Variable		Point	Expression
18.0ms	i	@	0	(/ (* i alpha) (* beta beta))
3.0ms	i	@	-inf	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1) (+ alpha (+ (* i 2) beta))))
2.0ms	alpha	@	0	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1) (+ alpha (+ (* i 2) beta))))
2.0ms	beta	@	0	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1) (+ alpha (+ (* i 2) beta))))
2.0ms	i	@	0	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1) (+ alpha (+ (* i 2) beta))))

rewrite552.0ms (3.9%)

Memory

-26.8MiB live, 764.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 944×	`/-lowering-/.f32`
5 944×	`/-lowering-/.f64`
5 100×	`-lowering-.f32`
5 100×	`-lowering-.f64`
3 644×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	158
1	223	158
2	2119	158
0	9138	149

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 958

Calls

Call 1

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

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

simplify513.0ms (3.6%)

Memory

10.8MiB live, 851.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 426×	`accelerator-lowering-fma.f32`
7 426×	`accelerator-lowering-fma.f64`
6 988×	`-lowering-.f32`
6 988×	`-lowering-.f64`
6 320×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	874	9226
1	2981	8757
0	8411	8157

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 540

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 beta)
(+ (/ alpha beta) (/ i beta))
(+ (/ alpha beta) (/ i beta))
(+ (/ alpha beta) (/ i beta))
(/ i beta)
(* i (+ (/ 1 beta) (/ alpha (* beta i))))
(* i (+ (/ 1 beta) (/ alpha (* beta i))))
(* i (+ (/ 1 beta) (/ alpha (* beta i))))
(/ i beta)
(* -1 (* i (- (* -1 (/ alpha (* beta i))) (/ 1 beta))))
(* -1 (* i (- (* -1 (/ alpha (* beta i))) (/ 1 beta))))
(* -1 (* i (- (* -1 (/ alpha (* beta i))) (/ 1 beta))))
(/ i beta)
(+ (/ alpha beta) (/ i beta))
(+ (/ alpha beta) (/ i beta))
(+ (/ alpha beta) (/ i beta))
(/ alpha beta)
(* alpha (+ (/ 1 beta) (/ i (* alpha beta))))
(* alpha (+ (/ 1 beta) (/ i (* alpha beta))))
(* alpha (+ (/ 1 beta) (/ i (* alpha beta))))
(/ alpha beta)
(* -1 (* alpha (- (* -1 (/ i (* alpha beta))) (/ 1 beta))))
(* -1 (* alpha (- (* -1 (/ i (* alpha beta))) (/ 1 beta))))
(* -1 (* alpha (- (* -1 (/ i (* alpha beta))) (/ 1 beta))))
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
(/ (+ alpha i) beta)
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)))
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)))
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i beta)
(/ i 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))
(/ (* 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))
(/ (* alpha i) (pow beta 2))
(/ (* alpha i) (pow beta 2))
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(* alpha i)
(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)
(/ (* beta i) (pow alpha 2))
(* i (+ (/ beta (pow alpha 2)) (/ i (pow alpha 2))))
(* i (+ (/ beta (pow alpha 2)) (/ i (pow alpha 2))))
(* i (+ (/ beta (pow alpha 2)) (/ i (pow alpha 2))))
(/ (pow i 2) (pow alpha 2))
(* (pow i 2) (+ (/ 1 (pow alpha 2)) (/ beta (* (pow alpha 2) i))))
(* (pow i 2) (+ (/ 1 (pow alpha 2)) (/ beta (* (pow alpha 2) i))))
(* (pow i 2) (+ (/ 1 (pow alpha 2)) (/ beta (* (pow alpha 2) i))))
(/ (pow i 2) (pow alpha 2))
(* (pow i 2) (+ (/ 1 (pow alpha 2)) (/ beta (* (pow alpha 2) i))))
(* (pow i 2) (+ (/ 1 (pow alpha 2)) (/ beta (* (pow alpha 2) i))))
(* (pow i 2) (+ (/ 1 (pow alpha 2)) (/ beta (* (pow alpha 2) i))))
(/ (pow i 2) (pow alpha 2))
(+ (/ (* beta i) (pow alpha 2)) (/ (pow i 2) (pow alpha 2)))
(+ (/ (* beta i) (pow alpha 2)) (/ (pow i 2) (pow alpha 2)))
(+ (/ (* beta i) (pow alpha 2)) (/ (pow i 2) (pow alpha 2)))
(/ (* beta i) (pow alpha 2))
(* beta (+ (/ i (pow alpha 2)) (/ (pow i 2) (* (pow alpha 2) beta))))
(* beta (+ (/ i (pow alpha 2)) (/ (pow i 2) (* (pow alpha 2) beta))))
(* beta (+ (/ i (pow alpha 2)) (/ (pow i 2) (* (pow alpha 2) beta))))
(/ (* beta i) (pow alpha 2))
(* -1 (* beta (+ (* -1 (/ i (pow alpha 2))) (* -1 (/ (pow i 2) (* (pow alpha 2) beta))))))
(* -1 (* beta (+ (* -1 (/ i (pow alpha 2))) (* -1 (/ (pow i 2) (* (pow alpha 2) beta))))))
(* -1 (* beta (+ (* -1 (/ i (pow alpha 2))) (* -1 (/ (pow i 2) (* (pow alpha 2) beta))))))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(/ (* i (+ beta i)) (pow alpha 2))
(* beta i)
(* i (+ beta i))
(* i (+ beta i))
(* i (+ beta i))
(pow i 2)
(* (pow i 2) (+ 1 (/ beta i)))
(* (pow i 2) (+ 1 (/ beta i)))
(* (pow i 2) (+ 1 (/ beta i)))
(pow i 2)
(* (pow i 2) (+ 1 (/ beta i)))
(* (pow i 2) (+ 1 (/ beta i)))
(* (pow i 2) (+ 1 (/ beta i)))
(pow i 2)
(+ (* beta i) (pow i 2))
(+ (* beta i) (pow i 2))
(+ (* beta i) (pow i 2))
(* beta i)
(* beta (+ i (/ (pow i 2) beta)))
(* beta (+ i (/ (pow i 2) beta)))
(* beta (+ i (/ (pow i 2) beta)))
(* beta i)
(* -1 (* beta (+ (* -1 i) (* -1 (/ (pow i 2) beta)))))
(* -1 (* beta (+ (* -1 i) (* -1 (/ (pow i 2) beta)))))
(* -1 (* beta (+ (* -1 i) (* -1 (/ (pow i 2) beta)))))
beta
(+ beta i)
(+ beta i)
(+ beta i)
i
(* i (+ 1 (/ beta i)))
(* i (+ 1 (/ beta i)))
(* i (+ 1 (/ beta i)))
i
(* -1 (* i (- (* -1 (/ beta i)) 1)))
(* -1 (* i (- (* -1 (/ beta i)) 1)))
(* -1 (* i (- (* -1 (/ beta i)) 1)))
i
(+ beta i)
(+ beta i)
(+ beta i)
beta
(* beta (+ 1 (/ i beta)))
(* beta (+ 1 (/ i beta)))
(* beta (+ 1 (/ i beta)))
beta
(* -1 (* beta (- (* -1 (/ i beta)) 1)))
(* -1 (* beta (- (* -1 (/ i beta)) 1)))
(* -1 (* beta (- (* -1 (/ i beta)) 1)))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
-1
(- (* 4 (pow i 2)) 1)
(- (* 4 (pow i 2)) 1)
(- (* 4 (pow i 2)) 1)
(* 4 (pow i 2))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* 4 (pow i 2))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* -1/4 (pow i 2))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(* 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))
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(/ (* beta (* i (+ alpha i))) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(* beta (+ (* -1 (/ (* beta (* i (* (+ alpha i) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)))) (* (pow (+ alpha (* 2 i)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (/ (* i (+ alpha i)) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))))
(* beta (+ (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (* (+ alpha i) (pow (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2))) (* (pow (+ alpha (* 2 i)) 3) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (* (+ alpha i) (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (* (+ alpha i) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* i (+ alpha i)) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))))
(* beta (+ (* beta (- (* beta (- (* -1 (* beta (+ (* -1 (/ (* i (* (+ alpha i) (* (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)))) (* (pow (+ alpha (* 2 i)) 3) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (+ (* -1 (/ (* (+ (* -1 (/ (* i (* (+ alpha i) (pow (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2))) (* (pow (+ alpha (* 2 i)) 3) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (* (+ alpha i) (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) (/ (* i (+ alpha i)) (* (pow (+ alpha (* 2 i)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))))) (+ (* -1 (/ (* i (* (+ alpha i) (pow (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1) 2))) (* (pow (+ alpha (* 2 i)) 3) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 3)))) (/ (* i (* (+ alpha i) (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2)))))) (/ (* i (* (+ alpha i) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (* (pow (+ alpha (* 2 i)) 2) (pow (- (pow (+ alpha (* 2 i)) 2) 1) 2))))) (/ (* i (+ alpha i)) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (+ (* -1 (/ (* i (* (+ alpha i) (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* i (* (+ alpha i) (pow (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))) 2)))) (* i (* (+ alpha i) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)))) (pow beta 2))) (* i (+ alpha i))) (/ (* i (* (+ alpha i) (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))))) beta)) (pow beta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* i (* (+ alpha i) (* (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))))) (+ (* -1 (* (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))) (+ (* -1 (* i (* (+ alpha i) (pow (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))) 2)))) (* i (* (+ alpha i) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)))))) (* i (* (+ alpha i) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))))) (pow beta 3))) (* i (+ alpha i))) (+ (* -1 (/ (* i (* (+ alpha i) (pow (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))) 2))) (pow beta 2))) (+ (/ (* i (* (+ alpha i) (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))))) beta) (/ (* i (* (+ alpha i) (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1))) (pow beta 2))))) (pow beta 2))
(/ (* i (+ alpha i)) (pow beta 2))
(/ (+ (* -1 (/ (* i (* (+ alpha i) (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* i (* (+ alpha i) (+ (* -2 (pow (+ alpha (* 2 i)) 2)) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1))))) (* i (* (+ alpha i) (pow (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 2)))) beta)) (* i (* (+ alpha i) (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i)))))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* i (* (+ alpha i) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (* i (* (+ alpha i) (* (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) (+ (* -2 (pow (+ alpha (* 2 i)) 2)) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1)))))) (* (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) (+ (* i (* (+ alpha i) (+ (* -2 (pow (+ alpha (* 2 i)) 2)) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1))))) (* i (* (+ alpha i) (pow (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 2))))))) beta)) (+ (* i (* (+ alpha i) (+ (* -2 (pow (+ alpha (* 2 i)) 2)) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1))))) (* i (* (+ alpha i) (pow (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) 2))))) beta)) (* i (* (+ alpha i) (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i)))))))) beta)) (* i (+ alpha i))) (pow beta 2))
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(* i (+ (* i (- (/ beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (/ (* alpha (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* -1 (* i (+ (/ (* alpha (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))) (- (/ beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (/ (* alpha (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))) (/ beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* i (+ (* i (- (+ (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))) (+ (/ (* alpha (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))) (- (/ beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (/ (* alpha (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))) (+ (* 8 (/ (* alpha beta) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2)))) (/ (* (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) (- (/ beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (/ (* alpha (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))))))) (+ (/ (* alpha (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))) (- (/ beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (/ (* alpha (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))) (/ beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* (pow (+ alpha beta) 2) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(* 1/8 (/ beta i))
(/ (- (+ (* 1/8 beta) (* 1/8 (/ (* alpha beta) i))) (* 1/64 (/ (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))) i))) i)
(/ (- (+ (* -1 (/ (+ (* 1/64 (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* 1/8 (* (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) (- (* 1/8 (* alpha beta)) (* 1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))))))) (pow i 2))) (+ (* 1/8 beta) (* 1/8 (/ (* alpha beta) i)))) (* 1/64 (/ (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))) i))) i)
(/ (- (+ (* -1 (/ (+ (* -1/8 (* (+ (* 1/64 (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))))) (* 1/8 (* (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) (- (* 1/8 (* alpha beta)) (* 1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))))))) (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))) (+ (* 1/64 (* beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))) (* 1/8 (* (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2))) (- (* 1/8 (* alpha beta)) (* 1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))))))))) (pow i 3))) (+ (* 1/8 beta) (* 1/8 (/ (* alpha beta) i)))) (+ (* 1/64 (/ (* beta (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2)))) (pow i 2))) (+ (* 1/64 (/ (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))) i)) (* 1/8 (/ (* (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) (- (* 1/8 (* alpha beta)) (* 1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))))) (pow i 2)))))) i)
(* 1/8 (/ beta i))
(* -1 (/ (- (+ (* -1/8 beta) (* -1/8 (/ (* alpha beta) i))) (* -1/64 (/ (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))) i))) i))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* -1/8 (* alpha beta)) (* -1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))))) (* -1 (/ (+ (* -1/8 (* (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) (- (* -1/8 (* alpha beta)) (* -1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))))))) (* -1/64 (* beta (+ (* -4 (pow (+ alpha beta) 2)) (* -2 (- (pow (+ alpha beta) 2) 1)))))) i))) i)) (* -1/8 beta)) i))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* -1/8 (* alpha beta)) (* -1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (+ (* -4 (pow (+ alpha beta) 2)) (* -2 (- (pow (+ alpha beta) 2) 1))) (- (* -1/8 (* alpha beta)) (* -1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))))))) (+ (* -1/64 (* beta (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))) (* 1/8 (* (+ (* -1/8 (* (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) (- (* -1/8 (* alpha beta)) (* -1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))))))) (* -1/64 (* beta (+ (* -4 (pow (+ alpha beta) 2)) (* -2 (- (pow (+ alpha beta) 2) 1)))))) (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))))) i)) (+ (* -1/8 (* (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) (- (* -1/8 (* alpha beta)) (* -1/64 (* beta (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))))))) (* -1/64 (* beta (+ (* -4 (pow (+ alpha beta) 2)) (* -2 (- (pow (+ alpha beta) 2) 1))))))) i))) i)) (* -1/8 beta)) i))
(/ (* beta (pow i 2)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (/ (* beta i) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* beta (* (pow i 2) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* beta (pow i 2)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))))
(+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* beta (* (pow i 2) (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))) (/ (* (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) (- (/ (* beta i) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* beta (* (pow i 2) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))))) (/ (* beta i) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* beta (* (pow i 2) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* beta (pow i 2)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))))
(+ (* alpha (- (+ (* alpha (- (* -1 (* alpha (+ (* -1 (/ (* (+ (/ (* beta (* (pow i 2) (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))) (/ (* (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) (- (/ (* beta i) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* beta (* (pow i 2) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) (+ (/ (* beta (pow i 2)) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))) (/ (* (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) (- (/ (* beta i) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* beta (* (pow i 2) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))))))) (+ (/ (* beta (* (pow i 2) (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))) (/ (* (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1) (- (/ (* beta i) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (/ (* beta (* (pow i 2) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))))) (/ (* beta i) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) (/ (* beta (* (pow i 2) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (pow (+ beta (* 2 i)) 2) (pow (- (pow (+ beta (* 2 i)) 2) 1) 2))))) (/ (* beta (pow i 2)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))))
(/ (* beta i) (pow alpha 2))
(/ (- (+ (* beta i) (/ (* beta (pow i 2)) alpha)) (/ (* beta (* i (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))) alpha)) (pow alpha 2))
(/ (- (+ (* -1 (/ (+ (* beta (* i (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) (- (* beta (pow i 2)) (* beta (* i (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i))))))))) (pow alpha 2))) (+ (* beta i) (/ (* beta (pow i 2)) alpha))) (/ (* beta (* i (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))) alpha)) (pow alpha 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) (+ (* beta (* i (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (* (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) (- (* beta (pow i 2)) (* beta (* i (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i))))))))))) (+ (* beta (* i (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) (* (- (* beta (pow i 2)) (* beta (* i (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i))))))) (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)))) (pow alpha 3))) (+ (* beta i) (/ (* beta (pow i 2)) alpha))) (+ (/ (* beta (* i (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))) alpha) (+ (/ (* beta (* i (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1))) (pow alpha 2)) (/ (* (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))) (- (* beta (pow i 2)) (* beta (* i (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))))) (pow alpha 2))))) (pow alpha 2))
(/ (* beta i) (pow alpha 2))
(/ (+ (* -1 (/ (- (* -1 (* beta (pow i 2))) (* -1 (* beta (* i (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))))))) alpha)) (* beta i)) (pow alpha 2))
(/ (+ (* -1 (/ (- (+ (* -1 (* beta (pow i 2))) (+ (* -1 (/ (* beta (* i (+ (* -2 (pow (+ beta (* 2 i)) 2)) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))))) alpha)) (* -1 (/ (* (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) (- (* -1 (* beta (pow i 2))) (* -1 (* beta (* i (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i)))))))))) alpha)))) (* -1 (* beta (* i (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))))))) alpha)) (* beta i)) (pow alpha 2))
(/ (+ (* -1 (/ (- (+ (* -1 (* beta (pow i 2))) (* -1 (/ (- (+ (* -1 (/ (* beta (* i (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))) alpha)) (+ (* -1 (/ (* (+ (* -2 (pow (+ beta (* 2 i)) 2)) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))) (- (* -1 (* beta (pow i 2))) (* -1 (* beta (* i (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i)))))))))) alpha)) (/ (* (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) (+ (* -1 (* beta (* i (+ (* -2 (pow (+ beta (* 2 i)) 2)) (* -1 (- (pow (+ beta (* 2 i)) 2) 1)))))) (* -1 (* (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) (- (* -1 (* beta (pow i 2))) (* -1 (* beta (* i (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))))))))))) alpha))) (+ (* -1 (* beta (* i (+ (* -2 (pow (+ beta (* 2 i)) 2)) (* -1 (- (pow (+ beta (* 2 i)) 2) 1)))))) (* -1 (* (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) (- (* -1 (* beta (pow i 2))) (* -1 (* beta (* i (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))))))))))) alpha))) (* -1 (* beta (* i (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))))))) alpha)) (* beta i)) (pow alpha 2))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* beta (* i (+ alpha i)))
(* alpha (* beta i))
(* i (+ (* alpha beta) (* beta i)))
(* i (+ (* alpha beta) (* beta i)))
(* i (+ (* alpha beta) (* beta i)))
(* beta (pow i 2))
(* (pow i 2) (+ beta (/ (* alpha beta) i)))
(* (pow i 2) (+ beta (/ (* alpha beta) i)))
(* (pow i 2) (+ beta (/ (* alpha beta) i)))
(* beta (pow i 2))
(* (pow i 2) (+ beta (/ (* alpha beta) i)))
(* (pow i 2) (+ beta (/ (* alpha beta) i)))
(* (pow i 2) (+ beta (/ (* alpha beta) i)))
(* beta (pow i 2))
(+ (* alpha (* beta i)) (* beta (pow i 2)))
(+ (* alpha (* beta i)) (* beta (pow i 2)))
(+ (* alpha (* beta i)) (* beta (pow i 2)))
(* alpha (* beta i))
(* alpha (+ (* beta i) (/ (* beta (pow i 2)) alpha)))
(* alpha (+ (* beta i) (/ (* beta (pow i 2)) alpha)))
(* alpha (+ (* beta i) (/ (* beta (pow i 2)) alpha)))
(* alpha (* beta i))
(* -1 (* alpha (+ (* -1 (* beta i)) (* -1 (/ (* beta (pow i 2)) alpha)))))
(* -1 (* alpha (+ (* -1 (* beta i)) (* -1 (/ (* beta (pow i 2)) alpha)))))
(* -1 (* alpha (+ (* -1 (* beta i)) (* -1 (/ (* beta (pow i 2)) alpha)))))
(* 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)))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))
(+ (* alpha (- (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2)) 1)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (+ (* alpha (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i))))) (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))) 1)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(+ (* alpha (- (+ (* alpha (+ alpha (+ beta (+ (* 2 beta) (+ (* 2 i) (* 4 i)))))) (+ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))) 1)) (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)))
(pow alpha 3)
(* (pow alpha 3) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 2 (/ i alpha)) (+ (* 4 (/ i alpha)) (/ beta alpha))))))
(* (pow alpha 3) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 2 (/ i alpha)) (+ (* 4 (/ i alpha)) (+ (/ beta alpha) (+ (/ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow alpha 2)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2)))))))) (/ 1 (pow alpha 2))))
(* (pow alpha 3) (- (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 2 (/ i alpha)) (+ (* 4 (/ i alpha)) (+ (/ beta alpha) (+ (/ (* (+ beta (* 2 i)) (+ (* 2 beta) (* 4 i))) (pow alpha 2)) (+ (/ (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 3)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))))) (/ 1 (pow alpha 2))))
(pow alpha 3)
(* -1 (* (pow alpha 3) (- (* -1 (/ (+ beta (+ (* 2 i) (* 2 (+ beta (* 2 i))))) alpha)) 1)))
(* -1 (* (pow alpha 3) (- (* -1 (/ (+ beta (+ (* -1 (/ (+ (* -2 (pow (+ beta (* 2 i)) 2)) (* -1 (- (pow (+ beta (* 2 i)) 2) 1))) alpha)) (+ (* 2 i) (* 2 (+ beta (* 2 i)))))) alpha)) 1)))
(* -1 (* (pow alpha 3) (- (* -1 (/ (+ beta (+ (* -1 (/ (+ (* -2 (pow (+ beta (* 2 i)) 2)) (+ (* -1 (- (pow (+ beta (* 2 i)) 2) 1)) (* -1 (/ (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1)) alpha)))) alpha)) (+ (* 2 i) (* 2 (+ beta (* 2 i)))))) alpha)) 1)))
(* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))
(+ (* i (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (* 4 (pow (+ alpha beta) 2)))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* i (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))))))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(+ (* i (+ (* 2 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* i (+ (* 4 (+ alpha beta)) (+ (* 8 i) (* 8 (+ alpha beta)))))))) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(* 8 (pow i 3))
(* (pow i 3) (+ 8 (+ (* 4 (/ (+ alpha beta) i)) (* 8 (/ (+ alpha beta) i)))))
(* (pow i 3) (+ 8 (+ (* 2 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (+ alpha beta) i)) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 8 (/ (+ alpha beta) i)))))))
(* (pow i 3) (+ 8 (+ (* 2 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (+ alpha beta) i)) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 8 (/ (+ alpha beta) i)) (/ (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)) (pow i 3))))))))
(* 8 (pow i 3))
(* -1 (* (pow i 3) (- (* -1 (/ (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta))) i)) 8)))
(* -1 (* (pow i 3) (- (* -1 (/ (+ (* -1 (/ (+ (* -4 (pow (+ alpha beta) 2)) (* -2 (- (pow (+ alpha beta) 2) 1))) i)) (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))) i)) 8)))
(* -1 (* (pow i 3) (- (* -1 (/ (+ (* -1 (/ (+ (* -4 (pow (+ alpha beta) 2)) (+ (* -2 (- (pow (+ alpha beta) 2) 1)) (* -1 (/ (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)) i)))) i)) (+ (* 4 (+ alpha beta)) (* 8 (+ alpha beta)))) i)) 8)))
(* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))
(+ (* beta (- (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2)) 1)) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (- (+ (* beta (+ alpha (+ (* 2 alpha) (+ (* 2 i) (* 4 i))))) (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))) 1)) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(+ (* beta (- (+ (* beta (+ alpha (+ beta (+ (* 2 alpha) (+ (* 2 i) (* 4 i)))))) (+ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))) 1)) (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)))
(pow beta 3)
(* (pow beta 3) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 2 (/ i beta)) (+ (* 4 (/ i beta)) (/ alpha beta))))))
(* (pow beta 3) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 2 (/ i beta)) (+ (* 4 (/ i beta)) (+ (/ alpha beta) (+ (/ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow beta 2)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2)))))))) (/ 1 (pow beta 2))))
(* (pow beta 3) (- (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 2 (/ i beta)) (+ (* 4 (/ i beta)) (+ (/ alpha beta) (+ (/ (* (+ alpha (* 2 i)) (+ (* 2 alpha) (* 4 i))) (pow beta 2)) (+ (/ (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 3)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))))) (/ 1 (pow beta 2))))
(pow beta 3)
(* -1 (* (pow beta 3) (- (* -1 (/ (+ alpha (+ (* 2 i) (* 2 (+ alpha (* 2 i))))) beta)) 1)))
(* -1 (* (pow beta 3) (- (* -1 (/ (+ alpha (+ (* -1 (/ (+ (* -2 (pow (+ alpha (* 2 i)) 2)) (* -1 (- (pow (+ alpha (* 2 i)) 2) 1))) beta)) (+ (* 2 i) (* 2 (+ alpha (* 2 i)))))) beta)) 1)))
(* -1 (* (pow beta 3) (- (* -1 (/ (+ alpha (+ (* -1 (/ (+ (* -2 (pow (+ alpha (* 2 i)) 2)) (+ (* -1 (- (pow (+ alpha (* 2 i)) 2) 1)) (* -1 (/ (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) beta)))) beta)) (+ (* 2 i) (* 2 (+ alpha (* 2 i)))))) beta)) 1)))
(- (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 beta) 2) 1)
(- (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(- (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2)) 1)
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))) (/ 1 (pow i 2))))
(* 4 (pow i 2))
(* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (- (pow (+ alpha beta) 2) 1) i))) i))))
(- (pow (+ 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))))

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

eval215.0ms (1.5%)

Memory: 23.0MiB live, 507.6MiB allocated
Compiler: Compiled 64 904 to 3 740 computations (94.2% saved)

prune254.0ms (1.8%)

Memory

-1.7MiB live, 462.1MiB allocated

Pruning

33 alts after pruning (30 fresh and 3 done)

	Pruned	Kept	Total
New	1 496	20	1 516
Fresh	0	10	10
Picked	4	1	5
Done	0	2	2
Total	1 500	33	1 533

Accuracy

98.5%

Counts

1 533 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.4%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
	31.3%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	13.8%	(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
	23.1%	(/.f64 (.f64 (+.f64 i alpha) #s(literal 1 binary64)) (.f64 beta (/.f64 beta i)))
	10.9%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (.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 alpha (fma.f64 i #s(literal 2 binary64) beta))))))
	10.6%	(/.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))))
✓	10.9%	(/.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))))
	10.9%	(/.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))))
	10.6%	(/.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))))
	16.9%	(/.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)))
	15.2%	(/.f64 (.f64 i i) (.f64 beta beta))
	5.4%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (fma.f64 i (fma.f64 #s(literal 4 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 #s(literal 2 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal -2 binary64))) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
▶	6.1%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
	5.2%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
	5.3%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
▶	5.5%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (.f64 (.f64 beta beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
	4.9%	(/.f64 (.f64 beta (.f64 i i)) (*.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))))
	23.0%	(/.f64 #s(literal 1 binary64) (.f64 beta (/.f64 beta (.f64 i (+.f64 i alpha)))))
▶	70.8%	(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
	16.0%	(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
✓	31.3%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	24.8%	(*.f64 (/.f64 (neg.f64 i) #s(literal -1 binary64)) (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
	27.8%	(*.f64 (/.f64 i beta) (/.f64 i beta))
	13.8%	(*.f64 (/.f64 i beta) (/.f64 alpha beta))
	31.2%	(*.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 #s(literal 1 binary64) i)))
▶	23.9%	(*.f64 (+.f64 i alpha) (/.f64 (/.f64 i beta) beta))
	11.2%	(.f64 (.f64 i (+.f64 i alpha)) (.f64 beta (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))))
	29.4%	(.f64 (.f64 alpha (+.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 i (*.f64 alpha beta)))) (/.f64 i beta))
	29.9%	(.f64 (exp.f64 (.f64 (log.f64 (/.f64 beta (+.f64 i alpha))) #s(literal -1 binary64))) (/.f64 i beta))
	12.0%	(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 alpha beta)))
	3.0%	(.f64 beta (/.f64 i (.f64 alpha alpha)))
▶	10.2%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	70.7%	#s(literal 1/16 binary64)

Compiler

Compiled 1 320 to 662 computations (49.8% saved)

simplify509.0ms (3.6%)

Memory

2.8MiB live, 757.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 alpha i)
✓	cost-diff	0	(*.f64 i (+.f64 alpha i))
✓	cost-diff	0	(.f64 beta (.f64 i (+.f64 alpha i)))
✓	cost-diff	0	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
✓	cost-diff	0	(+.f64 alpha i)
✓	cost-diff	0	(*.f64 i (+.f64 alpha i))
✓	cost-diff	0	(.f64 beta (.f64 i (+.f64 alpha i)))
✓	cost-diff	640	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (.f64 (.f64 beta beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
✓	cost-diff	0	(/.f64 i beta)
✓	cost-diff	0	(+.f64 i alpha)
✓	cost-diff	0	(*.f64 (+.f64 i alpha) (/.f64 (/.f64 i beta) beta))
✓	cost-diff	384	(/.f64 (/.f64 i 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 i i)
✓	cost-diff	0	(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
✓	cost-diff	0	(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))

Rules

16 496×	`accelerator-lowering-fma.f32`
16 496×	`accelerator-lowering-fma.f64`
5 136×	`+-lowering-+.f64`
5 136×	`+-lowering-+.f32`
3 980×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	229
1	98	229
2	361	227
3	1382	225
4	5514	225
5	7794	225
0	8337	210

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ 1/16 (/ 1/64 (* i i)))
1/16
(/ 1/64 (* i i))
1/64
(* i i)
i
(* alpha (/ i (* beta beta)))
alpha
(/ i (* beta beta))
i
(* beta beta)
beta
(* (+ i alpha) (/ (/ i beta) beta))
(+ i alpha)
i
alpha
(/ (/ i beta) beta)
(/ i beta)
beta
(/ (* beta (* i (+ alpha i))) (* (* beta beta) (+ alpha (+ (* i 2) beta))))
(* beta (* i (+ alpha i)))
beta
(* i (+ alpha i))
i
(+ alpha i)
alpha
(* (* beta beta) (+ alpha (+ (* i 2) beta)))
(* beta beta)
(+ alpha (+ (* i 2) beta))
(+ (* i 2) beta)
2
(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))
(* beta (* i (+ alpha i)))
beta
(* i (+ alpha i))
i
(+ alpha i)
alpha
(* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta)))
(+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1)
(+ alpha beta)
(+ (* i 4) (+ alpha beta))
4
-1
(+ alpha (+ (* i 2) beta))
(+ (* i 2) beta)
2

Outputs
(+ 1/16 (/ 1/64 (* i i)))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
1/16
#s(literal 1/16 binary64)
(/ 1/64 (* i i))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
1/64
#s(literal 1/64 binary64)
(* i i)
(*.f64 i i)
i
(* alpha (/ i (* beta beta)))
(.f64 i (/.f64 alpha (.f64 beta beta)))
alpha
(/ i (* beta beta))
(/.f64 i (*.f64 beta beta))
i
(* beta beta)
(*.f64 beta beta)
beta
(* (+ i alpha) (/ (/ i beta) beta))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(+ i alpha)
(+.f64 i alpha)
i
alpha
(/ (/ i beta) beta)
(/.f64 i (*.f64 beta beta))
(/ i beta)
(/.f64 i beta)
beta
(/ (* beta (* i (+ alpha i))) (* (* beta beta) (+ alpha (+ (* i 2) beta))))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(* beta (* i (+ alpha i)))
(.f64 i (.f64 beta (+.f64 i alpha)))
beta
(* i (+ alpha i))
(*.f64 i (+.f64 i alpha))
i
(+ alpha i)
(+.f64 i alpha)
alpha
(* (* beta beta) (+ alpha (+ (* i 2) beta)))
(.f64 beta (.f64 beta (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(* beta beta)
(*.f64 beta 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)
(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))
(/.f64 (.f64 i (.f64 beta (+.f64 i alpha))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))))
(* beta (* i (+ alpha i)))
(.f64 i (.f64 beta (+.f64 i alpha)))
beta
(* i (+ alpha i))
(*.f64 i (+.f64 i alpha))
i
(+ alpha i)
(+.f64 i alpha)
alpha
(* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta)))
(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64)))
(+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1)
(fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))
(+ alpha beta)
(+.f64 alpha beta)
(+ (* i 4) (+ alpha beta))
(+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))
4
#s(literal 4 binary64)
-1
#s(literal -1 binary64)
(+ 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)

localize131.0ms (0.9%)

Memory

-7.1MiB live, 169.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	99.6%	(fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64))
✓	accuracy	87.9%	(.f64 beta (.f64 i (+.f64 alpha i)))
✓	accuracy	34.4%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
✓	accuracy	100.0%	(+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))
✓	accuracy	87.9%	(.f64 beta (.f64 i (+.f64 alpha i)))
✓	accuracy	87.6%	(.f64 (.f64 beta beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	45.5%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (.f64 (.f64 beta beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
✓	accuracy	100.0%	(/.f64 i beta)
✓	accuracy	100.0%	(+.f64 i alpha)
✓	accuracy	99.8%	(/.f64 (/.f64 i beta) beta)
✓	accuracy	92.2%	(*.f64 (+.f64 i alpha) (/.f64 (/.f64 i beta) beta))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	86.9%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	accuracy	83.3%	(/.f64 i (*.f64 beta beta))
✓	accuracy	100.0%	(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	98.9%	(/.f64 #s(literal 1/64 binary64) (*.f64 i i))

Samples

86.0ms

256×

valid

Compiler

Compiled 216 to 35 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-mult: 40.0ms (68.1% of total)

ival-div: 9.0ms (15.3% of total)

ival-add: 9.0ms (15.3% of total)

exact: 1.0ms (1.7% of total)

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

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

series87.0ms (0.6%)

Memory

-10.0MiB live, 107.0MiB allocated

Counts

19 → 516

Calls

Call 1

Inputs
#<alt (+ 1/16 (/ 1/64 (* i i)))>
#<alt (/ 1/64 (* i i))>
#<alt (* i i)>
#<alt (* alpha (/ i (* beta beta)))>
#<alt (/ i (* beta beta))>
#<alt (* beta beta)>
#<alt (/ (/ i beta) beta)>
#<alt (* (+ i alpha) (/ (/ i beta) beta))>
#<alt (+ i alpha)>
#<alt (/ i beta)>
#<alt (/ (* beta (* i (+ alpha i))) (* (* beta beta) (+ alpha (+ (* i 2) beta))))>
#<alt (* beta (* i (+ alpha i)))>
#<alt (* i (+ alpha i))>
#<alt (+ alpha i)>
#<alt (/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))>
#<alt (* (* beta beta) (+ alpha (+ (* i 2) beta)))>
#<alt (+ alpha (+ (* i 2) beta))>
#<alt (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1)>
#<alt (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta)))>

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

Calls

129 calls:

Time	Variable		Point	Expression
34.0ms	beta	@	0	(/ (* beta (* i (+ alpha i))) (* (* beta beta) (+ alpha (+ (* i 2) beta))))
14.0ms	beta	@	-inf	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))
3.0ms	i	@	0	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))
2.0ms	alpha	@	0	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))
2.0ms	beta	@	0	(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))

rewrite472.0ms (3.3%)

Memory

22.9MiB live, 802.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 074×	`/-lowering-/.f32`
5 074×	`/-lowering-/.f64`
4 266×	`-lowering-.f32`
4 266×	`-lowering-.f64`
3 260×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	165
1	223	165
2	2376	165
0	8852	153

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 897

Calls

Call 1

Inputs
(+ 1/16 (/ 1/64 (* i i)))
(/ 1/64 (* i i))
(* i i)
(* alpha (/ i (* beta beta)))
(/ i (* beta beta))
(* beta beta)
(/ (/ i beta) beta)
(* (+ i alpha) (/ (/ i beta) beta))
(+ i alpha)
(/ i beta)
(/ (* beta (* i (+ alpha i))) (* (* beta beta) (+ alpha (+ (* i 2) beta))))
(* beta (* i (+ alpha i)))
(* i (+ alpha i))
(+ alpha i)
(/ (* beta (* i (+ alpha i))) (* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta))))
(* (* beta beta) (+ alpha (+ (* i 2) beta)))
(+ alpha (+ (* i 2) beta))
(+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1)
(* (+ (* (+ alpha beta) (+ (* i 4) (+ alpha beta))) -1) (+ alpha (+ (* i 2) beta)))

Outputs
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 i i)) #s(literal 1/16 binary64))
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(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (-.f64 (.f64 (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (-.f64 (.f64 (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (.f64 #s(literal -1 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 beta (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) (-.f64 (.f64 (.f64 beta (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) (.f64 beta (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64)))) (.f64 (.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) (.f64 beta (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64)))))))
(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))

simplify563.0ms (4%)

Memory

-5.5MiB live, 1 079.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 782×	`-lowering-.f32`
7 782×	`-lowering-.f64`
7 452×	`accelerator-lowering-fma.f32`
7 452×	`accelerator-lowering-fma.f64`
5 604×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1031	10870
1	3521	10674
0	8981	9772

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 516

Calls

Call 1

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

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

eval272.0ms (1.9%)

Memory: 36.3MiB live, 496.3MiB allocated
Compiler: Compiled 66 464 to 3 871 computations (94.2% saved)

prune263.0ms (1.9%)

Memory

-28.5MiB live, 584.4MiB allocated

Pruning

37 alts after pruning (31 fresh and 6 done)

	Pruned	Kept	Total
New	1 679	9	1 688
Fresh	3	22	25
Picked	2	3	5
Done	0	3	3
Total	1 684	37	1 721

Accuracy

98.5%

Counts

1 721 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.4%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
	31.3%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	13.8%	(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
	16.1%	(/.f64 (.f64 (/.f64 beta (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) (.f64 i (+.f64 i alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
	5.5%	(/.f64 (.f64 (+.f64 i alpha) (.f64 i beta)) (.f64 (.f64 beta beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
	23.1%	(/.f64 (.f64 (+.f64 i alpha) #s(literal 1 binary64)) (.f64 beta (/.f64 beta i)))
	10.9%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (.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 alpha (fma.f64 i #s(literal 2 binary64) beta))))))
	10.6%	(/.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))))
✓	10.9%	(/.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))))
	10.9%	(/.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))))
	10.6%	(/.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))))
	6.3%	(/.f64 (.f64 (.f64 i i) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 beta (fma.f64 i #s(literal 4 binary64) beta) #s(literal -1 binary64))))
	14.9%	(/.f64 (.f64 i i) (.f64 beta (fma.f64 i #s(literal 2 binary64) beta)))
	15.2%	(/.f64 (.f64 i i) (.f64 beta beta))
	5.4%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (fma.f64 i (fma.f64 #s(literal 4 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 #s(literal 2 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal -2 binary64))) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))
✓	6.1%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
	5.6%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha beta)))
	5.3%	(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	4.9%	(/.f64 (.f64 beta (.f64 i i)) (*.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))))
	5.4%	(/.f64 (*.f64 #s(literal 1/2 binary64) i) beta)
	5.4%	(/.f64 i beta)
	23.0%	(/.f64 #s(literal 1 binary64) (.f64 beta (/.f64 beta (.f64 i (+.f64 i alpha)))))
	4.2%	(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
✓	70.8%	(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
	16.0%	(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
✓	31.3%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	24.8%	(*.f64 (/.f64 (neg.f64 i) #s(literal -1 binary64)) (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
	27.8%	(*.f64 (/.f64 i beta) (/.f64 i beta))
	13.8%	(*.f64 (/.f64 i beta) (/.f64 alpha beta))
	31.2%	(*.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 #s(literal 1 binary64) i)))
	11.2%	(.f64 (.f64 i (+.f64 i alpha)) (.f64 beta (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))))
	29.4%	(.f64 (.f64 alpha (+.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 i (*.f64 alpha beta)))) (/.f64 i beta))
	29.9%	(.f64 (exp.f64 (.f64 (log.f64 (/.f64 beta (+.f64 i alpha))) #s(literal -1 binary64))) (/.f64 i beta))
	23.0%	(*.f64 i (/.f64 (/.f64 i beta) beta))
	12.0%	(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 alpha beta)))
✓	10.2%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	70.7%	#s(literal 1/16 binary64)

Compiler

Compiled 1 965 to 587 computations (70.1% saved)

regimes184.0ms (1.3%)

Memory

30.4MiB live, 144.9MiB allocated

Counts

58 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i beta)
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/.f64 (*.f64 #s(literal 1/2 binary64) i) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(.f64 beta (/.f64 i (.f64 alpha alpha)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/.f64 (.f64 i (+.f64 beta i)) (.f64 alpha alpha))
(/.f64 (.f64 i (+.f64 i beta)) (.f64 alpha alpha))
(*.f64 i (/.f64 (/.f64 i beta) beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))
(*.f64 (/.f64 i beta) (/.f64 i beta))
(/.f64 (.f64 i i) (.f64 beta (fma.f64 i #s(literal 2 binary64) beta)))
(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
(*.f64 (+.f64 i alpha) (/.f64 (/.f64 i beta) beta))
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
(.f64 i (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 alpha beta)))
(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 i i) #s(literal 4 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 beta (/.f64 beta (.f64 i (+.f64 i alpha)))))
(/.f64 (.f64 (+.f64 i alpha) #s(literal 1 binary64)) (.f64 beta (/.f64 beta i)))
(*.f64 (/.f64 (neg.f64 i) #s(literal -1 binary64)) (/.f64 (/.f64 (+.f64 i alpha) beta) beta))
(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (.f64 (.f64 beta beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 (+.f64 i alpha) (.f64 i beta)) (.f64 (.f64 beta beta) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 i i) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 beta (fma.f64 i #s(literal 4 binary64) beta) #s(literal -1 binary64))))
(/.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 beta (.f64 i i)) (*.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 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha beta)))
(.f64 (.f64 alpha (+.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 i (*.f64 alpha beta)))) (/.f64 i beta))
(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 #s(literal 1 binary64) i)))
(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha beta) (fma.f64 i #s(literal 4 binary64) (+.f64 alpha beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 beta (.f64 i (+.f64 alpha i))) (*.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 (/.f64 beta (fma.f64 (+.f64 alpha beta) (+.f64 beta (fma.f64 i #s(literal 4 binary64) alpha)) #s(literal -1 binary64))) (.f64 i (+.f64 i alpha))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
(.f64 (.f64 i (+.f64 i alpha)) (.f64 beta (/.f64 #s(literal 1 binary64) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))))
(/.f64 (.f64 (.f64 i 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 beta (.f64 i (+.f64 alpha i))) (fma.f64 i (fma.f64 #s(literal 4 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 #s(literal 2 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) #s(literal -2 binary64))) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha 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 (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 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 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (.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 alpha (fma.f64 i #s(literal 2 binary64) beta))))))
(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (/.f64 (/.f64 (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)) (+.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 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 #s(literal 1 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 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.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 (exp.f64 (.f64 (log.f64 (/.f64 beta (+.f64 i alpha))) #s(literal -1 binary64))) (/.f64 i beta))
(.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
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))

Calls

4 calls:

133.0ms	beta
17.0ms	i
16.0ms	alpha
14.0ms	(/.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
75.0%	2	`alpha`
87.5%	2	`beta`
81.6%	2	`i`
76.2%	2	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`

Compiler

Compiled 68 to 26 computations (61.8% saved)

regimes22.0ms (0.2%)

Memory

-28.0MiB live, 14.3MiB allocated

Counts

19 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i beta)
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/.f64 (*.f64 #s(literal 1/2 binary64) i) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(.f64 beta (/.f64 i (.f64 alpha alpha)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/.f64 (.f64 i (+.f64 beta i)) (.f64 alpha alpha))
(/.f64 (.f64 i (+.f64 i beta)) (.f64 alpha alpha))
(*.f64 i (/.f64 (/.f64 i beta) beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))
(*.f64 (/.f64 i beta) (/.f64 i beta))
(/.f64 (.f64 i i) (.f64 beta (fma.f64 i #s(literal 2 binary64) beta)))
(/.f64 (*.f64 (/.f64 i beta) alpha) beta)
(*.f64 (+.f64 i alpha) (/.f64 (/.f64 i beta) beta))

Outputs
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(*.f64 (/.f64 i beta) (/.f64 i beta))

Calls

1 calls:

21.0ms

beta

Results

Accuracy	Segments	Branch
84.6%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes11.0ms (0.1%)

Memory

27.0MiB live, 27.0MiB allocated

Counts

15 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i beta)
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/.f64 (*.f64 #s(literal 1/2 binary64) i) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(.f64 beta (/.f64 i (.f64 alpha alpha)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/.f64 (.f64 i (+.f64 beta i)) (.f64 alpha alpha))
(/.f64 (.f64 i (+.f64 i beta)) (.f64 alpha alpha))
(*.f64 i (/.f64 (/.f64 i beta) beta))
(*.f64 (/.f64 i beta) (/.f64 alpha beta))

Outputs
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(*.f64 i (/.f64 (/.f64 i beta) beta))

Calls

2 calls:

5.0ms	beta
5.0ms	i

Results

Accuracy	Segments	Branch
74.0%	2	`i`
80.2%	2	`beta`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes11.0ms (0.1%)

Memory

-18.0MiB live, 19.7MiB allocated

Counts

13 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i beta)
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/.f64 (*.f64 #s(literal 1/2 binary64) i) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(.f64 beta (/.f64 i (.f64 alpha alpha)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/.f64 (.f64 i (+.f64 beta i)) (.f64 alpha alpha))
(/.f64 (.f64 i (+.f64 i beta)) (.f64 alpha alpha))

Outputs
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))

Calls

2 calls:

7.0ms

beta

4.0ms

(/.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
72.6%	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)))`
75.9%	2	`beta`

Compiler

Compiled 60 to 20 computations (66.7% saved)

regimes9.0ms (0.1%)

Memory

22.6MiB live, 22.6MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i beta)
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/.f64 (*.f64 #s(literal 1/2 binary64) i) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))

Outputs
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))

Calls

4 calls:

2.0ms	beta
2.0ms	i
2.0ms	alpha
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
70.8%	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)))`
70.8%	1	`i`
70.8%	1	`alpha`
70.8%	1	`beta`

Compiler

Compiled 68 to 26 computations (61.8% saved)

regimes10.0ms (0.1%)

Memory

-18.9MiB live, 18.0MiB allocated

Accuracy

Total -43.1b remaining (-229.5%)

Threshold costs -43.1b (-229.5%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i beta)
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/.f64 (*.f64 #s(literal 1/2 binary64) i) beta)

Outputs
#s(literal 1/16 binary64)

Calls

4 calls:

4.0ms	alpha
2.0ms	i
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
70.7%	1	`beta`
70.7%	1	`i`
70.7%	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)))`
70.7%	1	`alpha`

Compiler

Compiled 68 to 26 computations (61.8% saved)

bsearch21.0ms (0.1%)

Memory

-14.7MiB live, 22.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	3.99977467754345e+209	2.8615582243391666e+210

Samples

8.0ms

96×

valid

Compiler

Compiled 203 to 125 computations (38.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 2.0ms (36% of total)

ival-mult: 2.0ms (36% of total)

ival-div: 1.0ms (18% 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)

bsearch14.0ms (0.1%)

Memory

23.2MiB live, 23.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	3.99977467754345e+209	2.8615582243391666e+210

Samples

8.0ms

96×

valid

Compiler

Compiled 191 to 113 computations (40.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 2.0ms (35% of total)

ival-mult: 2.0ms (35% of total)

ival-div: 1.0ms (17.5% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch39.0ms (0.3%)

Memory

-15.2MiB live, 28.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
36.0ms	1.6581342707761505e+205	1.5168188434012379e+209

Samples

32.0ms

128×

valid

Compiler

Compiled 235 to 151 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-add: 23.0ms (81% of total)

ival-mult: 3.0ms (10.6% of total)

ival-sub: 1.0ms (3.5% of total)

ival-div: 1.0ms (3.5% of total)

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

exact: 0.0ms (0% of total)

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

bsearch17.0ms (0.1%)

Memory

0.4MiB live, 38.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	1.0876769791184508e+222	2.7203512471863472e+224

Samples

11.0ms

112×

valid

Compiler

Compiled 213 to 135 computations (36.6% saved)

Precisions

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

ival-mult: 3.0ms (43.1% of total)

ival-add: 2.0ms (28.8% of total)

ival-sub: 1.0ms (14.4% of total)

ival-div: 1.0ms (14.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Memory

20.7MiB live, 20.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	82
1	35	82

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 beta #s(literal 460000000000000019031655827906207483061684248183002092561098084047519936375968654584986633598406773008179920264272431084885162205882014611280660669561696625193564426738591487368004365305283590129600855113990144 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 1149999999999999938080564746832833460266092083650513433965261036153361507039301206879862570987759656378542329043767483024797475748439261071672738360893729604920039393513338200372138728616850173335021523866484736 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 i beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 21999999999999998360573993361806535294371472977597624632562184140135872708168769061711485366487648559790752579439582670152684486450634765530998646286486511583551449754689843379495032736914413591679069061120 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 i (/.f64 (/.f64 i beta) beta)))
(if (<=.f64 beta #s(literal 2800000000000000130485060089497953191534240267858255211978745282452311787704641638803749594199747994498895134468759371622888332664819314655809741872979401633644804356628485421318564176506154667314087260160368679796193886208 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 alpha (/.f64 i (*.f64 beta beta))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
#s(literal 1/16 binary64)

Outputs
(if (<=.f64 beta #s(literal 460000000000000019031655827906207483061684248183002092561098084047519936375968654584986633598406773008179920264272431084885162205882014611280660669561696625193564426738591487368004365305283590129600855113990144 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 1149999999999999938080564746832833460266092083650513433965261036153361507039301206879862570987759656378542329043767483024797475748439261071672738360893729604920039393513338200372138728616850173335021523866484736 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 i beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 21999999999999998360573993361806535294371472977597624632562184140135872708168769061711485366487648559790752579439582670152684486450634765530998646286486511583551449754689843379495032736914413591679069061120 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 i (/.f64 (/.f64 i beta) beta)))
(if (<=.f64 beta #s(literal 2800000000000000130485060089497953191534240267858255211978745282452311787704641638803749594199747994498895134468759371622888332664819314655809741872979401633644804356628485421318564176506154667314087260160368679796193886208 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 alpha (/.f64 i (*.f64 beta beta))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
#s(literal 1/16 binary64)

soundness1.0s (7.1%)

Memory

2.2MiB live, 1 163.3MiB allocated

Rules

9 164×	`accelerator-lowering-fma.f32`
9 164×	`accelerator-lowering-fma.f64`
7 782×	`-lowering-.f32`
7 782×	`-lowering-.f64`
7 452×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	267
1	292	264
2	3225	263
0	9240	244
0	1089	12630
1	3841	11840
0	8260	10972
0	1031	10870
1	3521	10674
0	8981	9772
0	874	9226
1	2981	8757
0	8411	8157
0	1773	24272
1	6259	23842
0	8116	21887
0	34	158
1	223	158
2	2119	158
0	9138	149

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 485 to 278 computations (42.7% saved)

preprocess55.0ms (0.4%)

Memory: -22.6MiB live, 133.4MiB allocated
Compiler: Compiled 328 to 124 computations (62.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze15.0ms (0.1%)

sample2.4s (16.7%)

preprocess363.0ms (2.6%)

explain344.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify350.0ms (2.5%)

localize51.0ms (0.4%)

series91.0ms (0.6%)

rewrite725.0ms (5.1%)

simplify477.0ms (3.4%)

eval581.0ms (4.1%)

prune366.0ms (2.6%)

simplify530.0ms (3.7%)

localize127.0ms (0.9%)

series68.0ms (0.5%)

rewrite586.0ms (4.1%)

simplify544.0ms (3.8%)

eval265.0ms (1.9%)

prune284.0ms (2%)

simplify570.0ms (4%)

localize181.0ms (1.3%)

series59.0ms (0.4%)

rewrite552.0ms (3.9%)

simplify513.0ms (3.6%)

eval215.0ms (1.5%)

prune254.0ms (1.8%)

simplify509.0ms (3.6%)

localize131.0ms (0.9%)

series87.0ms (0.6%)

rewrite472.0ms (3.3%)

simplify563.0ms (4%)

eval272.0ms (1.9%)

prune263.0ms (1.9%)

regimes184.0ms (1.3%)

regimes22.0ms (0.2%)

regimes11.0ms (0.1%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

regimes10.0ms (0.1%)

bsearch21.0ms (0.1%)

bsearch14.0ms (0.1%)

bsearch39.0ms (0.3%)

bsearch17.0ms (0.1%)

simplify8.0ms (0.1%)

soundness1.0s (7.1%)

preprocess55.0ms (0.4%)

end0.0ms (0%)

Profiling