Metrics for Octave 3.8, jcobi/2

analyze45.0ms (0.3%)

Memory

-6.6MiB live, 73.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	28.1%	71.9%	0%	0%	0%	0
0%	0%	28.1%	71.9%	0%	0%	0%	1
0%	0%	28.1%	71.9%	0%	0%	0%	2
25%	7%	21.1%	71.9%	0%	0%	0%	3
62.5%	17.5%	10.5%	71.9%	0%	0%	0%	4
75%	21.1%	7%	71.9%	0%	0%	0%	5
81.3%	22.8%	5.3%	71.9%	0%	0%	0%	6
82.8%	23.2%	4.8%	71.9%	0%	0%	0%	7
83.6%	23.5%	4.6%	71.9%	0%	0%	0%	8
87.1%	24.5%	3.6%	71.9%	0%	0%	0%	9
89.1%	25%	3.1%	71.9%	0%	0%	0%	10
91.5%	25.7%	2.4%	71.9%	0%	0%	0%	11
93.6%	26.3%	1.8%	71.9%	0%	0%	0%	12

Compiler

Compiled 41 to 23 computations (43.9% saved)

sample2.5s (18.3%)

Memory

-79.5MiB live, 2 561.9MiB allocated

Samples

1.1s	6 577×	0	valid
617.0ms	1 215×	1	valid
180.0ms	448×	2	valid
5.0ms	16×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival->: 573.0ms (37.3% of total)

ival-add: 376.0ms (24.5% of total)

ival-div: 260.0ms (16.9% of total)

ival-mult: 139.0ms (9.1% of total)

ival-sub: 75.0ms (4.9% of total)

adjust: 69.0ms (4.5% of total)

ival-and: 22.0ms (1.4% of total)

exact: 19.0ms (1.2% of total)

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

Bogosity

preprocess405.0ms (3%)

Memory

6.7MiB live, 719.5MiB allocated

Algorithm

1×	egg-herbie

Rules

16 958×	`accelerator-lowering-fma.f32`
16 958×	`accelerator-lowering-fma.f64`
3 860×	`+-lowering-+.f64`
3 860×	`+-lowering-+.f32`
3 552×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	269
1	186	263
2	682	263
3	3464	261
0	15	29
1	33	29
2	108	29
3	478	29
4	2378	29
5	3830	29
6	5123	29
0	8033	26

Stop Event

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

Calls

Call 1

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

Outputs

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

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

explain254.0ms (1.9%)

Memory

26.1MiB live, 445.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
96	-	1	(1.0481348602569986e-184 -3.5332491521026136e-158 2.703693542344533e-128)	`(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))`
58	-	0	-	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
0	-	0	-	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`
0	-	0	-	`beta`
0	-	0	-	`(+.f64 alpha beta)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`alpha`
0	-	0	-	`(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))`
0	-	0	-	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`i`
0	-	0	-	`(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))`
0	-	0	-	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
0	-	0	-	`(-.f64 beta alpha)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) i)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))`	o/n	82	0
↳	`(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))`	overflow	82
`+.f64`	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`	cancellation	58	0

Confusion

	Predicted +	Predicted -
+	107	0
-	0	149

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	107	0	0
-	0	0	149

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	149
1	74
2	33

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

56.0ms	398×	0	valid
14.0ms	68×	1	valid
12.0ms	38×	2	valid
3.0ms	8×	3	valid

Compiler

Compiled 334 to 64 computations (80.8% saved)

Precisions

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

ival-div: 12.0ms (28.9% of total)

ival-add: 12.0ms (28.9% of total)

ival-mult: 8.0ms (19.3% of total)

adjust: 5.0ms (12% of total)

ival-sub: 3.0ms (7.2% of total)

exact: 1.0ms (2.4% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.7%	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))

Status

Accuracy

Program

▶

59.7%

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

Compiler

Compiled 32 to 15 computations (53.1% saved)

simplify441.0ms (3.3%)

Memory

10.6MiB live, 645.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

16 958×	`accelerator-lowering-fma.f32`
16 958×	`accelerator-lowering-fma.f64`
3 860×	`+-lowering-+.f64`
3 860×	`+-lowering-+.f32`
3 552×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	133
1	33	133
2	108	133
3	478	133
4	2378	133
5	3830	133
6	5123	133
0	8033	122

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize62.0ms (0.5%)

Memory

7.9MiB live, 120.3MiB 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)) #s(literal 2 binary64))
✓	accuracy	99.9%	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))
✓	accuracy	78.9%	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))
✓	accuracy	65.3%	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))

Samples

23.0ms	199×	0	valid
8.0ms	19×	2	valid
7.0ms	34×	1	valid
2.0ms	4×	3	valid

Compiler

Compiled 135 to 17 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-div: 6.0ms (28.7% of total)

ival-add: 6.0ms (28.7% of total)

ival-mult: 4.0ms (19.1% of total)

adjust: 2.0ms (9.6% of total)

ival-sub: 2.0ms (9.6% of total)

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

exact: 0.0ms (0% of total)

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

series73.0ms (0.5%)

Memory

-52.1MiB live, 107.3MiB allocated

Counts

6 → 216

Calls

Call 1

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

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

Calls

54 calls:

Time	Variable		Point	Expression
6.0ms	beta	@	-inf	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))
4.0ms	beta	@	0	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
3.0ms	alpha	@	inf	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
2.0ms	i	@	inf	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
2.0ms	alpha	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))

rewrite634.0ms (4.7%)

Memory

36.8MiB live, 581.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 612×	`/-lowering-/.f32`
5 612×	`/-lowering-/.f64`
5 576×	`-lowering-.f32`
5 576×	`-lowering-.f64`
3 560×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	112
1	115	112
2	1187	112
0	8698	101

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 386

Calls

Call 1

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

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

simplify530.0ms (3.9%)

Memory

-22.2MiB live, 744.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 344×	`-lowering-.f32`
6 344×	`-lowering-.f64`
6 302×	`accelerator-lowering-fma.f32`
6 302×	`accelerator-lowering-fma.f64`
5 416×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	964	13312
1	3265	11681
0	9032	10518

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval141.0ms (1%)

Memory: 25.2MiB live, 215.4MiB allocated
Compiler: Compiled 36 499 to 2 927 computations (92% saved)

prune128.0ms (0.9%)

Memory

-9.5MiB live, 266.2MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	668	14	682
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	669	14	683

Accuracy

100.0%

Counts

683 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.4%	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	59.6%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	21.4%	(fma.f64 i (.f64 #s(literal -1/2 binary64) (fma.f64 i (-.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 beta alpha)) (.f64 (+.f64 beta alpha) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta)))) (.f64 (.f64 #s(literal 4 binary64) (.f64 (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 beta alpha)) (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 beta alpha)))) (/.f64 (-.f64 beta alpha) (.f64 (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))) (.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (.f64 (.f64 #s(literal 2 binary64) (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (.f64 (+.f64 beta alpha) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta)))))
	23.2%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta) #s(literal 1 binary64))
▶	78.9%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64))
	59.7%	(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	21.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	16.8%	(/.f64 (-.f64 (.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (fma.f64 beta beta (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) (.f64 (+.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)))) (/.f64 (fma.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 (fma.f64 beta beta (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) (.f64 (+.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)))) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)))) alpha))) alpha)) (neg.f64 alpha))
	3.5%	(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
	24.7%	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
▶	19.2%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
▶	66.1%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))
	32.9%	#s(literal 1 binary64)
▶	60.0%	#s(literal 1/2 binary64)

Compiler

Compiled 1 062 to 414 computations (61% saved)

simplify329.0ms (2.4%)

Memory

9.6MiB live, 631.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

8 480×	`accelerator-lowering-fma.f32`
8 480×	`accelerator-lowering-fma.f64`
3 814×	`--lowering--.f32`
3 814×	`--lowering--.f64`
3 452×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	536
1	139	536
2	423	536
3	1674	522
4	6786	522
0	8181	452

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize289.0ms (2.1%)

Memory

-5.6MiB live, 526.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
✓	accuracy	91.1%	(/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha)
✓	accuracy	80.4%	(-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))))
✓	accuracy	57.8%	(fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))
✓	accuracy	100.0%	(+.f64 beta alpha)
✓	accuracy	100.0%	(*.f64 (-.f64 beta alpha) (+.f64 beta alpha))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	76.2%	(/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) alpha)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta)))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))
✓	accuracy	73.2%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))
✓	accuracy	100.0%	(+.f64 alpha beta)
✓	accuracy	100.0%	(/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	79.3%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64))

Samples

55.0ms	27×	1	valid
53.0ms	183×	0	valid
48.0ms	29×	2	valid
17.0ms	15×	3	valid
2.0ms	1×	5	exit
1.0ms	1×	4	valid

Compiler

Compiled 485 to 49 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

adjust: 52.0ms (36.1% of total)

ival-add: 26.0ms (18.1% of total)

ival-mult: 23.0ms (16% of total)

ival-sub: 22.0ms (15.3% of total)

ival-div: 20.0ms (13.9% of total)

exact: 1.0ms (0.7% of total)

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

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

series144.0ms (1.1%)

Memory

10.9MiB live, 195.5MiB allocated

Counts

21 → 588

Calls

Call 1

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

Outputs
#<alt (+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))>
#<alt (+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))>
#<alt (+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))>
#<alt (+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (+ (* beta (- (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 3) (pow (+ alpha (* 2 i)) 3)))) (+ (* -1 (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (+ (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))) (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))>
#<alt 2>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (* -1 (pow alpha 2)) (+ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))))))) (pow beta 3))) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta))))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))>
#<alt 2>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (* -1 (/ (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) beta)))>
#<alt (+ 2 (* -1 (/ (- (+ (* -1 (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) (/ (pow alpha 2) beta)) (+ (* -1 (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) beta)) (/ (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) beta))) beta)))>
#<alt (+ 2 (* -1 (/ (+ (* -1 (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) (* -1 (/ (+ (* -1 (- (pow alpha 2) (+ (* -1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))))))))) (* -1 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))))))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (pow alpha 2) (+ (* -1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))))))) beta))) beta))) beta)))>
#<alt (+ 1 (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))>
#<alt (+ 1 (+ (* alpha (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))))>
#<alt (+ 1 (+ (* alpha (- (+ (* -1 (* alpha (+ (/ 1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (/ (pow beta 2) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))))) (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))))>
#<alt (+ 1 (+ (* alpha (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (+ (* alpha (- (* alpha (- (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 3) (pow (+ beta (* 2 i)) 3))) (+ (* -1 (/ beta (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2)))) (+ (* -1 (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (+ (/ 1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (/ (pow beta 2) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2)))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))))) (+ (/ 1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (/ (pow beta 2) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))))>
#<alt (/ (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))) alpha)>
#<alt (/ (- (+ beta (+ (* -1 beta) (/ (pow beta 2) alpha))) (+ (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))) (+ (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))) alpha)) (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))) alpha)))) alpha)>
#<alt (/ (- (+ beta (+ (* -1 beta) (+ (* -1 (/ (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))))))) (pow alpha 2))) (/ (pow beta 2) alpha)))) (+ (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))) (+ (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))) alpha)) (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))) alpha)))) alpha)>
#<alt (/ (- (+ beta (+ (* -1 beta) (+ (* -1 (/ (+ (* -1 (* (+ 2 (+ (* 2 beta) (* 4 i))) (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))))))))) (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))))))) (pow alpha 3))) (/ (pow beta 2) alpha)))) (+ (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))) (+ (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))) alpha)) (+ (/ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))) (pow alpha 2)) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))) alpha) (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))))) (pow alpha 2))))))) alpha)>
#<alt (* -1 (/ (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))) alpha))>
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#<alt (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) (pow alpha 2)))>
#<alt (/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))>
#<alt (/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))>
#<alt (/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))>
#<alt (* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))>
#<alt (/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)>
#<alt (/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)>
#<alt (/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)>
#<alt (* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))>
#<alt (* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))>
#<alt (/ beta (+ 2 (+ beta (* 2 i))))>
#<alt (+ (* alpha (- (/ 1 (+ 2 (+ beta (* 2 i)))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))>
#<alt (+ (* alpha (- (+ (* alpha (- (/ beta (pow (+ 2 (+ beta (* 2 i))) 3)) (/ 1 (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ 1 (+ 2 (+ beta (* 2 i))))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))>
#<alt (+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ 1 (pow (+ 2 (+ beta (* 2 i))) 3)) (/ beta (pow (+ 2 (+ beta (* 2 i))) 4)))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 3))) (/ 1 (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ 1 (+ 2 (+ beta (* 2 i))))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ 2 (* 2 i)) alpha)))>
#<alt (- (+ 1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ beta (* 2 i)))) (pow alpha 2))) (+ (* 2 (/ i alpha)) (* 2 (/ 1 alpha))))>
#<alt (- (+ 1 (* -1 (/ (* (+ 2 (* 2 i)) (pow (+ 2 (+ beta (* 2 i))) 2)) (pow alpha 3)))) (+ (* -1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ beta (* 2 i)))) (pow alpha 2))) (+ (* 2 (/ i alpha)) (* 2 (/ 1 alpha)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))>
#<alt (+ 1 (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))) alpha))) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))>
#<alt (+ 1 (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 (+ beta (* 2 i))) 2) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))) alpha)) (* -1 (* (+ 2 (+ beta (* 2 i))) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))))) alpha))) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))>
#<alt (/ alpha (+ 2 (+ alpha (* 2 i))))>
#<alt (+ (* beta (- (/ 1 (+ 2 (+ alpha (* 2 i)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))>
#<alt (+ (* beta (- (+ (* beta (- (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))>
#<alt (+ (* beta (- (+ (* beta (- (+ (* beta (- (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 4)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3))) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ 2 (* 2 i)) beta)))>
#<alt (- (+ 1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta))))>
#<alt (- (+ 1 (* -1 (/ (* (+ 2 (* 2 i)) (pow (+ 2 (+ alpha (* 2 i))) 2)) (pow beta 3)))) (+ (* -1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))>
#<alt (+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))>
#<alt (+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 (+ alpha (* 2 i))) 2) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta)) (* -1 (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))>
#<alt (/ (+ alpha beta) (+ 2 (+ alpha beta)))>
#<alt (+ (* -2 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 2))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))>
#<alt (+ (* i (- (* 4 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 3))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))>
#<alt (+ (* i (- (* i (- (* -8 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 4))) (* -4 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 3))))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))>
#<alt (* 1/2 (/ (+ alpha beta) i))>
#<alt (/ (+ (* -1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)) (* 1/2 (+ alpha beta))) i)>
#<alt (/ (- (+ (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/2 (+ alpha beta))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i)>
#<alt (/ (- (+ (* -1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) (pow i 3))) (* 1/2 (+ alpha beta))) (+ (* -1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)))) i)>
#<alt (* 1/2 (/ (+ alpha beta) i))>
#<alt (* -1 (/ (+ (* -1/2 (+ alpha beta)) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) i)) (* 1/8 (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))>
#<alt beta>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt alpha>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt alpha>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt beta>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt beta>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt 2>
#<alt (+ 2 alpha)>
#<alt (+ 2 alpha)>
#<alt (+ 2 alpha)>
#<alt alpha>
#<alt (* alpha (+ 1 (* 2 (/ 1 alpha))))>
#<alt (* alpha (+ 1 (* 2 (/ 1 alpha))))>
#<alt (* alpha (+ 1 (* 2 (/ 1 alpha))))>
#<alt alpha>
#<alt (* alpha (+ 1 (* 2 (/ 1 alpha))))>
#<alt (* alpha (+ 1 (* 2 (/ 1 alpha))))>
#<alt (* alpha (+ 1 (* 2 (/ 1 alpha))))>
#<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>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt beta>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt beta>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt beta>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt alpha>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2))>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) (pow (+ 2 (* 4 i)) 2)))>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))>
#<alt (* 3 (pow beta 2))>
#<alt (* (pow beta 2) (+ 3 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta)))))>
#<alt (* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))>
#<alt (* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))>
#<alt (* 3 (pow beta 2))>
#<alt (* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) beta))))>
#<alt (* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))>
#<alt (* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) (pow (+ 2 (* 2 beta)) 2)))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))>
#<alt (* 12 (pow i 2))>
#<alt (* (pow i 2) (+ 12 (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (* 8 (/ (+ 2 (* 2 beta)) i)))))>
#<alt (* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))>
#<alt (* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))>
#<alt (* 12 (pow i 2))>
#<alt (* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) i))))>
#<alt (* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))>
#<alt (* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))>
#<alt (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha))>
#<alt (+ (* -1 (/ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) alpha)) (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)))>
#<alt (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))>
#<alt (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))>
#<alt (* -2 (/ (pow beta 2) alpha))>
#<alt (* (pow beta 2) (- (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta))) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))>
#<alt (* -2 (/ (pow beta 2) alpha))>
#<alt (* (pow beta 2) (- (+ (* -4 (/ (+ 2 (* 4 i)) (* alpha beta))) (+ (* 4 (/ i (* alpha beta))) (* 2 (/ 1 (* alpha beta))))) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))>
#<alt (/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) alpha)>
#<alt (- (+ (* -1 (/ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) alpha)) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))>
#<alt (- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))>
#<alt (- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))>
#<alt (* -12 (/ (pow i 2) alpha))>
#<alt (* (pow i 2) (- (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (* 12 (/ 1 alpha))))>
#<alt (* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))>
#<alt (* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))>
#<alt (* -12 (/ (pow i 2) alpha))>
#<alt (* (pow i 2) (- (+ (* -8 (/ (+ 2 (* 2 beta)) (* alpha i))) (+ (* 2 (/ beta (* alpha i))) (* 2 (/ (+ 2 beta) (* alpha i))))) (* 12 (/ 1 alpha))))>
#<alt (* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))>
#<alt (* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>

Calls

147 calls:

Time	Variable		Point	Expression
32.0ms	i	@	-inf	(/ (- (* beta beta) (+ (* (+ 2 (+ (* beta 2) (* i 4))) (+ 2 (+ (* beta 2) (* i 4)))) (* (+ (* 2 i) beta) (- -2 (+ (* 2 i) beta))))) alpha)
28.0ms	i	@	-inf	(- (* beta beta) (+ (* (+ 2 (+ (* beta 2) (* i 4))) (+ 2 (+ (* beta 2) (* i 4)))) (* (+ (* 2 i) beta) (- -2 (+ (* 2 i) beta)))))
7.0ms	i	@	-inf	(* 1/2 (+ (+ 2 (+ (* beta 2) (* i 4))) (/ (- (* beta beta) (+ (* (+ 2 (+ (* beta 2) (* i 4))) (+ 2 (+ (* beta 2) (* i 4)))) (* (+ (* 2 i) beta) (- -2 (+ (* 2 i) beta))))) alpha)))
5.0ms	alpha	@	-inf	(* (- beta alpha) (+ beta alpha))
4.0ms	beta	@	0	(+ 1/2 (* 1/2 (/ (- beta alpha) (+ (+ 2 alpha) beta))))

rewrite428.0ms (3.2%)

Memory

-5.3MiB live, 703.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 292×	`-lowering-.f32`
4 292×	`-lowering-.f64`
3 728×	`pow-lowering-pow.f64`
3 728×	`pow-lowering-pow.f32`
3 668×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	343
1	387	343
2	4466	343
0	8706	302

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 559

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))))
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simplify579.0ms (4.3%)

Memory

22.2MiB live, 808.4MiB allocated

Algorithm

1×	egg-herbie

Rules

5 776×	`accelerator-lowering-fma.f32`
5 776×	`accelerator-lowering-fma.f64`
5 644×	`-lowering-.f32`
5 644×	`-lowering-.f64`
4 448×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1891	20573
1	6208	20028
0	8058	18419

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 588

Calls

Call 1

Inputs
(+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (+ (* beta (- (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 3) (pow (+ alpha (* 2 i)) 3)))) (+ (* -1 (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (+ (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))) (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
2
(- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))
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1
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(/ beta (+ 2 beta))
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(+ 1/2 (* -1/8 (/ (pow alpha 2) (pow i 2))))
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(+ 1/2 (+ (* -1/8 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* 1/8 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))) (* 1/8 (/ beta (pow i 2)))))))
(* 1/8 (/ (pow beta 2) (pow i 2)))
(* (pow beta 2) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow beta 2) (+ (* -1/8 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (+ (/ 1/2 (pow beta 2)) (* 1/8 (/ 1 (pow i 2)))))))
(* (pow beta 2) (+ (* -1/8 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (+ (/ 1/2 (pow beta 2)) (* 1/8 (/ 1 (pow i 2)))))))
(* 1/8 (/ (pow beta 2) (pow i 2)))
(* (pow beta 2) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/8 (/ (pow alpha 2) (pow i 2)))) beta)) (* -1/8 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/8 (/ (pow alpha 2) (pow i 2)))) beta)) (* -1/8 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(+ 1/2 (* 1/8 (/ (pow beta 2) (pow i 2))))
(+ 1/2 (+ (* 1/8 (* alpha (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) (* 1/8 (/ (pow beta 2) (pow i 2)))))
(+ 1/2 (+ (* 1/8 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ alpha (pow i 2))) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))))))
(+ 1/2 (+ (* 1/8 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ alpha (pow i 2))) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))))))
(* -1/8 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (* 1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (+ (* 1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (+ (* 1/8 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/2 (pow alpha 2)))) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (+ (* 1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (+ (* 1/8 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/2 (pow alpha 2)))) (* 1/8 (/ 1 (pow i 2)))))
(* -1/8 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (* -1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/8 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/8 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))
(/ (+ (* 1/8 (* (+ alpha beta) (- beta alpha))) (* 1/2 (pow i 2))) (pow i 2))
(/ (+ (* 1/8 (* (+ alpha beta) (- beta alpha))) (* 1/2 (pow i 2))) (pow i 2))
(/ (+ (* 1/8 (* (+ alpha beta) (- beta alpha))) (* 1/2 (pow i 2))) (pow i 2))
1/2
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
1/2
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(* -1 (/ (pow alpha 2) (pow i 2)))
(+ (* -1 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))))
(+ (* -1 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1 (/ alpha (pow i 2))) (+ (/ alpha (pow i 2)) (/ beta (pow i 2))))))
(+ (* -1 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1 (/ alpha (pow i 2))) (+ (/ alpha (pow i 2)) (/ beta (pow i 2))))))
(/ (pow beta 2) (pow i 2))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2))))))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (* -1 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2)))))))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (* -1 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2)))))))
(/ (pow beta 2) (pow i 2))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2))))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))) (/ (pow alpha 2) (* beta (pow i 2)))) beta)) (/ 1 (pow i 2))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))) (/ (pow alpha 2) (* beta (pow i 2)))) beta)) (/ 1 (pow i 2))))
(/ (pow beta 2) (pow i 2))
(+ (* alpha (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2)))) (/ (pow beta 2) (pow i 2)))
(+ (* alpha (+ (* -1 (/ alpha (pow i 2))) (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) (/ (pow beta 2) (pow i 2)))
(+ (* alpha (+ (* -1 (/ alpha (pow i 2))) (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) (/ (pow beta 2) (pow i 2)))
(* -1 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (+ (* -1 (/ beta (* alpha (pow i 2)))) (/ beta (* alpha (pow i 2)))) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (+ (* -1 (/ beta (* alpha (pow i 2)))) (+ (/ beta (* alpha (pow i 2))) (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (+ (* -1 (/ beta (* alpha (pow i 2)))) (+ (/ beta (* alpha (pow i 2))) (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (/ 1 (pow i 2))))
(* -1 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ beta (pow i 2))) (+ (* -1 (/ (pow beta 2) (* alpha (pow i 2)))) (/ beta (pow i 2)))) alpha)) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ beta (pow i 2))) (+ (* -1 (/ (pow beta 2) (* alpha (pow i 2)))) (/ beta (pow i 2)))) alpha)) (/ 1 (pow i 2))))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(* -1 (pow alpha 2))
(+ (* -1 (pow alpha 2)) (* beta (+ alpha (* -1 alpha))))
(+ (* -1 (pow alpha 2)) (* beta (+ alpha (+ beta (* -1 alpha)))))
(+ (* -1 (pow alpha 2)) (* beta (+ alpha (+ beta (* -1 alpha)))))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (/ alpha beta))))
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))))
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (/ alpha beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha (* -1 alpha))) (/ (pow alpha 2) beta)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha (* -1 alpha))) (/ (pow alpha 2) beta)) beta))))
(pow beta 2)
(+ (* alpha (+ beta (* -1 beta))) (pow beta 2))
(+ (* alpha (+ beta (+ (* -1 alpha) (* -1 beta)))) (pow beta 2))
(+ (* alpha (+ beta (+ (* -1 alpha) (* -1 beta)))) (pow beta 2))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (+ (* -1 (/ beta alpha)) (/ beta alpha)) 1))
(* (pow alpha 2) (- (+ (* -1 (/ beta alpha)) (+ (/ beta alpha) (/ (pow beta 2) (pow alpha 2)))) 1))
(* (pow alpha 2) (- (+ (* -1 (/ beta alpha)) (+ (/ beta alpha) (/ (pow beta 2) (pow alpha 2)))) 1))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (* -1 (/ (+ beta (* -1 beta)) alpha)) 1))
(* (pow alpha 2) (- (* -1 (/ (+ beta (+ (* -1 beta) (* -1 (/ (pow beta 2) alpha)))) alpha)) 1))
(* (pow alpha 2) (- (* -1 (/ (+ beta (+ (* -1 beta) (* -1 (/ (pow beta 2) alpha)))) alpha)) 1))
(* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))))
(+ (* 1/2 (* beta (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))))) (* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha)))))
(+ (* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha)))) (* beta (+ (* -1 (/ beta alpha)) (* 1/2 (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha))))))))
(+ (* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha)))) (* beta (+ (* -1 (/ beta alpha)) (* 1/2 (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha))))))))
(* -1 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (* 1/2 (/ (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))) beta)) (/ 1 alpha)))
(* (pow beta 2) (- (+ (* 1/2 (/ (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))) beta)) (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) (pow beta 2)))) (/ 1 alpha)))
(* (pow beta 2) (- (+ (* 1/2 (/ (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))) beta)) (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) (pow beta 2)))) (/ 1 alpha)))
(* -1 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (* 1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) beta)) (/ 1 alpha)))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha)))))) (* -1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) beta))) beta)) (/ 1 alpha)))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha)))))) (* -1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) beta))) beta)) (/ 1 alpha)))
(* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))))
(+ (* 1/2 (* i (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))))) (* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))))
(+ (* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))) (* i (+ (* -6 (/ i alpha)) (* 1/2 (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha))))))))
(+ (* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))) (* i (+ (* -6 (/ i alpha)) (* 1/2 (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha))))))))
(* -6 (/ (pow i 2) alpha))
(* (pow i 2) (- (* 1/2 (/ (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))) i)) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (+ (* 1/2 (/ (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))) i)) (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) (pow i 2)))) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (+ (* 1/2 (/ (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))) i)) (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) (pow i 2)))) (* 6 (/ 1 alpha))))
(* -6 (/ (pow i 2) alpha))
(* (pow i 2) (- (* 1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) i)) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))))) (* -1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))))) (* -1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 6 (/ 1 alpha))))
(* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) alpha)
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) alpha)
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) alpha)
(* 1/2 (+ 2 (+ (* 2 beta) (* 4 i))))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(* 1/2 (+ 2 (+ (* 2 beta) (* 4 i))))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(* -1 (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(- (* -1 (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))))) (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(- (* beta (- (* -2 beta) (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))))) (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(- (* beta (- (* -2 beta) (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))))) (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(* -2 (pow beta 2))
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) beta)) 2))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (pow beta 2))) (+ 2 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta))))))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (pow beta 2))) (+ 2 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta))))))
(* -2 (pow beta 2))
(* (pow beta 2) (- (+ (* -4 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))) 2))
(* (pow beta 2) (- (* -1 (/ (- (+ (* -2 (/ (* i (+ 2 (* 2 i))) beta)) (/ (pow (+ 2 (* 4 i)) 2) beta)) (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i)))) beta)) 2))
(* (pow beta 2) (- (* -1 (/ (- (+ (* -2 (/ (* i (+ 2 (* 2 i))) beta)) (/ (pow (+ 2 (* 4 i)) 2) beta)) (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i)))) beta)) 2))
(- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(- (+ (* -1 (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))))) (pow beta 2)) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(- (+ (* i (- (* -12 i) (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))))) (pow beta 2)) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(- (+ (* i (- (* -12 i) (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))))) (pow beta 2)) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(* -12 (pow i 2))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) i)) 12))
(* (pow i 2) (- (/ (pow beta 2) (pow i 2)) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2))))))))
(* (pow i 2) (- (/ (pow beta 2) (pow i 2)) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2))))))))
(* -12 (pow i 2))
(* (pow i 2) (- (+ (* -8 (/ (+ 2 (* 2 beta)) i)) (+ (* 2 (/ beta i)) (* 2 (/ (+ 2 beta) i)))) 12))
(* (pow i 2) (- (* -1 (/ (- (* -1 (/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) i)) (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta))))) i)) 12))
(* (pow i 2) (- (* -1 (/ (- (* -1 (/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) i)) (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta))))) i)) 12))
(+ 2 (* 4 i))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(* 2 beta)
(* beta (+ 2 (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(* beta (+ 2 (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(* beta (+ 2 (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(* 2 beta)
(* -1 (* beta (- (* -1 (/ (+ 2 (* 4 i)) beta)) 2)))
(* -1 (* beta (- (* -1 (/ (+ 2 (* 4 i)) beta)) 2)))
(* -1 (* beta (- (* -1 (/ (+ 2 (* 4 i)) beta)) 2)))
(+ 2 (* 2 beta))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(* 4 i)
(* i (+ 4 (+ (* 2 (/ beta i)) (* 2 (/ 1 i)))))
(* i (+ 4 (+ (* 2 (/ beta i)) (* 2 (/ 1 i)))))
(* i (+ 4 (+ (* 2 (/ beta i)) (* 2 (/ 1 i)))))
(* 4 i)
(* -1 (* i (- (* -1 (/ (+ 2 (* 2 beta)) i)) 4)))
(* -1 (* i (- (* -1 (/ (+ 2 (* 2 beta)) i)) 4)))
(* -1 (* i (- (* -1 (/ (+ 2 (* 2 beta)) i)) 4)))
(* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha))
(+ (* 1/2 (* beta (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))))) (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha)))
(+ (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha)) (* beta (+ (* -1 (/ beta (pow alpha 2))) (* 1/2 (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2)))))))))
(+ (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha)) (* beta (+ (* -1 (/ beta (pow alpha 2))) (* 1/2 (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2)))))))))
(* -1 (/ (pow beta 2) (pow alpha 2)))
(* (pow beta 2) (- (* 1/2 (/ (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))) beta)) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (+ (* 1/2 (/ (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))) beta)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) (pow beta 2)))) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (+ (* 1/2 (/ (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))) beta)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) (pow beta 2)))) (/ 1 (pow alpha 2))))
(* -1 (/ (pow beta 2) (pow alpha 2)))
(* (pow beta 2) (- (* 1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) (* alpha beta))) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) beta))) beta)) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) beta))) beta)) (/ 1 (pow alpha 2))))
(* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha))
(+ (* 1/2 (* i (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))))) (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha)))
(+ (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha)) (* i (+ (* -6 (/ i (pow alpha 2))) (* 1/2 (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2)))))))))
(+ (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha)) (* i (+ (* -6 (/ i (pow alpha 2))) (* 1/2 (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2)))))))))
(* -6 (/ (pow i 2) (pow alpha 2)))
(* (pow i 2) (- (* 1/2 (/ (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))) i)) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (+ (* 1/2 (/ (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))) i)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) (pow i 2)))) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (+ (* 1/2 (/ (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))) i)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) (pow i 2)))) (* 6 (/ 1 (pow alpha 2)))))
(* -6 (/ (pow i 2) (pow alpha 2)))
(* (pow i 2) (- (* 1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) (* alpha i))) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) i))) i)) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) i))) i)) (* 6 (/ 1 (pow alpha 2)))))
(* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) (pow alpha 2)))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)
(/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)
(/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))
(* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))
(* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))
(/ beta (+ 2 (+ beta (* 2 i))))
(+ (* alpha (- (/ 1 (+ 2 (+ beta (* 2 i)))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))
(+ (* alpha (- (+ (* alpha (- (/ beta (pow (+ 2 (+ beta (* 2 i))) 3)) (/ 1 (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ 1 (+ 2 (+ beta (* 2 i))))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ 1 (pow (+ 2 (+ beta (* 2 i))) 3)) (/ beta (pow (+ 2 (+ beta (* 2 i))) 4)))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 3))) (/ 1 (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ 1 (+ 2 (+ beta (* 2 i))))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))
1
(+ 1 (* -1 (/ (+ 2 (* 2 i)) alpha)))
(- (+ 1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ beta (* 2 i)))) (pow alpha 2))) (+ (* 2 (/ i alpha)) (* 2 (/ 1 alpha))))
(- (+ 1 (* -1 (/ (* (+ 2 (* 2 i)) (pow (+ 2 (+ beta (* 2 i))) 2)) (pow alpha 3)))) (+ (* -1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ beta (* 2 i)))) (pow alpha 2))) (+ (* 2 (/ i alpha)) (* 2 (/ 1 alpha)))))
1
(+ 1 (* -1 (/ (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))
(+ 1 (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))) alpha))) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))
(+ 1 (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 (+ beta (* 2 i))) 2) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))) alpha)) (* -1 (* (+ 2 (+ beta (* 2 i))) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))))) alpha))) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))
(/ alpha (+ 2 (+ alpha (* 2 i))))
(+ (* beta (- (/ 1 (+ 2 (+ alpha (* 2 i)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))
(+ (* beta (- (+ (* beta (- (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 4)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3))) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))
1
(+ 1 (* -1 (/ (+ 2 (* 2 i)) beta)))
(- (+ 1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta))))
(- (+ 1 (* -1 (/ (* (+ 2 (* 2 i)) (pow (+ 2 (+ alpha (* 2 i))) 2)) (pow beta 3)))) (+ (* -1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta)))))
1
(+ 1 (* -1 (/ (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))
(+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))
(+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 (+ alpha (* 2 i))) 2) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta)) (* -1 (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))
(/ (+ alpha beta) (+ 2 (+ alpha beta)))
(+ (* -2 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 2))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))
(+ (* i (- (* 4 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 3))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))
(+ (* i (- (* i (- (* -8 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 4))) (* -4 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 3))))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))
(* 1/2 (/ (+ alpha beta) i))
(/ (+ (* -1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)) (* 1/2 (+ alpha beta))) i)
(/ (- (+ (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/2 (+ alpha beta))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i)
(/ (- (+ (* -1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) (pow i 3))) (* 1/2 (+ alpha beta))) (+ (* -1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)))) i)
(* 1/2 (/ (+ alpha beta) i))
(* -1 (/ (+ (* -1/2 (+ alpha beta)) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i))
(* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) i)) (* 1/8 (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))
beta
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
alpha
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
alpha
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
alpha
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
beta
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
beta
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
2
(+ 2 alpha)
(+ 2 alpha)
(+ 2 alpha)
alpha
(* alpha (+ 1 (* 2 (/ 1 alpha))))
(* alpha (+ 1 (* 2 (/ 1 alpha))))
(* alpha (+ 1 (* 2 (/ 1 alpha))))
alpha
(* alpha (+ 1 (* 2 (/ 1 alpha))))
(* alpha (+ 1 (* 2 (/ 1 alpha))))
(* alpha (+ 1 (* 2 (/ 1 alpha))))
(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
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
beta
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
beta
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
beta
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
alpha
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
alpha
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2))
(+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) (pow (+ 2 (* 4 i)) 2)))
(+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))
(+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))
(* 3 (pow beta 2))
(* (pow beta 2) (+ 3 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta)))))
(* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))
(* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))
(* 3 (pow beta 2))
(* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) beta))))
(* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))
(* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))
(+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))
(+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) (pow (+ 2 (* 2 beta)) 2)))
(+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))
(+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))
(* 12 (pow i 2))
(* (pow i 2) (+ 12 (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (* 8 (/ (+ 2 (* 2 beta)) i)))))
(* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))
(* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))
(* 12 (pow i 2))
(* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) i))))
(* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))
(* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))
(* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha))
(+ (* -1 (/ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) alpha)) (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)))
(+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))
(+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))
(* -2 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta))) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))
(* -2 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (+ (* -4 (/ (+ 2 (* 4 i)) (* alpha beta))) (+ (* 4 (/ i (* alpha beta))) (* 2 (/ 1 (* alpha beta))))) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))
(/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) alpha)
(- (+ (* -1 (/ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) alpha)) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))
(- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))
(- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))
(* -12 (/ (pow i 2) alpha))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (* 12 (/ 1 alpha))))
(* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))
(* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))
(* -12 (/ (pow i 2) alpha))
(* (pow i 2) (- (+ (* -8 (/ (+ 2 (* 2 beta)) (* alpha i))) (+ (* 2 (/ beta (* alpha i))) (* 2 (/ (+ 2 beta) (* alpha i))))) (* 12 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)

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

eval280.0ms (2.1%)

Memory: -28.2MiB live, 493.0MiB allocated
Compiler: Compiled 59 604 to 5 040 computations (91.5% saved)

prune200.0ms (1.5%)

Memory

27.8MiB live, 449.5MiB allocated

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	1 342	13	1 355
Fresh	5	4	9
Picked	4	1	5
Done	0	0	0
Total	1 351	18	1 369

Accuracy

100.0%

Counts

1 369 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.0%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
	59.6%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	43.4%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	23.2%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta) #s(literal 1 binary64))
	51.9%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
▶	44.4%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	77.8%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	15.5%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))) alpha)
	21.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	24.7%	(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) (.f64 #s(literal 2 binary64) beta)))) alpha)
	20.0%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 i i) #s(literal -12 binary64)) alpha))) alpha)
▶	28.8%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta))))
	3.5%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
	19.2%	(.f64 (+.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha)) (/.f64 #s(literal 1/2 binary64) alpha))
	21.6%	(.f64 #s(literal 1/2 binary64) (fma.f64 i (-.f64 (/.f64 #s(literal 4 binary64) alpha) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 8 binary64)) (.f64 alpha alpha)) (/.f64 (.f64 #s(literal 2 binary64) (+.f64 (/.f64 beta alpha) (/.f64 (+.f64 #s(literal 2 binary64) beta) alpha))) alpha))) (/.f64 (-.f64 (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (/.f64 (.f64 beta beta) alpha))) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64))) alpha) (/.f64 (*.f64 beta (+.f64 #s(literal 2 binary64) beta)) alpha))) alpha)))
	18.2%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
▶	32.9%	#s(literal 1 binary64)
✓	60.0%	#s(literal 1/2 binary64)

Compiler

Compiled 796 to 458 computations (42.5% saved)

simplify335.0ms (2.5%)

Memory

2.1MiB live, 631.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

9 880×	`accelerator-lowering-fma.f32`
9 880×	`accelerator-lowering-fma.f64`
4 876×	`-lowering-.f32`
4 876×	`-lowering-.f64`
1 972×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	266
1	83	266
2	180	266
3	504	266
4	1751	266
5	5856	266
0	8229	246

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize179.0ms (1.3%)

Memory

32.9MiB live, 420.9MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i)
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	100.0%	(*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) i)
✓	accuracy	100.0%	(/.f64 (+.f64 beta alpha) i)
✓	accuracy	99.8%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 alpha beta)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta)))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 alpha beta))
✓	accuracy	63.8%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta))))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	96.3%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))

Samples

49.0ms	49×	2	valid
34.0ms	77×	1	valid
27.0ms	130×	0	valid

Compiler

Compiled 249 to 34 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 28.0ms (36.8% of total)

ival-div: 19.0ms (25% of total)

ival-add: 15.0ms (19.7% of total)

adjust: 9.0ms (11.8% of total)

ival-sub: 3.0ms (3.9% of total)

exact: 1.0ms (1.3% of total)

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

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

series77.0ms (0.6%)

Memory

9.0MiB live, 206.4MiB allocated

Counts

18 → 552

Calls

Call 1

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

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

Calls

138 calls:

Time	Variable		Point	Expression
12.0ms	beta	@	-inf	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ (* (+ alpha beta) 1/2) i)) 1)
8.0ms	alpha	@	0	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)
3.0ms	beta	@	0	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ (* (+ alpha beta) 1/2) i)) 1)
2.0ms	i	@	0	(/ (+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1) 2)
2.0ms	alpha	@	0	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ (* (+ alpha beta) 1/2) i)) 1)

rewrite524.0ms (3.9%)

Memory

-31.5MiB live, 621.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 180×	`/-lowering-/.f32`
6 180×	`/-lowering-/.f64`
4 222×	`-lowering-.f32`
4 222×	`-lowering-.f64`
2 822×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	196
1	244	196
2	2472	196
0	8670	181

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 931

Calls

Call 1

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

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

simplify554.0ms (4.1%)

Memory

-29.0MiB live, 589.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6 456×	`-lowering-.f32`
6 456×	`-lowering-.f64`
5 276×	`accelerator-lowering-fma.f32`
5 276×	`accelerator-lowering-fma.f64`
3 646×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1627	13050
1	5318	12184
0	8145	11298

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 552

Calls

Call 1

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

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

eval380.0ms (2.8%)

Memory: 42.1MiB live, 508.5MiB allocated
Compiler: Compiled 61 015 to 5 593 computations (90.8% saved)

prune270.0ms (2%)

Memory

-6.9MiB live, 670.1MiB allocated

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	1 830	10	1 840
Fresh	1	11	12
Picked	4	1	5
Done	0	1	1
Total	1 835	23	1 858

Accuracy

100.0%

Counts

1 858 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	28.8%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	45.8%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) beta) i) #s(literal 1/2 binary64))
	45.9%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
▶	23.2%	(fma.f64 (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
	59.6%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	43.4%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	29.2%	(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
	51.9%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
▶	46.2%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	77.5%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	15.5%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))) alpha)
	21.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	24.7%	(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) (.f64 #s(literal 2 binary64) beta)))) alpha)
	20.0%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 i i) #s(literal -12 binary64)) alpha))) alpha)
	4.2%	(/.f64 (*.f64 #s(literal 1/4 binary64) beta) i)
	8.1%	(/.f64 beta alpha)
	27.7%	(-.f64 #s(literal 1 binary64) (/.f64 alpha beta))
▶	3.5%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
	19.2%	(.f64 (+.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha)) (/.f64 #s(literal 1/2 binary64) alpha))
	21.6%	(.f64 #s(literal 1/2 binary64) (fma.f64 i (-.f64 (/.f64 #s(literal 4 binary64) alpha) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 8 binary64)) (.f64 alpha alpha)) (/.f64 (.f64 #s(literal 2 binary64) (+.f64 (/.f64 beta alpha) (/.f64 (+.f64 #s(literal 2 binary64) beta) alpha))) alpha))) (/.f64 (-.f64 (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (/.f64 (.f64 beta beta) alpha))) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64))) alpha) (/.f64 (*.f64 beta (+.f64 #s(literal 2 binary64) beta)) alpha))) alpha)))
▶	18.2%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
✓	32.9%	#s(literal 1 binary64)
✓	60.0%	#s(literal 1/2 binary64)

Compiler

Compiled 874 to 512 computations (41.4% saved)

simplify331.0ms (2.4%)

Memory

-11.8MiB live, 427.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) i beta)
✓	cost-diff	0	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta)
✓	cost-diff	128	(+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64))))
✓	cost-diff	384	(fma.f64 (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 #s(literal -2 binary64) beta)
✓	cost-diff	0	(-.f64 beta (-.f64 #s(literal -2 binary64) beta))
✓	cost-diff	0	(/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)
✓	cost-diff	512	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
✓	cost-diff	192	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) i beta)
✓	cost-diff	0	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))

Rules

6 718×	`accelerator-lowering-fma.f32`
6 718×	`accelerator-lowering-fma.f64`
3 880×	`-lowering-.f32`
3 880×	`-lowering-.f64`
2 140×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	224
1	80	224
2	164	224
3	400	221
4	1092	216
5	3955	216
0	8556	192

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize115.0ms (0.8%)

Memory

28.9MiB live, 260.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i)
✓	accuracy	100.0%	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	98.5%	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64))))
✓	accuracy	100.0%	(*.f64 alpha #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta)
✓	accuracy	100.0%	(-.f64 beta (-.f64 #s(literal -2 binary64) beta))
✓	accuracy	100.0%	(-.f64 #s(literal -2 binary64) beta)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
✓	accuracy	100.0%	(/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))

Samples

68.0ms

256×

valid

Compiler

Compiled 207 to 37 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-add: 13.0ms (32.7% of total)

ival-mult: 13.0ms (32.7% of total)

ival-div: 11.0ms (27.7% of total)

ival-sub: 2.0ms (5% of total)

exact: 1.0ms (2.5% of total)

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

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

series39.0ms (0.3%)

Memory

7.3MiB live, 84.9MiB allocated

Counts

20 → 480

Calls

Call 1

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

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

Calls

120 calls:

Time	Variable		Point	Expression
3.0ms	i	@	inf	(/ (+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1) 2)
2.0ms	alpha	@	inf	(+ (* (/ beta (+ (* 2 i) beta)) (/ (* (+ alpha beta) 1/2) i)) 1)
1.0ms	i	@	0	(+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)
1.0ms	i	@	0	(+ (* (/ (+ 2 (+ (* i 4) (* alpha 2))) beta) -1/2) 1)
1.0ms	beta	@	-inf	(+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)

rewrite384.0ms (2.8%)

Memory

-42.6MiB live, 812.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 964×	`/-lowering-/.f32`
4 964×	`/-lowering-/.f64`
4 100×	`accelerator-lowering-fma.f32`
4 100×	`accelerator-lowering-fma.f64`
3 936×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	186
1	240	186
2	2299	186
0	8809	164

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 660

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 beta beta) (.f64 beta beta)) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) (fma.f64 beta (/.f64 beta (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 beta (/.f64 beta (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))))) (/.f64 (/.f64 (.f64 (.f64 beta beta) (.f64 beta beta)) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))))))
(fma.f64 beta (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1 binary64))
(fma.f64 beta (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))
(fma.f64 beta (/.f64 beta (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1 binary64))
(fma.f64 beta (/.f64 (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1 binary64))
(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))
(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (*.f64 (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1 binary64) beta)) #s(literal 1 binary64))
(fma.f64 (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1 binary64))
(fma.f64 (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (*.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 #s(literal 1 binary64) beta)) #s(literal 1 binary64))
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(pow.f64 (/.f64 (-.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (-.f64 #s(literal 4 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal -1 binary64))
(.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 (fma.f64 #s(literal 2 binary64) i beta) #s(literal 2 binary64)) #s(literal 4 binary64))))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))
(*.f64 #s(literal 2 binary64) alpha)
(*.f64 alpha #s(literal 2 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 i (.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 i)) (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 beta alpha) i)))
(neg.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 beta alpha) i)))
(neg.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 beta alpha)) i))
(/.f64 #s(literal 1 binary64) (/.f64 i (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 i (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 i (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) i)
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 beta alpha)) (neg.f64 i))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 i (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 i (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha))) #s(literal 1/2 binary64)) (.f64 (fma.f64 beta (-.f64 beta alpha) (.f64 alpha alpha)) i))
(/.f64 (.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) #s(literal 1/2 binary64)) (*.f64 (-.f64 alpha beta) i))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) #s(literal 1 binary64)) i)
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 beta alpha))) (neg.f64 (neg.f64 i)))
(/.f64 (.f64 (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha))) (/.f64 #s(literal 1/2 binary64) i)) (fma.f64 beta (-.f64 beta alpha) (*.f64 alpha alpha)))
(/.f64 (.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) (/.f64 #s(literal 1/2 binary64) i)) (-.f64 alpha beta))
(/.f64 (neg.f64 (.f64 (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha))) #s(literal 1/2 binary64))) (neg.f64 (.f64 (fma.f64 beta (-.f64 beta alpha) (.f64 alpha alpha)) i)))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (-.f64 alpha beta) i)))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) #s(literal 1 binary64))) (neg.f64 i))
(/.f64 (neg.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 beta alpha)))) (neg.f64 (neg.f64 (neg.f64 i))))
(/.f64 (neg.f64 (.f64 (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha))) (/.f64 #s(literal 1/2 binary64) i))) (neg.f64 (fma.f64 beta (-.f64 beta alpha) (*.f64 alpha alpha))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) (/.f64 #s(literal 1/2 binary64) i))) (neg.f64 (-.f64 alpha beta)))
(pow.f64 (/.f64 i (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 i (*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) i))
(.f64 #s(literal 1/2 binary64) (.f64 (+.f64 beta alpha) (/.f64 #s(literal 1 binary64) i)))
(*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 beta alpha) i))
(*.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 (+.f64 beta alpha)) i))
(*.f64 (+.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) i))
(.f64 (.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) (/.f64 #s(literal 1 binary64) i))
(.f64 (.f64 #s(literal -1/2 binary64) (+.f64 beta alpha)) (/.f64 #s(literal 1 binary64) (neg.f64 i)))
(.f64 (/.f64 #s(literal 1 binary64) i) (.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)))
(.f64 (/.f64 #s(literal 1 binary64) i) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) i) (+.f64 beta alpha))
(*.f64 (/.f64 (+.f64 beta alpha) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) i))
(*.f64 (/.f64 (neg.f64 (+.f64 beta alpha)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) i))
(+.f64 (.f64 #s(literal 1/2 binary64) beta) (.f64 #s(literal 1/2 binary64) alpha))
(+.f64 (.f64 #s(literal 1/2 binary64) alpha) (.f64 #s(literal 1/2 binary64) beta))
(+.f64 (.f64 beta #s(literal 1/2 binary64)) (.f64 alpha #s(literal 1/2 binary64)))
(+.f64 (.f64 alpha #s(literal 1/2 binary64)) (.f64 beta #s(literal 1/2 binary64)))
(fma.f64 beta #s(literal 1/2 binary64) (*.f64 alpha #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) beta (*.f64 #s(literal 1/2 binary64) alpha))
(fma.f64 #s(literal 1/2 binary64) alpha (*.f64 #s(literal 1/2 binary64) beta))
(fma.f64 alpha #s(literal 1/2 binary64) (*.f64 beta #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha))) #s(literal 1/2 binary64)) (fma.f64 beta (-.f64 beta alpha) (*.f64 alpha alpha)))
(/.f64 (.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) #s(literal 1/2 binary64)) (-.f64 alpha beta))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha)))) (fma.f64 beta (-.f64 beta alpha) (*.f64 alpha alpha)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 beta alpha) (-.f64 alpha beta))) (-.f64 alpha beta))
(/.f64 (neg.f64 (.f64 (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 beta (-.f64 beta alpha) (*.f64 alpha alpha))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) #s(literal 1/2 binary64))) (neg.f64 (-.f64 alpha beta)))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 beta (.f64 beta beta) (.f64 alpha (.f64 alpha alpha))))) (neg.f64 (fma.f64 beta (-.f64 beta alpha) (*.f64 alpha alpha))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 beta alpha) (-.f64 alpha beta)))) (neg.f64 (-.f64 alpha beta)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) beta) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) alpha) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) beta) (.f64 #s(literal 1/2 binary64) beta) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) alpha) (.f64 #s(literal 1/2 binary64) alpha)) (.f64 (.f64 #s(literal 1/2 binary64) beta) (.f64 #s(literal 1/2 binary64) alpha)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) alpha) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) beta) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) alpha) (.f64 #s(literal 1/2 binary64) alpha) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) beta) (.f64 #s(literal 1/2 binary64) beta)) (.f64 (.f64 #s(literal 1/2 binary64) alpha) (.f64 #s(literal 1/2 binary64) beta)))))
(/.f64 (+.f64 (pow.f64 (.f64 beta #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 alpha #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 beta #s(literal 1/2 binary64)) (.f64 beta #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 alpha #s(literal 1/2 binary64)) (.f64 alpha #s(literal 1/2 binary64))) (.f64 (.f64 beta #s(literal 1/2 binary64)) (.f64 alpha #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 alpha #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 beta #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 alpha #s(literal 1/2 binary64)) (.f64 alpha #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 beta #s(literal 1/2 binary64)) (.f64 beta #s(literal 1/2 binary64))) (.f64 (.f64 alpha #s(literal 1/2 binary64)) (.f64 beta #s(literal 1/2 binary64))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 beta alpha))
(*.f64 (+.f64 beta alpha) #s(literal 1/2 binary64))

simplify461.0ms (3.4%)

Memory

23.5MiB live, 782.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 102×	`accelerator-lowering-fma.f32`
9 102×	`accelerator-lowering-fma.f64`
7 292×	`-lowering-.f32`
7 292×	`-lowering-.f64`
5 918×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	949	7279
1	3151	7072
0	8768	6491

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

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

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

eval183.0ms (1.3%)

Memory: 19.5MiB live, 359.2MiB allocated
Compiler: Compiled 33 557 to 3 662 computations (89.1% saved)

prune244.0ms (1.8%)

Memory

-13.7MiB live, 365.2MiB allocated

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	1 281	5	1 286
Fresh	0	16	16
Picked	3	2	5
Done	0	2	2
Total	1 284	25	1 309

Accuracy

100.0%

Counts

1 309 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	28.8%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	45.8%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) beta) i) #s(literal 1/2 binary64))
	45.9%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
	25.0%	(fma.f64 (/.f64 (*.f64 i #s(literal 4 binary64)) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
	59.6%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	43.4%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	29.2%	(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
	51.9%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	48.0%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 #s(literal 1/2 binary64) beta) i) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	77.5%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	15.5%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))) alpha)
	21.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	24.7%	(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) (.f64 #s(literal 2 binary64) beta)))) alpha)
	20.0%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 i i) #s(literal -12 binary64)) alpha))) alpha)
	4.2%	(/.f64 (*.f64 #s(literal 1/4 binary64) beta) i)
	8.1%	(/.f64 beta alpha)
	14.2%	(/.f64 #s(literal 1 binary64) alpha)
	27.7%	(-.f64 #s(literal 1 binary64) (/.f64 alpha beta))
	19.2%	(.f64 (+.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha)) (/.f64 #s(literal 1/2 binary64) alpha))
	21.6%	(.f64 #s(literal 1/2 binary64) (fma.f64 i (-.f64 (/.f64 #s(literal 4 binary64) alpha) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 8 binary64)) (.f64 alpha alpha)) (/.f64 (.f64 #s(literal 2 binary64) (+.f64 (/.f64 beta alpha) (/.f64 (+.f64 #s(literal 2 binary64) beta) alpha))) alpha))) (/.f64 (-.f64 (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (/.f64 (.f64 beta beta) alpha))) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64))) alpha) (/.f64 (*.f64 beta (+.f64 #s(literal 2 binary64) beta)) alpha))) alpha)))
✓	18.2%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
	18.2%	(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 beta (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) beta))) alpha))
✓	32.9%	#s(literal 1 binary64)
✓	60.0%	#s(literal 1/2 binary64)
	3.5%	#s(literal 0 binary64)

Compiler

Compiled 1 378 to 493 computations (64.2% saved)

regimes142.0ms (1%)

Memory

-1.7MiB live, 114.5MiB allocated

Counts

43 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) alpha)
(/.f64 beta alpha)
(-.f64 #s(literal 1 binary64) (/.f64 alpha beta))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1/4 binary64) beta) i)
(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
(fma.f64 (/.f64 (*.f64 i #s(literal 4 binary64)) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta))))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))
(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) (.f64 #s(literal 2 binary64) beta)))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta) #s(literal 1 binary64))
(fma.f64 (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 beta (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) beta))) alpha))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) beta) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 #s(literal 1/2 binary64) beta) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))) alpha)
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 i i) #s(literal -12 binary64)) alpha))) alpha)
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
(.f64 (+.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha)) (/.f64 #s(literal 1/2 binary64) alpha))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
(.f64 #s(literal 1/2 binary64) (fma.f64 i (-.f64 (/.f64 #s(literal 4 binary64) alpha) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 8 binary64)) (.f64 alpha alpha)) (/.f64 (.f64 #s(literal 2 binary64) (+.f64 (/.f64 beta alpha) (/.f64 (+.f64 #s(literal 2 binary64) beta) alpha))) alpha))) (/.f64 (-.f64 (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (/.f64 (.f64 beta beta) alpha))) (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64))) alpha) (/.f64 (*.f64 beta (+.f64 #s(literal 2 binary64) beta)) alpha))) alpha)))
(fma.f64 i (.f64 #s(literal -1/2 binary64) (fma.f64 i (-.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 beta alpha)) (.f64 (+.f64 beta alpha) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta)))) (.f64 (.f64 #s(literal 4 binary64) (.f64 (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 beta alpha)) (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 beta alpha)))) (/.f64 (-.f64 beta alpha) (.f64 (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))) (.f64 (+.f64 beta alpha) (+.f64 beta alpha)))))) (.f64 (.f64 #s(literal 2 binary64) (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (.f64 (+.f64 beta alpha) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta)))))
(/.f64 (-.f64 (.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (fma.f64 beta beta (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) (.f64 (+.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)))) (/.f64 (fma.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 (fma.f64 beta beta (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) (.f64 (+.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)))) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)))) alpha))) alpha)) (neg.f64 alpha))

Outputs

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

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

Calls

7 calls:

33.0ms	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
33.0ms	(*.f64 #s(literal 2 binary64) i)
28.0ms	beta
12.0ms	alpha
12.0ms	i

Results

Accuracy	Segments	Branch
91.2%	2	`alpha`
78.9%	1	`beta`
78.9%	1	`i`
98.7%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
98.7%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
98.7%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`
78.9%	1	`(*.f64 #s(literal 2 binary64) i)`

Compiler

Compiled 108 to 55 computations (49.1% saved)

regimes48.0ms (0.4%)

Memory

-0.4MiB live, 40.8MiB allocated

Counts

34 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) alpha)
(/.f64 beta alpha)
(-.f64 #s(literal 1 binary64) (/.f64 alpha beta))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1/4 binary64) beta) i)
(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
(fma.f64 (/.f64 (*.f64 i #s(literal 4 binary64)) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta))))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))
(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) (.f64 #s(literal 2 binary64) beta)))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta) #s(literal 1 binary64))
(fma.f64 (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 beta (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) beta))) alpha))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) beta) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 #s(literal 1/2 binary64) beta) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))) alpha)
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 i i) #s(literal -12 binary64)) alpha))) alpha)
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))

Outputs

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

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

Calls

3 calls:

30.0ms

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

9.0ms

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

8.0ms

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

Results

Accuracy	Segments	Branch
98.0%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
98.0%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
98.0%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes34.0ms (0.2%)

Memory

1.3MiB live, 40.1MiB allocated

Counts

33 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) alpha)
(/.f64 beta alpha)
(-.f64 #s(literal 1 binary64) (/.f64 alpha beta))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1/4 binary64) beta) i)
(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
(fma.f64 (/.f64 (*.f64 i #s(literal 4 binary64)) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta))))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))
(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) (.f64 #s(literal 2 binary64) beta)))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta) #s(literal 1 binary64))
(fma.f64 (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 beta (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) beta))) alpha))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) beta) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 #s(literal 1/2 binary64) beta) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))) alpha)
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 i i) #s(literal -12 binary64)) alpha))) alpha)
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))

Outputs

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

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

Calls

3 calls:

15.0ms

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

8.0ms

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

8.0ms

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

Results

Accuracy	Segments	Branch
97.5%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
97.5%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
97.5%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes36.0ms (0.3%)

Memory

-1.5MiB live, 37.4MiB allocated

Counts

31 → 3

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) alpha)
(/.f64 beta alpha)
(-.f64 #s(literal 1 binary64) (/.f64 alpha beta))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1/4 binary64) beta) i)
(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha))
(fma.f64 (/.f64 (*.f64 i #s(literal 4 binary64)) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta))))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))
(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) (.f64 #s(literal 2 binary64) beta)))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta) #s(literal 1 binary64))
(fma.f64 (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) (*.f64 alpha #s(literal 2 binary64)))) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 beta (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) beta))) alpha))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) beta) i) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 #s(literal 1/2 binary64) beta) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))) alpha)
(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 i i) #s(literal -12 binary64)) alpha))) alpha)

Outputs

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

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

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

Calls

3 calls:

19.0ms

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

8.0ms

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

8.0ms

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

Results

Accuracy	Segments	Branch
96.0%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
96.0%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
96.0%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes39.0ms (0.3%)

Memory

-3.9MiB live, 35.1MiB allocated

Counts

26 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

Calls

3 calls:

24.0ms

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

7.0ms

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

6.0ms

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

Results

Accuracy	Segments	Branch
95.9%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
95.9%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
95.9%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes22.0ms (0.2%)

Memory

-5.4MiB live, 36.4MiB allocated

Counts

17 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

Calls

4 calls:

7.0ms	alpha
5.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))
5.0ms	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
4.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
78.7%	3	`alpha`
89.0%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
89.0%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
89.0%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 94 to 44 computations (53.2% saved)

regimes14.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

15 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

Calls

3 calls:

4.0ms

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

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
88.5%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
88.5%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
88.5%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes30.0ms (0.2%)

Memory

-21.7MiB live, 17.2MiB allocated

Counts

12 → 3

Calls

Call 1

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

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

Calls

3 calls:

22.0ms

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

4.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
88.3%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
88.3%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
88.3%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes10.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

10 → 3

Calls

Call 1

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

Outputs
(/.f64 #s(literal 1 binary64) alpha)
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (/.f64 alpha beta))

Calls

3 calls:

3.0ms

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

3.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
84.3%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
84.3%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
84.3%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes7.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

6 → 3

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) alpha)
(/.f64 beta alpha)

Outputs
(/.f64 #s(literal 1 binary64) alpha)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

Calls

3 calls:

2.0ms

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

2.0ms

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

2.0ms

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

Results

Accuracy	Segments	Branch
84.1%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
84.1%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
84.1%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes35.0ms (0.3%)

Memory

-17.5MiB live, 21.6MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))

Outputs
#s(literal 1/2 binary64)
#s(literal 1 binary64)

Calls

7 calls:

23.0ms	i
2.0ms	beta
2.0ms	(*.f64 #s(literal 2 binary64) i)
2.0ms	alpha
2.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
60.0%	1	`alpha`
60.0%	1	`i`
60.0%	1	`(*.f64 #s(literal 2 binary64) i)`
72.0%	2	`beta`
74.9%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
74.9%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
74.9%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 108 to 55 computations (49.1% saved)

regimes9.0ms (0.1%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)

Outputs
#s(literal 1/2 binary64)

Calls

6 calls:

2.0ms	(*.f64 #s(literal 2 binary64) i)
2.0ms	i
2.0ms	beta
1.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))
1.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
60.0%	1	`i`
60.0%	1	`(*.f64 #s(literal 2 binary64) i)`
60.0%	1	`beta`
60.0%	1	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
60.0%	1	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
60.0%	1	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 104 to 52 computations (50% saved)

regimes28.0ms (0.2%)

Memory

-23.3MiB live, 16.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

7 calls:

20.0ms	alpha
1.0ms	(*.f64 #s(literal 2 binary64) i)
1.0ms	i
1.0ms	beta
1.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
3.5%	1	`alpha`
3.5%	1	`beta`
3.5%	1	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
3.5%	1	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
3.5%	1	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`
3.5%	1	`i`
3.5%	1	`(*.f64 #s(literal 2 binary64) i)`

Compiler

Compiled 108 to 55 computations (49.1% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.697193943235198e-13	1.1899759887876764e-5
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.697193943235198e-13	1.1899759887876764e-5
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.697193943235198e-13	1.1899759887876764e-5
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0014328358652715037	0.9711715914082585
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0014328358652715037	0.9711715914082585
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0014328358652715037	0.9711715914082585
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0014328358652715037	0.9711715914082585
0.0ms	-0.9999999951450913	-6.583876026617223e-6

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch10.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	0.0014328358652715037	0.9711715914082585

Samples

4.0ms

128×

valid

Compiler

Compiled 115 to 102 computations (11.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (62% of total)

ival-add: 1.0ms (62% of total)

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

exact: 0.0ms (0% of total)

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

simplify88.0ms (0.7%)

Memory

-22.3MiB live, 36.8MiB allocated

Algorithm

1×	egg-herbie

Rules

316×	`distribute-lft-neg-in_binary64`
292×	`neg-mul-1_binary64`
244×	`unsub-neg_binary64`
208×	`distribute-neg-in_binary64`
202×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	751
1	108	751
2	126	751
3	143	751
4	191	751
5	271	751
6	384	751
7	557	751
8	770	751
9	964	751
10	1136	751
11	1248	751
12	1316	751
13	1354	751
14	1375	751
15	1387	751
16	1399	751
17	1411	751
18	1417	751
19	1420	751
20	1421	751

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) (fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 alpha beta))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 alpha beta))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)

Outputs
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) (fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) (fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha #s(literal 2 binary64))))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha #s(literal 2 binary64))))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 #s(literal 2 binary64) alpha) beta))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 beta (-.f64 beta #s(literal -2 binary64))) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha #s(literal 2 binary64))))))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta alpha)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 beta (-.f64 beta #s(literal -2 binary64))) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha beta)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta (-.f64 #s(literal -2 binary64) beta)) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 alpha beta))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 beta (-.f64 beta #s(literal -2 binary64))) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 alpha beta))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 alpha beta))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 alpha beta))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 1152921504606847/576460752303423488 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)

soundness1.4s (10.5%)

Memory

40.8MiB live, 858.6MiB allocated

Rules

9 102×	`accelerator-lowering-fma.f32`
9 102×	`accelerator-lowering-fma.f64`
7 292×	`-lowering-.f32`
7 292×	`-lowering-.f64`
6 456×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	186
1	240	186
2	2299	186
0	8809	164
0	1891	20573
1	6208	20028
0	8058	18419
0	32	196
1	244	196
2	2472	196
0	8670	181
0	949	7279
1	3151	7072
0	8768	6491
0	15	112
1	115	112
2	1187	112
0	8698	101
0	964	13312
1	3265	11681
0	9032	10518
0	1627	13050
1	5318	12184
0	8145	11298

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
1×	iter limit
1×	node limit

Compiler

Compiled 1 315 to 475 computations (63.9% saved)

preprocess68.0ms (0.5%)

Memory: -16.4MiB live, 180.4MiB allocated
Compiler: Compiled 1 572 to 188 computations (88% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze45.0ms (0.3%)

sample2.5s (18.3%)

preprocess405.0ms (3%)

explain254.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify441.0ms (3.3%)

localize62.0ms (0.5%)

series73.0ms (0.5%)

rewrite634.0ms (4.7%)

simplify530.0ms (3.9%)

eval141.0ms (1%)

prune128.0ms (0.9%)

simplify329.0ms (2.4%)

localize289.0ms (2.1%)

series144.0ms (1.1%)

rewrite428.0ms (3.2%)

simplify579.0ms (4.3%)

eval280.0ms (2.1%)

prune200.0ms (1.5%)

simplify335.0ms (2.5%)

localize179.0ms (1.3%)

series77.0ms (0.6%)

rewrite524.0ms (3.9%)

simplify554.0ms (4.1%)

eval380.0ms (2.8%)

prune270.0ms (2%)

simplify331.0ms (2.4%)

localize115.0ms (0.8%)

series39.0ms (0.3%)

rewrite384.0ms (2.8%)

simplify461.0ms (3.4%)

eval183.0ms (1.3%)

prune244.0ms (1.8%)

regimes142.0ms (1%)

regimes48.0ms (0.4%)

regimes34.0ms (0.2%)

regimes36.0ms (0.3%)

regimes39.0ms (0.3%)

regimes22.0ms (0.2%)

regimes14.0ms (0.1%)

regimes30.0ms (0.2%)

regimes10.0ms (0.1%)

regimes7.0ms (0.1%)

regimes35.0ms (0.3%)

regimes9.0ms (0.1%)

regimes28.0ms (0.2%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch10.0ms (0.1%)

simplify88.0ms (0.7%)

soundness1.4s (10.5%)

preprocess68.0ms (0.5%)

end0.0ms (0%)

Profiling