Metrics for Octave 3.8, jcobi/4

analyze27.0ms (0.2%)

Memory

-10.7MiB live, 33.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 65 to 24 computations (63.1% saved)

sample1.4s (10.2%)

Memory

31.2MiB live, 2 441.1MiB allocated

Samples

1.0s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 711.0ms

ival-mult: 239.0ms (33.6% of total)

ival-add: 160.0ms (22.5% of total)

ival->: 148.0ms (20.8% of total)

ival-div: 96.0ms (13.5% of total)

ival-sub: 36.0ms (5.1% of total)

ival-and: 16.0ms (2.2% of total)

exact: 14.0ms (2% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

preprocess394.0ms (2.8%)

Memory

-12.6MiB live, 734.6MiB allocated

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Call 2

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

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

Symmetry

(sort alpha beta)

explain267.0ms (1.9%)

Memory

12.2MiB live, 368.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
212	-	-	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`
148	-	-	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`i`
0	-	-	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`
0	-	-	`(*.f64 #s(literal 2 binary64) i)`
0	-	-	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`
0	-	-	`beta`
0	-	-	`(+.f64 alpha beta)`
0	-	-	`(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))`
0	-	-	`(+.f64 (+.f64 alpha beta) i)`
0	-	-	`alpha`
0	-	-	`(*.f64 beta alpha)`
0	-	-	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`
0	-	-	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`
0	-	-	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`
0	-	-	`#s(literal 2 binary64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`	o/o	160	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	144
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	212
↳	`(*.f64 beta alpha)`	overflow	7
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	286
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	160
`/.f64`	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`	o/o	130	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	144
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	212
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	286
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(*.f64 beta alpha)`	overflow	7
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	160
↳	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`	overflow	130
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))`	overflow	160
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	160
`/.f64`	`(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))`	o/n	52	0
↳	`(+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))`	overflow	144
↳	`(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))`	overflow	212
↳	`(*.f64 beta alpha)`	overflow	7
↳	`(*.f64 i (+.f64 (+.f64 alpha beta) i))`	overflow	286
`/.f64`	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`	n/o	18	0
↳	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`	overflow	2
↳	`(*.f64 #s(literal 2 binary64) i)`	overflow	2
↳	`(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))`	overflow	160
↳	`(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))`	overflow	160

Confusion

	Predicted +	Predicted -
+	212	0
-	0	44

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	212	0	0
-	0	0	44

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	44
1	64
2	148

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

53.0ms

512×

valid

Compiler

Compiled 482 to 72 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 14.0ms (43.9% of total)

ival-add: 9.0ms (28.2% of total)

ival-div: 6.0ms (18.8% of total)

ival-sub: 2.0ms (6.3% of total)

exact: 1.0ms (3.1% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	17.6%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Status

Accuracy

Program

▶

17.6%

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

Compiler

Compiled 56 to 17 computations (69.6% saved)

simplify366.0ms (2.6%)

Memory

22.0MiB live, 647.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize55.0ms (0.4%)

Memory

-5.4MiB live, 71.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
✓	accuracy	99.9%	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
✓	accuracy	44.4%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
✓	accuracy	29.2%	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))))

Samples

25.0ms

256×

valid

Compiler

Compiled 185 to 19 computations (89.7% saved)

Precisions

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

ival-mult: 6.0ms (39.2% of total)

ival-add: 4.0ms (26.1% of total)

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

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

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

exact: 0.0ms (0% of total)

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

series192.0ms (1.4%)

Memory

13.0MiB live, 54.2MiB allocated

Counts

7 → 252

Calls

Call 1

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

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

Calls

63 calls:

Time	Variable		Point	Expression
140.0ms	beta	@	0	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
4.0ms	beta	@	0	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
4.0ms	i	@	inf	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
3.0ms	i	@	0	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))
3.0ms	alpha	@	0	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1))

rewrite728.0ms (5.2%)

Memory

-101.5MiB live, 833.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 609

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (neg.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (neg.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))) (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (neg.f64 (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))) (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))))
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simplify619.0ms (4.4%)

Memory

19.8MiB live, 983.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

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

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

eval206.0ms (1.5%)

Memory: 3.9MiB live, 376.9MiB allocated
Compiler: Compiled 120 771 to 4 630 computations (96.2% saved)

prune227.0ms (1.6%)

Memory

-4.2MiB live, 401.4MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	1 397	15	1 412
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1 398	15	1 413

Accuracy

84.3%

Counts

1 413 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	15.5%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
	6.7%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (.f64 beta beta))
	16.1%	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
▶	13.8%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
▶	13.8%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
	33.8%	(/.f64 (.f64 (.f64 i i) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
	19.5%	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
▶	16.8%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
	45.0%	(.f64 (pow.f64 (.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 alpha (+.f64 i beta))))) #s(literal -1 binary64)) (pow.f64 (.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))) #s(literal -1 binary64)))
▶	40.2%	(.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
	45.1%	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64)))) (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
	40.1%	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
	26.3%	(.f64 (/.f64 i (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 (.f64 (+.f64 alpha (+.f64 i beta)) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
	37.4%	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
▶	65.6%	#s(literal 1/16 binary64)

Compiler

Compiled 1 186 to 468 computations (60.5% saved)

simplify365.0ms (2.6%)

Memory

-13.4MiB live, 632.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

9 196×	`accelerator-lowering-fma.f32`
9 196×	`accelerator-lowering-fma.f64`
5 434×	`-lowering-.f32`
5 434×	`-lowering-.f64`
3 510×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	509
1	144	509
2	745	478
3	4311	449
4	6930	449
0	8276	409

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize527.0ms (3.8%)

Memory

18.6MiB live, 256.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	99.8%	(.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
✓	accuracy	39.4%	(/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
✓	accuracy	39.4%	(/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
✓	accuracy	100.0%	(*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	99.9%	(.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)))
✓	accuracy	16.1%	(/.f64 (.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
✓	accuracy	100.0%	(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))
✓	accuracy	99.9%	(.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)))
✓	accuracy	16.1%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
✓	accuracy	100.0%	(+.f64 alpha i)
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	100.0%	(*.f64 i (+.f64 alpha i))
✓	accuracy	66.3%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))

Samples

60.0ms

256×

valid

Compiler

Compiled 455 to 36 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 18.0ms (52% of total)

ival-add: 10.0ms (28.9% of total)

ival-div: 7.0ms (20.2% of total)

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

exact: 0.0ms (0% of total)

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

series94.0ms (0.7%)

Memory

-15.6MiB live, 102.9MiB allocated

Counts

20 → 588

Calls

Call 1

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

Outputs
#<alt (/ (* alpha i) (pow beta 2))>
#<alt (* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))>
#<alt (* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))>
#<alt (* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))>
#<alt (/ (pow i 2) (pow beta 2))>
#<alt (* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))>
#<alt (* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))>
#<alt (* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))>
#<alt (/ (pow i 2) (pow beta 2))>
#<alt (* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))>
#<alt (* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))>
#<alt (* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))>
#<alt (/ (pow i 2) (pow beta 2))>
#<alt (+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))>
#<alt (+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))>
#<alt (+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))>
#<alt (/ (* alpha i) (pow beta 2))>
#<alt (* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))>
#<alt (* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))>
#<alt (* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))>
#<alt (/ (* alpha i) (pow beta 2))>
#<alt (* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))>
#<alt (* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))>
#<alt (* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (/ (* i (+ alpha i)) (pow beta 2))>
#<alt (* alpha i)>
#<alt (* i (+ alpha i))>
#<alt (* i (+ alpha i))>
#<alt (* i (+ alpha i))>
#<alt (pow i 2)>
#<alt (* (pow i 2) (+ 1 (/ alpha i)))>
#<alt (* (pow i 2) (+ 1 (/ alpha i)))>
#<alt (* (pow i 2) (+ 1 (/ alpha i)))>
#<alt (pow i 2)>
#<alt (* (pow i 2) (+ 1 (/ alpha i)))>
#<alt (* (pow i 2) (+ 1 (/ alpha i)))>
#<alt (* (pow i 2) (+ 1 (/ alpha i)))>
#<alt (pow i 2)>
#<alt (+ (* alpha i) (pow i 2))>
#<alt (+ (* alpha i) (pow i 2))>
#<alt (+ (* alpha i) (pow i 2))>
#<alt (* alpha i)>
#<alt (* alpha (+ i (/ (pow i 2) alpha)))>
#<alt (* alpha (+ i (/ (pow i 2) alpha)))>
#<alt (* alpha (+ i (/ (pow i 2) alpha)))>
#<alt (* alpha i)>
#<alt (* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))>
#<alt (* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))>
#<alt (* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))>
#<alt i>
#<alt (+ alpha i)>
#<alt (+ alpha i)>
#<alt (+ alpha i)>
#<alt alpha>
#<alt (* alpha (+ 1 (/ i alpha)))>
#<alt (* alpha (+ 1 (/ i alpha)))>
#<alt (* alpha (+ 1 (/ i alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (* -1 (/ i alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ i alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ i alpha)) 1)))>
#<alt alpha>
#<alt (+ alpha i)>
#<alt (+ alpha i)>
#<alt (+ alpha i)>
#<alt i>
#<alt (* i (+ 1 (/ alpha i)))>
#<alt (* i (+ 1 (/ alpha i)))>
#<alt (* i (+ 1 (/ alpha i)))>
#<alt i>
#<alt (* -1 (* i (- (* -1 (/ alpha i)) 1)))>
#<alt (* -1 (* i (- (* -1 (/ alpha i)) 1)))>
#<alt (* -1 (* i (- (* -1 (/ alpha i)) 1)))>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (pow beta 2)>
#<alt (/ (pow i 2) (- (pow beta 2) 1))>
#<alt (* (pow i 2) (+ (* -1 (* i (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1))))>
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#<alt (* (pow i 2) (+ (* i (- (* i (- (* -1 (* i (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))) (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* -1 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (* 32 (/ 1 (* beta (pow (- (pow beta 2) 1) 2)))))))) (+ (* -1 (/ (* (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3))) (+ (* 4 (/ beta (pow (- (pow beta 2) 1) 2))) (* 2 (/ 1 (* beta (- (pow beta 2) 1)))))) (* (pow beta 2) (- (pow beta 2) 1)))) (+ (* 3 (/ 1 (* (pow beta 2) (- (pow beta 2) 1)))) (* 20 (/ 1 (pow (- (pow beta 2) 1) 2))))))) (+ (* 2 (/ 1 (* beta (- (pow beta 2) 1)))) (* 4 (/ beta (pow (- (pow beta 2) 1) 2)))))) (/ 1 (- (pow beta 2) 1))))>
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#<alt 1/16>
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#<alt (- (+ 1/16 (+ (* -1 (/ (- (+ (* 1/256 (/ (* (pow beta 2) (- (pow beta 2) 1)) i)) (+ (* 1/16 (/ (* (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))))) i)) (* 2 (/ (* beta (+ (* -2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/256 (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3)))))) i)))) (+ (* -2 (* beta (- (* 1/16 (pow beta 2)) (* 1/256 (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* 1/256 (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3)))))) (pow i 3))) (* 1/16 (/ (pow beta 2) (pow i 2))))) (* 1/256 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) (pow i 2))))>
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#<alt (pow i 2)>
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#<alt (pow i 2)>
#<alt (pow i 2)>
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#<alt (pow i 2)>
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#<alt (* alpha beta)>
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#<alt 1/16>
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#<alt 1/16>
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#<alt i>
#<alt (* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))>
#<alt (* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))>
#<alt (* -1 (* i (- (* -1 (/ (+ alpha beta) i)) 1)))>
#<alt (+ alpha i)>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt (+ alpha (+ beta i))>
#<alt beta>
#<alt (* beta (+ 1 (+ (/ alpha beta) (/ i beta))))>
#<alt (* beta (+ 1 (+ (/ alpha beta) (/ i beta))))>
#<alt (* beta (+ 1 (+ (/ alpha beta) (/ i beta))))>
#<alt beta>
#<alt (* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ (+ alpha i) beta)) 1)))>
#<alt (* (pow beta 2) (- (pow beta 2) 1))>
#<alt (+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (* 4 (pow beta 3)))) (* (pow beta 2) (- (pow beta 2) 1)))>
#<alt (+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (+ (* 4 (pow beta 3)) (* i (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))))))) (* (pow beta 2) (- (pow beta 2) 1)))>
#<alt (+ (* i (+ (* 4 (* beta (- (pow beta 2) 1))) (+ (* 4 (pow beta 3)) (* i (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (+ (* 16 (pow beta 2)) (* 32 (* beta i))))))))) (* (pow beta 2) (- (pow beta 2) 1)))>
#<alt (* 16 (pow i 4))>
#<alt (* (pow i 4) (+ 16 (* 32 (/ beta i))))>
#<alt (* (pow i 4) (+ 16 (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i)))))))>
#<alt (* (pow i 4) (+ 16 (+ (* 4 (/ (* beta (- (pow beta 2) 1)) (pow i 3))) (+ (* 4 (/ (- (pow beta 2) 1) (pow i 2))) (+ (* 4 (/ (pow beta 2) (pow i 2))) (+ (* 4 (/ (pow beta 3) (pow i 3))) (+ (* 16 (/ (pow beta 2) (pow i 2))) (* 32 (/ beta i)))))))))>
#<alt (* 16 (pow i 4))>
#<alt (* (pow i 4) (+ 16 (* 32 (/ beta i))))>
#<alt (* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2)))) i))) i))))>
#<alt (* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 beta) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* beta (- (pow beta 2) 1))) (* -4 (pow beta 3))) i)) (+ (* 4 (- (pow beta 2) 1)) (+ (* 4 (pow beta 2)) (* 16 (pow beta 2))))) i))) i))))>
#<alt (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1)))>
#<alt (+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (* 16 (pow i 3)))))>
#<alt (+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1))))))>
#<alt (+ (* 4 (* (pow i 2) (- (* 4 (pow i 2)) 1))) (* beta (+ (* 4 (* i (- (* 4 (pow i 2)) 1))) (+ (* 16 (pow i 3)) (* beta (- (+ (* 8 (* beta i)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1))))))>
#<alt (pow beta 4)>
#<alt (* (pow beta 4) (+ 1 (* 8 (/ i beta))))>
#<alt (* (pow beta 4) (- (+ 1 (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 2) (pow beta 2)))))) (/ 1 (pow beta 2))))>
#<alt (* (pow beta 4) (- (+ 1 (+ (* 4 (/ (* i (- (* 4 (pow i 2)) 1)) (pow beta 3))) (+ (* 8 (/ i beta)) (+ (* 8 (/ (pow i 2) (pow beta 2))) (+ (* 16 (/ (pow i 2) (pow beta 2))) (* 16 (/ (pow i 3) (pow beta 3)))))))) (/ 1 (pow beta 2))))>
#<alt (pow beta 4)>
#<alt (* (pow beta 4) (+ 1 (* 8 (/ i beta))))>
#<alt (* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* 8 (pow i 2)) (* 16 (pow i 2))) 1) beta))) beta))))>
#<alt (* (pow beta 4) (+ 1 (* -1 (/ (+ (* -8 i) (* -1 (/ (- (+ (* -1 (/ (+ (* -16 (pow i 3)) (* -4 (* i (- (* 4 (pow i 2)) 1)))) beta)) (+ (* 8 (pow i 2)) (* 16 (pow i 2)))) 1) beta))) beta))))>
#<alt (pow beta 2)>
#<alt (+ (* 4 (* beta i)) (pow beta 2))>
#<alt (+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2))>
#<alt (+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ beta i))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ beta i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (pow beta 2) i))) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (pow beta 2) i))) i))))>
#<alt (* 4 (pow i 2))>
#<alt (+ (* 4 (* beta i)) (* 4 (pow i 2)))>
#<alt (+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i))))>
#<alt (+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 4 (/ i beta))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 4 (/ i beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -4 (/ (pow i 2) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -4 (/ (pow i 2) beta))) beta))))>
#<alt (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1))>
#<alt (+ (* alpha (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))>
#<alt (+ (* alpha (+ (* alpha (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (pow (+ (* 2 beta) (* 4 i)) 2)) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))>
#<alt (+ (* alpha (+ (* alpha (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (+ (* alpha (+ (* 4 beta) (* 8 i))) (pow (+ (* 2 beta) (* 4 i)) 2))) 1)) (+ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i)))))) (* (pow (+ beta (* 2 i)) 2) (- (pow (+ beta (* 2 i)) 2) 1)))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (+ 1 (+ (* 4 (/ beta alpha)) (* 8 (/ i alpha)))))>
#<alt (* (pow alpha 4) (- (+ 1 (+ (* 2 (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))) (+ (* 4 (/ beta alpha)) (+ (* 8 (/ i alpha)) (/ (pow (+ (* 2 beta) (* 4 i)) 2) (pow alpha 2)))))) (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 4) (- (+ 1 (+ (* 2 (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))) (+ (* 4 (/ beta alpha)) (+ (* 8 (/ i alpha)) (+ (/ (* (+ (* 2 beta) (* 4 i)) (- (pow (+ beta (* 2 i)) 2) 1)) (pow alpha 3)) (+ (/ (* (pow (+ beta (* 2 i)) 2) (+ (* 2 beta) (* 4 i))) (pow alpha 3)) (/ (pow (+ (* 2 beta) (* 4 i)) 2) (pow alpha 2)))))))) (/ 1 (pow alpha 2))))>
#<alt (pow alpha 4)>
#<alt (* (pow alpha 4) (+ 1 (* 4 (/ (+ beta (* 2 i)) alpha))))>
#<alt (* (pow alpha 4) (+ 1 (* -1 (/ (+ (* -4 (+ beta (* 2 i))) (* -1 (/ (- (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2))) 1) alpha))) alpha))))>
#<alt (* (pow alpha 4) (+ 1 (* -1 (/ (+ (* -4 (+ beta (* 2 i))) (* -1 (/ (- (+ (* -1 (/ (+ (* -2 (* (+ beta (* 2 i)) (- (pow (+ beta (* 2 i)) 2) 1))) (* -2 (pow (+ beta (* 2 i)) 3))) alpha)) (+ (* 2 (pow (+ beta (* 2 i)) 2)) (* 4 (pow (+ beta (* 2 i)) 2)))) 1) alpha))) alpha))))>
#<alt (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))>
#<alt (+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3)))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))>
#<alt (+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (pow (+ alpha beta) 3)) (* i (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))>
#<alt (+ (* i (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (+ (* 4 (pow (+ alpha beta) 3)) (* i (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (+ (* 16 (pow (+ alpha beta) 2)) (* 32 (* i (+ alpha beta)))))))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))>
#<alt (* 16 (pow i 4))>
#<alt (* (pow i 4) (+ 16 (* 32 (/ (+ alpha beta) i))))>
#<alt (* (pow i 4) (+ 16 (+ (* 4 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 32 (/ (+ alpha beta) i)))))))>
#<alt (* (pow i 4) (+ 16 (+ (* 4 (/ (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)) (pow i 3))) (+ (* 4 (/ (- (pow (+ alpha beta) 2) 1) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 2) (pow i 2))) (+ (* 4 (/ (pow (+ alpha beta) 3) (pow i 3))) (+ (* 16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 32 (/ (+ alpha beta) i)))))))))>
#<alt (* 16 (pow i 4))>
#<alt (* (pow i 4) (+ 16 (* 32 (/ (+ alpha beta) i))))>
#<alt (* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 (+ alpha beta)) (* -1 (/ (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))) i))) i))))>
#<alt (* (pow i 4) (+ 16 (* -1 (/ (+ (* -32 (+ alpha beta)) (* -1 (/ (+ (* -1 (/ (+ (* -4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* -4 (pow (+ alpha beta) 3))) i)) (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2))))) i))) i))))>
#<alt (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1))>
#<alt (+ (* beta (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))>
#<alt (+ (* beta (+ (* beta (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (pow (+ (* 2 alpha) (* 4 i)) 2)) 1)) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))>
#<alt (+ (* beta (+ (* beta (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (+ (* beta (+ (* 4 alpha) (* 8 i))) (pow (+ (* 2 alpha) (* 4 i)) 2))) 1)) (+ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i)))))) (* (pow (+ alpha (* 2 i)) 2) (- (pow (+ alpha (* 2 i)) 2) 1)))>
#<alt (pow beta 4)>
#<alt (* (pow beta 4) (+ 1 (+ (* 4 (/ alpha beta)) (* 8 (/ i beta)))))>
#<alt (* (pow beta 4) (- (+ 1 (+ (* 2 (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))) (+ (* 4 (/ alpha beta)) (+ (* 8 (/ i beta)) (/ (pow (+ (* 2 alpha) (* 4 i)) 2) (pow beta 2)))))) (/ 1 (pow beta 2))))>
#<alt (* (pow beta 4) (- (+ 1 (+ (* 2 (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))) (+ (* 4 (/ alpha beta)) (+ (* 8 (/ i beta)) (+ (/ (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1)) (pow beta 3)) (+ (/ (* (pow (+ alpha (* 2 i)) 2) (+ (* 2 alpha) (* 4 i))) (pow beta 3)) (/ (pow (+ (* 2 alpha) (* 4 i)) 2) (pow beta 2)))))))) (/ 1 (pow beta 2))))>
#<alt (pow beta 4)>
#<alt (* (pow beta 4) (+ 1 (* 4 (/ (+ alpha (* 2 i)) beta))))>
#<alt (* (pow beta 4) (+ 1 (* -1 (/ (+ (* -4 (+ alpha (* 2 i))) (* -1 (/ (- (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2))) 1) beta))) beta))))>
#<alt (* (pow beta 4) (+ 1 (* -1 (/ (+ (* -4 (+ alpha (* 2 i))) (* -1 (/ (- (+ (* -1 (/ (+ (* -2 (* (+ alpha (* 2 i)) (- (pow (+ alpha (* 2 i)) 2) 1))) (* -2 (pow (+ alpha (* 2 i)) 3))) beta)) (+ (* 2 (pow (+ alpha (* 2 i)) 2)) (* 4 (pow (+ alpha (* 2 i)) 2)))) 1) beta))) beta))))>
#<alt (pow (+ beta (* 2 i)) 2)>
#<alt (+ (* alpha (+ (* 2 beta) (* 4 i))) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (+ alpha (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 2))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (* 4 (/ i alpha)))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))>
#<alt (* (pow alpha 2) (+ 1 (+ (* 2 (/ beta alpha)) (+ (* 4 (/ i alpha)) (/ (pow (+ beta (* 2 i)) 2) (pow alpha 2))))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (+ 1 (* 2 (/ (+ beta (* 2 i)) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))>
#<alt (* (pow alpha 2) (+ 1 (* -1 (/ (+ (* -2 (+ beta (* 2 i))) (* -1 (/ (pow (+ beta (* 2 i)) 2) alpha))) alpha))))>
#<alt (pow (+ alpha beta) 2)>
#<alt (+ (* 4 (* i (+ alpha beta))) (pow (+ alpha beta) 2))>
#<alt (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))>
#<alt (+ (* i (+ (* 4 i) (* 4 (+ alpha beta)))) (pow (+ alpha beta) 2))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (* (pow i 2) (+ 4 (+ (* 4 (/ (+ alpha beta) i)) (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (+ 4 (* 4 (/ (+ alpha beta) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))>
#<alt (* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 (+ alpha beta)) (* -1 (/ (pow (+ alpha beta) 2) i))) i))))>
#<alt (pow (+ alpha (* 2 i)) 2)>
#<alt (+ (* beta (+ (* 2 alpha) (* 4 i))) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (+ beta (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 2))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (* 4 (/ i beta)))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))>
#<alt (* (pow beta 2) (+ 1 (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (/ (pow (+ alpha (* 2 i)) 2) (pow beta 2))))))>
#<alt (pow beta 2)>
#<alt (* (pow beta 2) (+ 1 (* 2 (/ (+ alpha (* 2 i)) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))>
#<alt (* (pow beta 2) (+ 1 (* -1 (/ (+ (* -2 (+ alpha (* 2 i))) (* -1 (/ (pow (+ alpha (* 2 i)) 2) beta))) beta))))>
#<alt (/ i (+ alpha beta))>
#<alt (* i (+ (* -3 (/ i (pow (+ alpha beta) 2))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* 8 (/ i (pow (+ alpha beta) 3))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt (* i (+ (* i (- (* i (+ (* -20 (/ i (pow (+ alpha beta) 4))) (* 8 (/ 1 (pow (+ alpha beta) 3))))) (* 3 (/ 1 (pow (+ alpha beta) 2))))) (/ 1 (+ alpha beta))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (- (+ 1/4 (* -1 (/ (+ (* -1/64 (pow (+ alpha beta) 4)) (* 1/16 (pow (+ alpha beta) 4))) (pow i 4)))) (+ (* -1/16 (/ (pow (+ alpha beta) 3) (pow i 3))) (* 1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))))>
#<alt (+ 1/4 (+ (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2))) (* 1/16 (/ (pow (+ alpha beta) 3) (pow i 3)))))>
#<alt (+ 1/4 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow (+ alpha beta) 4)) (* 1/64 (pow (+ alpha beta) 4))) i)) (* -1/16 (pow (+ alpha beta) 3))) (pow i 3))) (* -1/16 (/ (pow (+ alpha beta) 2) (pow i 2)))))>
#<alt (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2))>
#<alt (+ (* alpha (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))>
#<alt (+ (* alpha (- (+ (* -1 (* alpha (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))>
#<alt (+ (* alpha (- (+ (* alpha (- (* alpha (- (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 beta) (* 4 i)) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2)))) (pow (+ beta (* 2 i)) 2))) (/ i (pow (+ beta (* 2 i)) 4))))) (+ (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 4)) (/ (* (+ (* 2 beta) (* 4 i)) (- (/ i (pow (+ beta (* 2 i)) 2)) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (pow (+ beta (* 2 i)) 2))))) (/ i (pow (+ beta (* 2 i)) 2))) (/ (* i (* (+ beta i) (+ (* 2 beta) (* 4 i)))) (pow (+ beta (* 2 i)) 4)))) (/ (* i (+ beta i)) (pow (+ beta (* 2 i)) 2)))>
#<alt (/ i alpha)>
#<alt (/ (- (+ i (/ (* i (+ beta i)) alpha)) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 2))) (/ (* i (+ beta i)) alpha))) (/ (* i (+ (* 2 beta) (* 4 i))) alpha)) alpha)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 beta) (* 4 i)) (+ (* i (pow (+ beta (* 2 i)) 2)) (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))))) (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i)))))) (pow alpha 3))) (/ (* i (+ beta i)) alpha))) (+ (/ (* i (+ (* 2 beta) (* 4 i))) alpha) (+ (/ (* i (pow (+ beta (* 2 i)) 2)) (pow alpha 2)) (/ (* (+ (* 2 beta) (* 4 i)) (- (* i (+ beta i)) (* i (+ (* 2 beta) (* 4 i))))) (pow alpha 2))))) alpha)>
#<alt (/ i alpha)>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -1 (/ (* i (pow (+ beta (* 2 i)) 2)) alpha)) (* i (+ beta i)))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ beta (* 2 i)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (/ (* (pow (+ beta (* 2 i)) 2) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i)))))) alpha)) (+ (* -2 (* (+ beta (* 2 i)) (- (* i (+ beta i)) (* 2 (* i (+ beta (* 2 i))))))) (* -1 (* i (pow (+ beta (* 2 i)) 2))))) alpha)) (* i (+ beta i))) (* 2 (* i (+ beta (* 2 i))))) alpha))) alpha))>
#<alt (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2))>
#<alt (+ (* beta (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (+ (* beta (- (+ (* -1 (* beta (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (+ (* beta (- (+ (* beta (- (* beta (- (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 6)) (+ (* -1 (/ (* (+ (* 2 alpha) (* 4 i)) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2)))) (pow (+ alpha (* 2 i)) 2))) (/ i (pow (+ alpha (* 2 i)) 4))))) (+ (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 4)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (/ i (pow (+ alpha (* 2 i)) 2)) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (pow (+ alpha (* 2 i)) 2))))) (/ i (pow (+ alpha (* 2 i)) 2))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) (pow (+ alpha (* 2 i)) 4)))) (/ (* i (+ alpha i)) (pow (+ alpha (* 2 i)) 2)))>
#<alt (/ i beta)>
#<alt (/ (- (+ i (/ (* i (+ alpha i)) beta)) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 2))) (/ (* i (+ alpha i)) beta))) (/ (* i (+ (* 2 alpha) (* 4 i))) beta)) beta)>
#<alt (/ (- (+ i (+ (* -1 (/ (+ (* -1 (* (+ (* 2 alpha) (* 4 i)) (+ (* i (pow (+ alpha (* 2 i)) 2)) (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))))) (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i)))))) (pow beta 3))) (/ (* i (+ alpha i)) beta))) (+ (/ (* i (+ (* 2 alpha) (* 4 i))) beta) (+ (/ (* i (pow (+ alpha (* 2 i)) 2)) (pow beta 2)) (/ (* (+ (* 2 alpha) (* 4 i)) (- (* i (+ alpha i)) (* i (+ (* 2 alpha) (* 4 i))))) (pow beta 2))))) beta)>
#<alt (/ i beta)>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -2 (/ (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -1 (/ (* i (pow (+ alpha (* 2 i)) 2)) beta)) (* i (+ alpha i)))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))>
#<alt (* -1 (/ (+ (* -1 i) (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (/ (* (+ alpha (* 2 i)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i)))))) beta)) (+ (* -2 (* (+ alpha (* 2 i)) (- (* i (+ alpha i)) (* 2 (* i (+ alpha (* 2 i))))))) (* -1 (* i (pow (+ alpha (* 2 i)) 2))))) beta)) (* i (+ alpha i))) (* 2 (* i (+ alpha (* 2 i))))) beta))) beta))>

Calls

147 calls:

Time	Variable		Point	Expression
11.0ms	alpha	@	-inf	(+ alpha (+ i beta))
7.0ms	i	@	inf	(/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
6.0ms	i	@	-inf	(* (* i i) (* (+ beta i) (+ beta i)))
2.0ms	beta	@	0	(/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
2.0ms	i	@	0	(/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* (+ (* i 2) beta) (+ (* i 2) beta)) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))

rewrite462.0ms (3.3%)

Memory

26.5MiB live, 745.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 136×	`/-lowering-/.f32`
5 136×	`/-lowering-/.f64`
4 070×	`-lowering-.f32`
4 070×	`-lowering-.f64`
2 746×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	282
1	275	273
2	3070	272
0	8619	253

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1 226

Calls

Call 1

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

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

simplify970.0ms (6.9%)

Memory

26.9MiB live, 845.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 904×	`-lowering-.f32`
6 904×	`-lowering-.f64`
6 440×	`accelerator-lowering-fma.f32`
6 440×	`accelerator-lowering-fma.f64`
4 510×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1985	25612
1	6874	25600
0	8006	23362

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 588

Calls

Call 1

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

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

eval598.0ms (4.3%)

Memory: -22.9MiB live, 623.8MiB allocated
Compiler: Compiled 160 292 to 6 909 computations (95.7% saved)

prune296.0ms (2.1%)

Memory

-11.5MiB live, 760.0MiB allocated

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	2 386	20	2 406
Fresh	7	3	10
Picked	2	3	5
Done	0	0	0
Total	2 395	26	2 421

Accuracy

98.4%

Counts

2 421 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	15.5%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
	13.8%	(/.f64 (fma.f64 i i (neg.f64 (/.f64 (.f64 (.f64 i (.f64 i i)) #s(literal 6 binary64)) beta))) (.f64 beta beta))
	16.8%	(/.f64 (fma.f64 i alpha (.f64 i i)) (.f64 beta beta))
	23.6%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
	35.7%	(/.f64 (.f64 (/.f64 (.f64 i i) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 i beta) (+.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	35.7%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	13.8%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i beta)) (.f64 beta beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
	3.5%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (fma.f64 beta beta (.f64 #s(literal 4 binary64) (.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
✓	13.8%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
▶	11.0%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i (+.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
▶	19.5%	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
✓	16.8%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
	15.2%	(/.f64 (.f64 i i) (.f64 beta beta))
	9.3%	(/.f64 (.f64 i alpha) (.f64 beta beta))
	27.9%	(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 i i)) (fma.f64 (*.f64 i i) #s(literal 4 binary64) #s(literal -1 binary64)))
	13.3%	(.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
	17.6%	(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
	35.7%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	13.4%	(.f64 (/.f64 (+.f64 alpha i) beta) (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
▶	40.1%	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
▶	16.8%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
	17.4%	(.f64 (.f64 i (+.f64 i beta)) (/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
▶	9.4%	(.f64 alpha (/.f64 i (.f64 beta beta)))
	15.8%	(.f64 alpha (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 alpha (*.f64 beta beta)))))
	30.4%	(.f64 #s(literal 1/4 binary64) (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
✓	65.6%	#s(literal 1/16 binary64)

Compiler

Compiled 1 125 to 553 computations (50.8% saved)

simplify366.0ms (2.6%)

Memory

7.4MiB live, 556.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (+.f64 beta i) (+.f64 beta i))
✓	cost-diff	0	(*.f64 i i)
✓	cost-diff	0	(.f64 (.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)))
✓	cost-diff	1664	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i (+.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
✓	cost-diff	0	(*.f64 i (+.f64 alpha i))
✓	cost-diff	0	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
✓	cost-diff	128	(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
✓	cost-diff	128	(-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 i (+.f64 i alpha))
✓	cost-diff	0	(*.f64 beta beta)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 beta beta))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
✓	cost-diff	0	(*.f64 beta beta)
✓	cost-diff	0	(/.f64 i (*.f64 beta beta))
✓	cost-diff	0	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	cost-diff	0	(/.f64 (*.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	cost-diff	384	(fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta))
✓	cost-diff	384	(/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
✓	cost-diff	384	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))

Rules

11 518×	`accelerator-lowering-fma.f32`
11 518×	`accelerator-lowering-fma.f64`
5 436×	`-lowering-.f32`
5 436×	`-lowering-.f64`
3 394×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	433
1	180	431
2	819	419
3	4973	391
4	6674	387
0	8014	356

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize160.0ms (1.1%)

Memory

-1.3MiB live, 230.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))
✓	accuracy	99.9%	(.f64 (.f64 #s(literal 4 binary64) (*.f64 i (+.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 i i) (*.f64 (+.f64 beta i) (+.f64 beta i)))
✓	accuracy	18.1%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (.f64 #s(literal 4 binary64) (.f64 i (+.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
✓	accuracy	100.0%	(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))
✓	accuracy	100.0%	(*.f64 i (+.f64 alpha i))
✓	accuracy	100.0%	(.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))
✓	accuracy	44.4%	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	100.0%	(*.f64 i (+.f64 i alpha))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 beta beta))
✓	accuracy	66.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i (+.f64 i alpha)))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	90.7%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	accuracy	83.3%	(/.f64 i (*.f64 beta beta))
✓	accuracy	90.6%	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
✓	accuracy	55.9%	(/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
✓	accuracy	47.7%	(/.f64 (*.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
✓	accuracy	47.3%	(/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))

Samples

74.0ms

256×

valid

Compiler

Compiled 405 to 48 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 27.0ms (52.2% of total)

ival-add: 13.0ms (25.1% of total)

ival-div: 10.0ms (19.3% of total)

ival-sub: 1.0ms (1.9% of total)

exact: 1.0ms (1.9% of total)

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

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

series91.0ms (0.7%)

Memory

12.1MiB live, 85.7MiB allocated

Counts

22 → 624

Calls

Call 1

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

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

Calls

156 calls:

Time	Variable		Point	Expression
12.0ms	beta	@	inf	(* (* 4 (* i (+ i beta))) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1))
8.0ms	beta	@	0	(/ (/ (+ (* i (+ alpha (+ i beta))) (* alpha beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
8.0ms	i	@	0	(/ (* (* i i) (* (+ beta i) (+ beta i))) (* (* 4 (* i (+ i beta))) (+ (* (+ (* i 2) beta) (+ (* i 2) beta)) -1)))
2.0ms	alpha	@	0	(/ (/ (+ (* i (+ alpha (+ i beta))) (* alpha beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))
2.0ms	i	@	0	(/ (/ (+ (* i (+ alpha (+ i beta))) (* alpha beta)) (+ alpha (+ (* i 2) beta))) (+ (* (+ alpha (+ (* i 2) beta)) (+ alpha (+ (* i 2) beta))) -1))

rewrite401.0ms (2.9%)

Memory

6.8MiB live, 635.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 036×	`-lowering-.f32`
6 036×	`-lowering-.f64`
4 480×	`/-lowering-/.f32`
4 480×	`/-lowering-/.f64`
2 674×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	278
1	379	264
2	4044	263
0	9526	246

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 788

Calls

Call 1

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

Outputs
(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))
(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 i (+.f64 i (+.f64 alpha beta)))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 i (+.f64 alpha beta))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))))
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))
(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) #s(literal 1 binary64)) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta)))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta)))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) #s(literal 1 binary64)) (.f64 (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (*.f64 i (+.f64 i (+.f64 alpha beta))))))
(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))) (.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))) (.f64 (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 i (+.f64 i (+.f64 alpha beta)))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (*.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) #s(literal 1 binary64)) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (.f64 i (+.f64 i (+.f64 alpha beta))))))
(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 i (+.f64 i (+.f64 alpha beta)))) (.f64 (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 i (+.f64 i (+.f64 alpha beta))))) (.f64 (.f64 (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64)) (/.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))))
(/.f64 (.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (-.f64 #s(literal 0 binary64) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)))) (.f64 i (+.f64 i (+.f64 alpha beta)))) (.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))))
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simplify613.0ms (4.4%)

Memory

16.0MiB live, 1 020.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 768×	`-lowering-.f32`
7 768×	`-lowering-.f64`
6 638×	`accelerator-lowering-fma.f32`
6 638×	`accelerator-lowering-fma.f64`
4 548×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2195	22025
1	7574	22021
0	8831	20149

Stop Event

1×	iter limit
1×	node limit

Counts

624 → 624

Calls

Call 1

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

Outputs
(/ (* alpha (* beta i)) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))
(/.f64 (.f64 alpha (.f64 beta i)) (*.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
(* i (+ (* i (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
(.f64 i (fma.f64 i (-.f64 (fma.f64 alpha (/.f64 beta (.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))) (/.f64 (.f64 alpha (.f64 beta (.f64 #s(literal 4 binary64) (fma.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))))) (.f64 (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))))) (/.f64 (.f64 alpha beta) (.f64 (+.f64 alpha beta) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))))
(* i (+ (* i (- (+ (* i (- (+ (* 2 (/ alpha (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (* 2 (/ beta (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (+ (/ (* alpha (* beta (+ (* 4 (- (pow (+ alpha beta) 2) 1)) (+ (* 4 (pow (+ alpha beta) 2)) (* 16 (pow (+ alpha beta) 2)))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))) (/ (* (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))) (- (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1)))))) (+ (/ 1 (- (pow (+ alpha beta) 2) 1)) (/ (* alpha beta) (* (pow (+ alpha beta) 2) (- (pow (+ alpha beta) 2) 1))))) (/ (* alpha (* beta (+ (* 4 (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1))) (* 4 (pow (+ alpha beta) 3))))) (* (pow (+ alpha beta) 3) (pow (- (pow (+ alpha beta) 2) 1) 2))))) (/ (* alpha beta) (* (+ alpha beta) (- (pow (+ alpha beta) 2) 1)))))
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(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(/ (+ (* -1 (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta)) (* i (+ alpha i))) (pow beta 2))
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(/ (- (+ (* -1 (/ (+ (* -1 (* i (* (+ alpha i) (pow (+ (* 2 alpha) (* 4 i)) 2)))) (* i (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)))) (pow beta 2))) (* i (+ alpha i))) (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta)) (pow beta 2))
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(/ (- (+ (* -1 (/ (+ (* -1 (* i (* (+ alpha i) (* (+ (* 2 alpha) (* 4 i)) (- (pow (+ alpha (* 2 i)) 2) 1))))) (* -1 (* (+ (* -1 (* i (* (+ alpha i) (pow (+ (* 2 alpha) (* 4 i)) 2)))) (* i (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1)))) (+ (* 2 alpha) (* 4 i))))) (pow beta 3))) (* i (+ alpha i))) (+ (* -1 (/ (* i (* (+ alpha i) (pow (+ (* 2 alpha) (* 4 i)) 2))) (pow beta 2))) (+ (/ (* i (* (+ alpha i) (+ (* 2 alpha) (* 4 i)))) beta) (/ (* i (* (+ alpha i) (- (pow (+ alpha (* 2 i)) 2) 1))) (pow beta 2))))) (pow beta 2))
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(* alpha i)
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(* -1 (* alpha (+ (* -1 i) (* -1 (/ (pow i 2) alpha)))))
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(.f64 (.f64 beta (.f64 beta beta)) (.f64 #s(literal 4 binary64) (+.f64 i (.f64 i (/.f64 (.f64 #s(literal 5 binary64) i) beta)))))
(* (pow beta 3) (+ (* 4 i) (+ (* 4 (/ (* i (+ i (* 4 i))) beta)) (* 4 (/ (* i (- (* 8 (pow i 2)) 1)) (pow beta 2))))))
(.f64 (.f64 beta (.f64 beta beta)) (fma.f64 #s(literal 4 binary64) (fma.f64 i (/.f64 (.f64 #s(literal 5 binary64) i) beta) (/.f64 (.f64 i (fma.f64 (.f64 i i) #s(literal 8 binary64) #s(literal -1 binary64))) (.f64 beta beta))) (.f64 i #s(literal 4 binary64))))
(* (pow beta 3) (+ (* 4 i) (+ (* 4 (/ (* i (+ i (* 4 i))) beta)) (+ (* 4 (/ (* i (- (* 8 (pow i 2)) 1)) (pow beta 2))) (* 4 (/ (* (pow i 2) (- (* 4 (pow i 2)) 1)) (pow beta 3)))))))
(.f64 (.f64 beta (.f64 beta beta)) (fma.f64 #s(literal 4 binary64) (+.f64 i (.f64 i (/.f64 (.f64 #s(literal 5 binary64) i) beta))) (.f64 #s(literal 4 binary64) (fma.f64 i (/.f64 (fma.f64 (.f64 i i) #s(literal 8 binary64) #s(literal -1 binary64)) (.f64 beta beta)) (/.f64 (.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))) (.f64 beta (*.f64 beta beta)))))))
(* 4 (* (pow beta 3) i))
(.f64 #s(literal 4 binary64) (.f64 i (.f64 beta (.f64 beta beta))))
(* -1 (* (pow beta 3) (+ (* -4 i) (* -4 (/ (* i (+ i (* 4 i))) beta)))))
(neg.f64 (.f64 (.f64 beta (.f64 beta beta)) (.f64 #s(literal -4 binary64) (+.f64 i (.f64 i (/.f64 (.f64 #s(literal 5 binary64) i) beta))))))
(* -1 (* (pow beta 3) (+ (* -4 i) (* -1 (/ (+ (* -4 (/ (* i (+ (* -4 (pow i 2)) (* -1 (- (* 4 (pow i 2)) 1)))) beta)) (* 4 (* i (+ i (* 4 i))))) beta)))))
(neg.f64 (.f64 (.f64 beta (.f64 beta beta)) (fma.f64 i #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (/.f64 (.f64 i (fma.f64 (.f64 i i) #s(literal -4 binary64) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))))) beta) (.f64 (.f64 i #s(literal 4 binary64)) (*.f64 #s(literal 5 binary64) i))) beta)))))
(* -1 (* (pow beta 3) (+ (* -4 i) (* -1 (/ (+ (* -1 (/ (+ (* -4 (/ (* (pow i 2) (- (* 4 (pow i 2)) 1)) beta)) (* 4 (* i (+ (* -4 (pow i 2)) (* -1 (- (* 4 (pow i 2)) 1)))))) beta)) (* 4 (* i (+ i (* 4 i))))) beta)))))
(neg.f64 (.f64 (.f64 beta (.f64 beta beta)) (fma.f64 i #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (.f64 #s(literal 5 binary64) i)) (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i (fma.f64 (.f64 i i) #s(literal -4 binary64) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64))))) (.f64 #s(literal -4 binary64) (.f64 (.f64 i i) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 i i) #s(literal -1 binary64)) beta)))) beta))) beta)))))
(- (pow beta 2) 1)
(fma.f64 beta beta #s(literal -1 binary64))
(- (+ (* 4 (* beta i)) (pow beta 2)) 1)
(fma.f64 (*.f64 beta i) #s(literal 4 binary64) (fma.f64 beta beta #s(literal -1 binary64)))
(- (+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2)) 1)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 beta i)) (fma.f64 beta beta #s(literal -1 binary64)))
(- (+ (* i (+ (* 4 beta) (* 4 i))) (pow beta 2)) 1)
(fma.f64 i (*.f64 #s(literal 4 binary64) (+.f64 beta i)) (fma.f64 beta beta #s(literal -1 binary64)))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ beta i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 beta i) #s(literal 4 binary64)))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))) (/ 1 (pow i 2))))
(.f64 (.f64 i i) (+.f64 #s(literal 4 binary64) (-.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta i) (/.f64 (.f64 beta beta) (.f64 i i))) (/.f64 #s(literal 1 binary64) (*.f64 i i)))))
(* (pow i 2) (- (+ 4 (+ (* 4 (/ beta i)) (/ (pow beta 2) (pow i 2)))) (/ 1 (pow i 2))))
(.f64 (.f64 i i) (+.f64 #s(literal 4 binary64) (-.f64 (fma.f64 #s(literal 4 binary64) (/.f64 beta i) (/.f64 (.f64 beta beta) (.f64 i i))) (/.f64 #s(literal 1 binary64) (*.f64 i i)))))
(* 4 (pow i 2))
(.f64 #s(literal 4 binary64) (.f64 i i))
(* (pow i 2) (+ 4 (* 4 (/ beta i))))
(.f64 (.f64 i i) (fma.f64 #s(literal 4 binary64) (/.f64 beta i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (- (pow beta 2) 1) i))) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 beta #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) i))) i) #s(literal 4 binary64)))
(* (pow i 2) (+ 4 (* -1 (/ (+ (* -4 beta) (* -1 (/ (- (pow beta 2) 1) i))) i))))
(.f64 (.f64 i i) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 beta #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) i))) i) #s(literal 4 binary64)))
(- (* 4 (pow i 2)) 1)
(fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64))
(- (+ (* 4 (* beta i)) (* 4 (pow i 2))) 1)
(fma.f64 #s(literal 4 binary64) (*.f64 i (+.f64 beta i)) #s(literal -1 binary64))
(- (+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i)))) 1)
(+.f64 (fma.f64 beta (fma.f64 i #s(literal 4 binary64) beta) (.f64 #s(literal 4 binary64) (.f64 i i))) #s(literal -1 binary64))
(- (+ (* 4 (pow i 2)) (* beta (+ beta (* 4 i)))) 1)
(+.f64 (fma.f64 beta (fma.f64 i #s(literal 4 binary64) beta) (.f64 #s(literal 4 binary64) (.f64 i i))) #s(literal -1 binary64))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 4 (/ i beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 2) (- (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (-.f64 (fma.f64 #s(literal 4 binary64) (+.f64 (/.f64 i beta) (/.f64 (.f64 i i) (.f64 beta beta))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))
(* (pow beta 2) (- (+ 1 (+ (* 4 (/ i beta)) (* 4 (/ (pow i 2) (pow beta 2))))) (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (-.f64 (fma.f64 #s(literal 4 binary64) (+.f64 (/.f64 i beta) (/.f64 (.f64 i i) (.f64 beta beta))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 beta beta))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (+ 1 (* 4 (/ i beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal 4 binary64) (/.f64 i beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -1 (/ (- (* 4 (pow i 2)) 1) beta))) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 i #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64)) beta))) beta) #s(literal 1 binary64)))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -4 i) (* -1 (/ (- (* 4 (pow i 2)) 1) beta))) beta))))
(.f64 (.f64 beta beta) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 i #s(literal -4 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 i i) #s(literal -1 binary64)) beta))) beta) #s(literal 1 binary64)))

eval198.0ms (1.4%)

Memory: 41.5MiB live, 293.1MiB allocated
Compiler: Compiled 65 458 to 4 785 computations (92.7% saved)

prune219.0ms (1.6%)

Memory

-11.2MiB live, 388.2MiB allocated

Pruning

37 alts after pruning (33 fresh and 4 done)

	Pruned	Kept	Total
New	1 504	19	1 523
Fresh	4	14	18
Picked	4	1	5
Done	0	3	3
Total	1 512	37	1 549

Accuracy

98.5%

Counts

1 549 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.7%	(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
	15.5%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
	13.8%	(/.f64 (fma.f64 i i (neg.f64 (/.f64 (.f64 (.f64 i (.f64 i i)) #s(literal 6 binary64)) beta))) (.f64 beta beta))
	23.6%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
	35.7%	(/.f64 (.f64 (/.f64 (.f64 i i) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 i beta) (+.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
▶	16.8%	(/.f64 (.f64 (/.f64 i (.f64 beta beta)) (*.f64 (+.f64 i alpha) (-.f64 i alpha))) (-.f64 i alpha))
▶	35.7%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
	13.8%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i beta)) (.f64 beta beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
	3.5%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (fma.f64 beta beta (.f64 #s(literal 4 binary64) (.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
✓	13.8%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
	15.8%	(/.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
	19.5%	(/.f64 (.f64 i (+.f64 alpha i)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	19.5%	(/.f64 (.f64 i (+.f64 alpha i)) (fma.f64 beta (+.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 alpha #s(literal 2 binary64)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	16.1%	(/.f64 (.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	16.1%	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 #s(literal 4 binary64) (*.f64 i (+.f64 alpha beta)))) #s(literal 1 binary64)))
✓	16.8%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
	18.0%	(/.f64 (*.f64 i i) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	15.2%	(/.f64 (.f64 i i) (.f64 beta beta))
	9.3%	(/.f64 (.f64 i alpha) (.f64 beta beta))
	5.4%	(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
	27.9%	(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 i i)) (fma.f64 (*.f64 i i) #s(literal 4 binary64) #s(literal -1 binary64)))
▶	2.0%	(/.f64 i alpha)
	44.2%	(*.f64 (pow.f64 (/.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (+.f64 i alpha)) #s(literal -1 binary64)) (pow.f64 (/.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) i) #s(literal -1 binary64)))
	13.3%	(.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
	21.2%	(*.f64 (/.f64 (+.f64 i alpha) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) i)
	44.3%	(*.f64 (/.f64 (+.f64 i alpha) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64)))) (/.f64 i (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
	17.6%	(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
	35.7%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	38.5%	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (/.f64 (*.f64 i (+.f64 beta i)) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
	17.4%	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (+.f64 alpha i) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
	10.2%	(*.f64 (/.f64 alpha beta) (/.f64 i beta))
	15.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i i))
	16.8%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) beta) (/.f64 #s(literal 1 binary64) beta)) (*.f64 i (+.f64 i alpha)))
▶	17.4%	(.f64 (.f64 i (+.f64 i beta)) (/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
	17.4%	(.f64 i (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
✓	9.4%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	65.6%	#s(literal 1/16 binary64)

Compiler

Compiled 1 529 to 775 computations (49.3% saved)

simplify294.0ms (2.1%)

Memory

-9.1MiB live, 463.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
✓	cost-diff	0	(+.f64 i beta)
✓	cost-diff	0	(*.f64 i (+.f64 i beta))
✓	cost-diff	0	(.f64 (.f64 i (+.f64 i beta)) (/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
✓	cost-diff	0	(*.f64 beta beta)
✓	cost-diff	0	(/.f64 i (*.f64 beta beta))
✓	cost-diff	0	(.f64 (/.f64 i (.f64 beta beta)) (*.f64 (+.f64 i alpha) (-.f64 i alpha)))
✓	cost-diff	1408	(/.f64 (.f64 (/.f64 i (.f64 beta beta)) (*.f64 (+.f64 i alpha) (-.f64 i alpha))) (-.f64 i alpha))
✓	cost-diff	0	(+.f64 i alpha)
✓	cost-diff	0	(/.f64 i beta)
✓	cost-diff	0	(*.f64 (/.f64 i beta) (+.f64 i alpha))
✓	cost-diff	384	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
✓	cost-diff	0	(/.f64 i alpha)
✓	cost-diff	0	(*.f64 i i)
✓	cost-diff	0	(fma.f64 beta beta #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
✓	cost-diff	0	(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))

Rules

6 780×	`accelerator-lowering-fma.f32`
6 780×	`accelerator-lowering-fma.f64`
4 218×	`-lowering-.f32`
4 218×	`-lowering-.f64`
2 532×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	253
1	106	233
2	443	229
3	2258	229
4	6298	229
0	8053	210

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize95.0ms (0.7%)

Memory

12.6MiB live, 127.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 (fma.f64 i #s(literal 2 binary64) beta) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
✓	accuracy	99.9%	(*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
✓	accuracy	39.5%	(.f64 (.f64 i (+.f64 i beta)) (/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
✓	accuracy	25.5%	(/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	86.4%	(/.f64 (.f64 (/.f64 i (.f64 beta beta)) (*.f64 (+.f64 i alpha) (-.f64 i alpha))) (-.f64 i alpha))
✓	accuracy	83.3%	(/.f64 i (*.f64 beta beta))
✓	accuracy	79.2%	(.f64 (/.f64 i (.f64 beta beta)) (*.f64 (+.f64 i alpha) (-.f64 i alpha)))
✓	accuracy	100.0%	(/.f64 i beta)
✓	accuracy	100.0%	(+.f64 i alpha)
✓	accuracy	99.7%	(*.f64 (/.f64 i beta) (+.f64 i alpha))
✓	accuracy	94.7%	(/.f64 (*.f64 (/.f64 i beta) (+.f64 i alpha)) beta)
✓	accuracy	100.0%	(/.f64 i alpha)
✓	accuracy	100.0%	(fma.f64 beta beta #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	99.7%	(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
✓	accuracy	67.1%	(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))

Samples

57.0ms

256×

valid

Compiler

Compiled 236 to 35 computations (85.2% saved)

Precisions

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

ival-mult: 20.0ms (50.1% of total)

ival-div: 10.0ms (25% of total)

ival-add: 8.0ms (20% of total)

ival-sub: 1.0ms (2.5% of total)

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

exact: 0.0ms (0% of total)

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

series31.0ms (0.2%)

Memory

24.5MiB live, 24.5MiB allocated

Counts

19 → 468

Calls

Call 1

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

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

Calls

117 calls:

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

rewrite930.0ms (6.6%)

Memory

-88.0MiB live, 542.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 000×	`/-lowering-/.f32`
6 000×	`/-lowering-/.f64`
3 350×	`accelerator-lowering-fma.f32`
3 350×	`accelerator-lowering-fma.f64`
3 336×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	177
1	223	172
2	2185	172
0	8509	157

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 983

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i)) #s(literal 1/16 binary64))
(+.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i)))
(-.f64 (/.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/16 binary64))) (/.f64 #s(literal 1/256 binary64) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/16 binary64))))
(-.f64 (/.f64 #s(literal 1/256 binary64) (-.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i)))) (/.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) (-.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i)))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
(fma.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 i i)) #s(literal -1/64 binary64)) #s(literal 1/16 binary64))
(fma.f64 (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal -1/64 binary64) #s(literal 1/16 binary64))
(fma.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (/.f64 #s(literal 1 binary64) (.f64 i i)) #s(literal 1/16 binary64))
(fma.f64 (/.f64 #s(literal -1/64 binary64) i) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) i) #s(literal 1/16 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64)))))
(/.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)))) (.f64 (.f64 i (.f64 i i)) (.f64 i (.f64 i i)))) #s(literal 1/4096 binary64)) (-.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) #s(literal 1/256 binary64)) (.f64 (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/1024 binary64))))
(/.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)))) (.f64 (.f64 i (.f64 i i)) (.f64 i (.f64 i i)))) #s(literal 1/4096 binary64)) (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) #s(literal 1/16 binary64))) (*.f64 i i))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) #s(literal 1/16 binary64))) (.f64 i i))) (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)))) (.f64 (.f64 i (.f64 i i)) (.f64 i (*.f64 i i)))) #s(literal 1/4096 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i))) (-.f64 #s(literal 1/256 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))))))
(/.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) #s(literal -1/256 binary64)) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal -1/16 binary64)))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)))) (.f64 (.f64 i (.f64 i i)) (.f64 i (.f64 i i)))) #s(literal 1/4096 binary64))) (neg.f64 (-.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) #s(literal 1/256 binary64)) (.f64 (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/1024 binary64)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)))) (.f64 (.f64 i (.f64 i i)) (.f64 i (.f64 i i)))) #s(literal 1/4096 binary64))) (neg.f64 (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) #s(literal 1/16 binary64))) (*.f64 i i)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) #s(literal -1/256 binary64))) (neg.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal -1/16 binary64))))
(/.f64 (-.f64 #s(literal 1/256 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i)))) (-.f64 #s(literal 1/16 binary64) (/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/16 binary64))) (.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/16 binary64)) #s(literal 1/256 binary64))) (.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/16 binary64)) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal -1/16 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)))) (.f64 (.f64 i (.f64 i i)) (.f64 i (.f64 i i)))) #s(literal 1/4096 binary64)))) (neg.f64 (neg.f64 (-.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) #s(literal 1/256 binary64)) (.f64 (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (.f64 i i)) #s(literal -1/1024 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (.f64 (.f64 i i) (.f64 i i))) #s(literal -1/256 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal -1/16 binary64)))))
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(/.f64 (+.f64 (pow.f64 (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (-.f64 (.f64 (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) (.f64 (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (-.f64 (.f64 (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))) (.f64 (.f64 (.f64 i #s(literal 2 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))) (.f64 beta (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))))
(.f64 (fma.f64 i #s(literal 2 binary64) beta) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
(.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
(.f64 (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)))
(.f64 (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) (fma.f64 i #s(literal 2 binary64) beta))
(.f64 (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))

simplify515.0ms (3.7%)

Memory

24.2MiB live, 813.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 362×	`accelerator-lowering-fma.f32`
9 362×	`accelerator-lowering-fma.f64`
6 872×	`+-lowering-+.f64`
6 872×	`+-lowering-+.f32`
6 292×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	921	8445
1	3128	8101
0	8579	7555

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

Calls

Call 1

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

Outputs
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (* -1/64 (/ (pow beta 2) (pow i 2))) (* 1/64 (/ 1 (pow i 2)))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(+ 1/16 (+ (* -1/64 (/ (pow beta 2) (pow i 2))) (* 1/64 (/ 1 (pow i 2)))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(+ 1/16 (+ (* -1/64 (/ (pow beta 2) (pow i 2))) (* 1/64 (/ 1 (pow i 2)))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(* -1/64 (/ (pow beta 2) (pow i 2)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 beta beta)) (*.f64 i i))
(* (pow beta 2) (- (+ (/ 1/64 (* (pow beta 2) (pow i 2))) (* 1/16 (/ 1 (pow beta 2)))) (* 1/64 (/ 1 (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 i i) (.f64 beta beta))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 beta beta)) (/.f64 #s(literal -1/64 binary64) (*.f64 i i)))))
(* (pow beta 2) (- (+ (/ 1/64 (* (pow beta 2) (pow i 2))) (* 1/16 (/ 1 (pow beta 2)))) (* 1/64 (/ 1 (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 i i) (.f64 beta beta))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 beta beta)) (/.f64 #s(literal -1/64 binary64) (*.f64 i i)))))
(* (pow beta 2) (- (+ (/ 1/64 (* (pow beta 2) (pow i 2))) (* 1/16 (/ 1 (pow beta 2)))) (* 1/64 (/ 1 (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 i i) (.f64 beta beta))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 beta beta)) (/.f64 #s(literal -1/64 binary64) (*.f64 i i)))))
(* -1/64 (/ (pow beta 2) (pow i 2)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 beta beta)) (*.f64 i i))
(* (pow beta 2) (- (+ (/ 1/64 (* (pow beta 2) (pow i 2))) (* 1/16 (/ 1 (pow beta 2)))) (* 1/64 (/ 1 (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 i i) (.f64 beta beta))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 beta beta)) (/.f64 #s(literal -1/64 binary64) (*.f64 i i)))))
(* (pow beta 2) (- (+ (/ 1/64 (* (pow beta 2) (pow i 2))) (* 1/16 (/ 1 (pow beta 2)))) (* 1/64 (/ 1 (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 i i) (.f64 beta beta))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 beta beta)) (/.f64 #s(literal -1/64 binary64) (*.f64 i i)))))
(* (pow beta 2) (- (+ (/ 1/64 (* (pow beta 2) (pow i 2))) (* 1/16 (/ 1 (pow beta 2)))) (* 1/64 (/ 1 (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 i i) (.f64 beta beta))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 beta beta)) (/.f64 #s(literal -1/64 binary64) (*.f64 i i)))))
(* -1/64 (/ (- (pow beta 2) 1) (pow i 2)))
(/.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64)) (.f64 i i))
(/ (+ (* -1/64 (- (pow beta 2) 1)) (* 1/16 (pow i 2))) (pow i 2))
(/.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 i i) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (*.f64 i i))
(/ (+ (* -1/64 (- (pow beta 2) 1)) (* 1/16 (pow i 2))) (pow i 2))
(/.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 i i) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (*.f64 i i))
(/ (+ (* -1/64 (- (pow beta 2) 1)) (* 1/16 (pow i 2))) (pow i 2))
(/.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 i i) (fma.f64 #s(literal -1/64 binary64) (.f64 beta beta) #s(literal 1/64 binary64))) (*.f64 i i))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* -1/64 (/ (- (pow beta 2) 1) (pow i 2))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
(+ 1/16 (* -1/64 (/ (- (pow beta 2) 1) (pow i 2))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
(+ 1/16 (* -1/64 (/ (- (pow beta 2) 1) (pow i 2))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* -1/64 (/ (- (pow beta 2) 1) (pow i 2))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
(+ 1/16 (* -1/64 (/ (- (pow beta 2) 1) (pow i 2))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
(+ 1/16 (* -1/64 (/ (- (pow beta 2) 1) (pow i 2))))
(fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))
(/ -1 (pow i 2))
(/.f64 #s(literal -1 binary64) (*.f64 i i))
(- (/ (pow beta 2) (pow i 2)) (/ 1 (pow i 2)))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(- (/ (pow beta 2) (pow i 2)) (/ 1 (pow i 2)))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(- (/ (pow beta 2) (pow i 2)) (/ 1 (pow i 2)))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (pow beta 2) (pow i 2))
(/.f64 (.f64 beta beta) (.f64 i i))
(* (pow beta 2) (- (/ 1 (pow i 2)) (/ 1 (* (pow beta 2) (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 i i)) (/.f64 #s(literal -1 binary64) (.f64 (.f64 i i) (.f64 beta beta)))))
(* (pow beta 2) (- (/ 1 (pow i 2)) (/ 1 (* (pow beta 2) (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 i i)) (/.f64 #s(literal -1 binary64) (.f64 (.f64 i i) (.f64 beta beta)))))
(* (pow beta 2) (- (/ 1 (pow i 2)) (/ 1 (* (pow beta 2) (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 i i)) (/.f64 #s(literal -1 binary64) (.f64 (.f64 i i) (.f64 beta beta)))))
(/ (pow beta 2) (pow i 2))
(/.f64 (.f64 beta beta) (.f64 i i))
(* (pow beta 2) (- (/ 1 (pow i 2)) (/ 1 (* (pow beta 2) (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 i i)) (/.f64 #s(literal -1 binary64) (.f64 (.f64 i i) (.f64 beta beta)))))
(* (pow beta 2) (- (/ 1 (pow i 2)) (/ 1 (* (pow beta 2) (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 i i)) (/.f64 #s(literal -1 binary64) (.f64 (.f64 i i) (.f64 beta beta)))))
(* (pow beta 2) (- (/ 1 (pow i 2)) (/ 1 (* (pow beta 2) (pow i 2)))))
(.f64 (.f64 beta beta) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 i i)) (/.f64 #s(literal -1 binary64) (.f64 (.f64 i i) (.f64 beta beta)))))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
(/ (- (pow beta 2) 1) (pow i 2))
(/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i))
-1
#s(literal -1 binary64)
(- (pow beta 2) 1)
(fma.f64 beta beta #s(literal -1 binary64))
(- (pow beta 2) 1)
(fma.f64 beta beta #s(literal -1 binary64))
(- (pow beta 2) 1)
(fma.f64 beta beta #s(literal -1 binary64))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (- 1 (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))
(* (pow beta 2) (- 1 (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))
(* (pow beta 2) (- 1 (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))
(pow beta 2)
(*.f64 beta beta)
(* (pow beta 2) (- 1 (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))
(* (pow beta 2) (- 1 (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))
(* (pow beta 2) (- 1 (/ 1 (pow beta 2))))
(.f64 (.f64 beta beta) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 beta beta))))
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ i alpha)
(/.f64 i alpha)
(/ (* alpha i) (pow beta 2))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(.f64 i (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 i (*.f64 beta beta))))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(.f64 i (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 i (*.f64 beta beta))))
(* i (+ (/ alpha (pow beta 2)) (/ i (pow beta 2))))
(.f64 i (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 i (*.f64 beta beta))))
(/ (pow i 2) (pow beta 2))
(/.f64 (.f64 i i) (.f64 beta beta))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(/ (pow i 2) (pow beta 2))
(/.f64 (.f64 i i) (.f64 beta beta))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(* (pow i 2) (+ (/ 1 (pow beta 2)) (/ alpha (* (pow beta 2) i))))
(.f64 (.f64 i i) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (/.f64 alpha (.f64 i (*.f64 beta beta)))))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (* i (+ alpha i)) (pow beta 2))
(/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta))
(/ (pow i 2) (pow beta 2))
(/.f64 (.f64 i i) (.f64 beta beta))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(fma.f64 alpha (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta)))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(fma.f64 alpha (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta)))
(+ (/ (* alpha i) (pow beta 2)) (/ (pow i 2) (pow beta 2)))
(fma.f64 alpha (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (*.f64 beta beta)))
(/ (* alpha i) (pow beta 2))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(.f64 alpha (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 (*.f64 beta beta) alpha))))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(.f64 alpha (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 (*.f64 beta beta) alpha))))
(* alpha (+ (/ i (pow beta 2)) (/ (pow i 2) (* alpha (pow beta 2)))))
(.f64 alpha (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 (.f64 i i) (.f64 (*.f64 beta beta) alpha))))
(/ (* alpha i) (pow beta 2))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 i (.f64 beta beta))) (/.f64 (.f64 i i) (.f64 (*.f64 beta beta) alpha))) (-.f64 #s(literal 0 binary64) alpha))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 i (.f64 beta beta))) (/.f64 (.f64 i i) (.f64 (*.f64 beta beta) alpha))) (-.f64 #s(literal 0 binary64) alpha))
(* -1 (* alpha (+ (* -1 (/ i (pow beta 2))) (* -1 (/ (pow i 2) (* alpha (pow beta 2)))))))
(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 i (.f64 beta beta))) (/.f64 (.f64 i i) (.f64 (*.f64 beta beta) alpha))) (-.f64 #s(literal 0 binary64) alpha))
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(pow beta 4)
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eval205.0ms (1.5%)

Memory: 21.8MiB live, 323.7MiB allocated
Compiler: Compiled 49 587 to 4 065 computations (91.8% saved)

prune426.0ms (3%)

Memory

-17.1MiB live, 335.4MiB allocated

Pruning

48 alts after pruning (42 fresh and 6 done)

	Pruned	Kept	Total
New	1 588	15	1 603
Fresh	1	27	28
Picked	3	2	5
Done	0	4	4
Total	1 592	48	1 640

Accuracy

98.5%

Counts

1 640 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.6%	(fma.f64 #s(literal -1/64 binary64) (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/16 binary64))
	64.2%	(fma.f64 #s(literal -1/64 binary64) (*.f64 (/.f64 (+.f64 beta #s(literal 1 binary64)) i) (/.f64 (+.f64 beta #s(literal -1 binary64)) i)) #s(literal 1/16 binary64))
	15.5%	(/.f64 (fma.f64 i (+.f64 alpha i) (.f64 i (-.f64 (/.f64 (.f64 (+.f64 alpha i) (+.f64 (+.f64 alpha i) i)) beta) (/.f64 (.f64 (+.f64 alpha i) (fma.f64 alpha #s(literal 4 binary64) (.f64 i #s(literal 8 binary64)))) beta)))) (*.f64 beta beta))
	13.8%	(/.f64 (fma.f64 i i (neg.f64 (/.f64 (.f64 (.f64 i (.f64 i i)) #s(literal 6 binary64)) beta))) (.f64 beta beta))
	35.7%	(/.f64 (/.f64 (+.f64 i alpha) (/.f64 beta i)) beta)
	23.6%	(/.f64 (/.f64 (*.f64 i (+.f64 i alpha)) beta) beta)
	21.4%	(/.f64 (/.f64 (*.f64 i i) beta) beta)
	13.6%	(/.f64 (-.f64 (.f64 i i) (/.f64 (.f64 (.f64 i (.f64 i i)) #s(literal 6 binary64)) beta)) (*.f64 beta beta))
	35.7%	(/.f64 (.f64 (/.f64 (.f64 i i) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta))) (.f64 (+.f64 i beta) (+.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	33.5%	(/.f64 (*.f64 (/.f64 i beta) i) beta)
	35.7%	(/.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) beta) i) (+.f64 i alpha)) beta)
	13.8%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i beta)) (.f64 beta beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
	3.5%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (fma.f64 beta beta (.f64 #s(literal 4 binary64) (.f64 i beta))) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
✓	13.8%	(/.f64 (.f64 (.f64 i i) (.f64 (+.f64 beta i) (+.f64 beta i))) (.f64 (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))
	15.8%	(/.f64 (*.f64 i (+.f64 alpha i)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64)))
	19.5%	(/.f64 (.f64 i (+.f64 alpha i)) (fma.f64 i (.f64 #s(literal 4 binary64) (+.f64 i (+.f64 alpha beta))) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	19.5%	(/.f64 (.f64 i (+.f64 alpha i)) (fma.f64 beta (+.f64 beta (fma.f64 i #s(literal 4 binary64) (.f64 alpha #s(literal 2 binary64)))) (fma.f64 (fma.f64 i #s(literal 2 binary64) alpha) (fma.f64 i #s(literal 2 binary64) alpha) #s(literal -1 binary64))))
	16.1%	(/.f64 (.f64 i (+.f64 alpha i)) (fma.f64 #s(literal 4 binary64) (.f64 i (+.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) #s(literal -1 binary64))))
	16.1%	(/.f64 (.f64 i (+.f64 alpha i)) (-.f64 (fma.f64 (+.f64 alpha beta) (+.f64 alpha beta) (.f64 #s(literal 4 binary64) (*.f64 i (+.f64 alpha beta)))) #s(literal 1 binary64)))
✓	16.8%	(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
	18.0%	(/.f64 (*.f64 i i) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))
	15.2%	(/.f64 (.f64 i i) (.f64 beta beta))
	9.3%	(/.f64 (.f64 i alpha) (.f64 beta beta))
	5.4%	(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
	35.8%	(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 i alpha) beta)) (/.f64 beta i))
	17.6%	(/.f64 (.f64 #s(literal 1 binary64) (+.f64 i alpha)) (/.f64 (.f64 beta beta) i))
	26.0%	(/.f64 (.f64 #s(literal 1 binary64) (+.f64 i alpha)) (.f64 (/.f64 beta i) beta))
	27.9%	(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 i i)) (fma.f64 (*.f64 i i) #s(literal 4 binary64) #s(literal -1 binary64)))
✓	2.0%	(/.f64 i alpha)
	35.0%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) beta) (*.f64 (-.f64 #s(literal 0 binary64) i) (/.f64 (+.f64 i alpha) beta))))
	26.0%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 beta i) beta) (.f64 #s(literal 1 binary64) (+.f64 i alpha))))
	56.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/64 binary64) (/.f64 (fma.f64 beta beta #s(literal -1 binary64)) (*.f64 i i)) #s(literal 1/16 binary64))))
	65.6%	(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
	44.2%	(*.f64 (pow.f64 (/.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64))) (+.f64 i alpha)) #s(literal -1 binary64)) (pow.f64 (/.f64 (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))) i) #s(literal -1 binary64)))
	13.3%	(.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) (/.f64 i (+.f64 alpha beta)))
	21.2%	(*.f64 (/.f64 (+.f64 i alpha) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))) i)
	44.3%	(*.f64 (/.f64 (+.f64 i alpha) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64)))) (/.f64 i (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64)))))
	17.6%	(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
	35.7%	(*.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta))
	38.5%	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (/.f64 (*.f64 i (+.f64 beta i)) (fma.f64 i #s(literal 2 binary64) beta)) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
	17.4%	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (/.f64 (+.f64 alpha i) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
	10.2%	(*.f64 (/.f64 alpha beta) (/.f64 i beta))
	15.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i i))
✓	17.4%	(.f64 (.f64 i (+.f64 i beta)) (/.f64 (.f64 i (+.f64 i beta)) (.f64 (fma.f64 i #s(literal 2 binary64) beta) (*.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 (fma.f64 i #s(literal 2 binary64) beta) (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
	8.9%	(.f64 (.f64 i (+.f64 i beta)) (/.f64 i (.f64 beta (.f64 beta beta))))
	17.4%	(.f64 i (/.f64 (/.f64 (fma.f64 i (+.f64 alpha (+.f64 i beta)) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta))) (fma.f64 (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) (+.f64 alpha (fma.f64 i #s(literal 2 binary64) beta)) #s(literal -1 binary64))))
✓	9.4%	(.f64 alpha (/.f64 i (.f64 beta beta)))
✓	65.6%	#s(literal 1/16 binary64)

Compiler

Compiled 2 449 to 757 computations (69.1% saved)

regimes87.0ms (0.6%)

Memory

22.1MiB live, 138.6MiB allocated

Counts

70 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

22.0ms	beta
21.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))
21.0ms	alpha
19.0ms	i

Results

Accuracy	Segments	Branch
70.2%	2	`alpha`
83.5%	2	`beta`
81.5%	2	`i`
75.6%	2	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`

Compiler

Compiled 68 to 26 computations (61.8% saved)

regimes16.0ms (0.1%)

Memory

-12.3MiB live, 25.3MiB allocated

Counts

45 → 2

Calls

Call 1

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

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

Calls

1 calls:

14.0ms

beta

Results

Accuracy	Segments	Branch
82.5%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes10.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

30 → 2

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

beta

Results

Accuracy	Segments	Branch
82.5%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes8.0ms (0.1%)

Memory

-27.1MiB live, 11.8MiB allocated

Counts

18 → 2

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

beta

Results

Accuracy	Segments	Branch
82.5%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes6.0ms (0%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

17 → 2

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

beta

Results

Accuracy	Segments	Branch
81.8%	2	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes12.0ms (0.1%)

Memory

20.7MiB live, 20.7MiB allocated

Counts

11 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i alpha)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)
(/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 beta beta)) (*.f64 i i))
(*.f64 (/.f64 alpha beta) (/.f64 i beta))

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

Calls

3 calls:

4.0ms

beta

4.0ms

3.0ms

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

Results

Accuracy	Segments	Branch
70.9%	2	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`
70.8%	2	`i`
68.2%	2	`beta`

Compiler

Compiled 64 to 23 computations (64.1% saved)

regimes13.0ms (0.1%)

Memory

-53.1MiB live, 6.2MiB allocated

Counts

8 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i alpha)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
(/.f64 (.f64 i i) (.f64 beta beta))
(.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i)

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

Calls

1 calls:

12.0ms

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

Results

Accuracy	Segments	Branch
70.8%	2	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`

Compiler

Compiled 56 to 17 computations (69.6% saved)

regimes6.0ms (0%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i alpha)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i alpha) (.f64 beta beta))
(/.f64 (.f64 i i) (.f64 beta beta))

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

Calls

2 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
69.8%	2	`i`
70.5%	2	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`

Compiler

Compiled 60 to 20 computations (66.7% saved)

regimes11.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i alpha)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(.f64 alpha (/.f64 i (.f64 beta beta)))
(/.f64 (.f64 i alpha) (.f64 beta beta))

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

Calls

4 calls:

3.0ms	i
3.0ms	alpha
3.0ms	beta
2.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
68.2%	2	`beta`
65.6%	1	`i`
65.6%	1	`alpha`
65.6%	1	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`

Compiler

Compiled 68 to 26 computations (61.8% saved)

regimes4.0ms (0%)

Memory

-34.5MiB live, 4.7MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 1/16 binary64)
(/.f64 i alpha)
(/.f64 (*.f64 i #s(literal 1/4 binary64)) beta)
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))

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

Calls

1 calls:

2.0ms

beta

Results

Accuracy	Segments	Branch
65.6%	1	`beta`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes8.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Accuracy

Total -40.7b remaining (-184.6%)

Threshold costs -40.7b (-184.6%)

Counts

3 → 1

Calls

Call 1

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

Outputs
#s(literal 1/16 binary64)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
65.6%	1	`(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64)))`
65.6%	1	`alpha`
65.6%	1	`i`
65.6%	1	`beta`

Compiler

Compiled 68 to 26 computations (61.8% saved)

bsearch14.0ms (0.1%)

Memory

19.5MiB live, 19.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	4.825658201740958e+70	2.099018785681484e+71

Samples

8.0ms

96×

valid

Compiler

Compiled 287 to 173 computations (39.7% saved)

Precisions

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

ival-add: 2.0ms (34.9% of total)

ival-mult: 2.0ms (34.9% of total)

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

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

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

exact: 0.0ms (0% of total)

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

bsearch17.0ms (0.1%)

Memory

-17.2MiB live, 21.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	1.4026536186848612e+163	4.679205318151233e+164

Samples

11.0ms

112×

valid

Compiler

Compiled 241 to 156 computations (35.3% saved)

Precisions

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

ival-mult: 3.0ms (45% of total)

ival-add: 2.0ms (30% of total)

ival-sub: 1.0ms (15% of total)

ival-div: 1.0ms (15% of total)

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

exact: 0.0ms (0% of total)

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

bsearch15.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.4026536186848612e+163	4.679205318151233e+164

Samples

10.0ms

112×

valid

Compiler

Compiled 227 to 142 computations (37.4% saved)

Precisions

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

ival-mult: 3.0ms (44.6% of total)

ival-add: 2.0ms (29.7% of total)

ival-div: 1.0ms (14.9% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch17.0ms (0.1%)

Memory

-18.2MiB live, 19.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	1.4026536186848612e+163	4.679205318151233e+164

Samples

11.0ms

112×

valid

Compiler

Compiled 227 to 142 computations (37.4% saved)

Precisions

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

ival-div: 3.0ms (35.4% of total)

ival-mult: 3.0ms (35.4% of total)

ival-add: 2.0ms (23.6% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch15.0ms (0.1%)

Memory

20.1MiB live, 20.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.4026536186848612e+163	4.679205318151233e+164

Samples

9.0ms

112×

valid

Compiler

Compiled 213 to 135 computations (36.6% saved)

Precisions

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

ival-mult: 3.0ms (44.9% of total)

ival-add: 2.0ms (29.9% of total)

ival-div: 1.0ms (15% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.634427847668428e-10	0.06248350779374211

Compiler

Compiled 59 to 23 computations (61% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.634427847668428e-10	0.06248350779374211

Compiler

Compiled 59 to 23 computations (61% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.634427847668428e-10	0.06248350779374211

Compiler

Compiled 59 to 23 computations (61% saved)

bsearch20.0ms (0.1%)

Memory

-11.5MiB live, 28.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	8.889532522788125e+261	2.083721967023328e+266

Samples

14.0ms

128×

valid

Compiler

Compiled 235 to 151 computations (35.7% saved)

Precisions

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

ival-div: 4.0ms (39% of total)

ival-mult: 3.0ms (29.3% of total)

ival-add: 2.0ms (19.5% of total)

ival-sub: 1.0ms (9.8% of total)

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

exact: 0.0ms (0% of total)

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

simplify15.0ms (0.1%)

Memory

-20.0MiB live, 17.6MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
24×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-lft-identity_binary64`
2×	`mul-1-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	352
1	102	352
2	105	352
3	110	352

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 beta #s(literal 208000000000000002826574440430970039374165660004003097797874734870822912 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 (+.f64 i alpha) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64)))) (/.f64 i (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
(if (<=.f64 beta #s(literal 15999999999999999005599034209862359463208402551023487766011605054762973742117840039885687951424688974958399673950307408050920433502538389372207838731224822419816448 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (+.f64 i alpha) beta)) (/.f64 beta i)))
(if (<=.f64 beta #s(literal 30000000000000001332168704667067968928271318091371336647836257566611034246247676731166325460361286831240448925672604857758253281137641325011616793212250695678296064 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 (/.f64 i beta) (+.f64 i alpha)) beta))
(if (<=.f64 beta #s(literal 68000000000000002167136926439067117588146837458254417178678317660603555363554273482275494896434918149960097688320363419541966779026551844709337505790113802566500352 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 429999999999999995652167653055083225117014761716172313317513372469268128677854037666592487554618481224361137996524960865007928928623392128949175335040096178020548608 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 (/.f64 i beta) i) beta))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (/.f64 (.f64 i i) (.f64 beta beta)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 beta #s(literal 8999999999999999795959558556514947537987820844012540503764914737608588057919899397837661490586579927210850224244110069857545258699750948966376934438797714900636592392265520015309047604419332509888983370023044682174364307254745004301577003075036220158027273076736 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 alpha (/.f64 i (*.f64 beta beta))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
#s(literal 1/16 binary64)

Outputs
(if (<=.f64 beta #s(literal 208000000000000002826574440430970039374165660004003097797874734870822912 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 (+.f64 i alpha) (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal 1 binary64)))) (/.f64 i (+.f64 alpha (+.f64 (fma.f64 i #s(literal 2 binary64) beta) #s(literal -1 binary64))))))
(if (<=.f64 beta #s(literal 15999999999999999005599034209862359463208402551023487766011605054762973742117840039885687951424688974958399673950307408050920433502538389372207838731224822419816448 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (+.f64 i alpha) beta)) (/.f64 beta i)))
(if (<=.f64 beta #s(literal 15999999999999999005599034209862359463208402551023487766011605054762973742117840039885687951424688974958399673950307408050920433502538389372207838731224822419816448 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 beta i)))
(if (<=.f64 beta #s(literal 30000000000000001332168704667067968928271318091371336647836257566611034246247676731166325460361286831240448925672604857758253281137641325011616793212250695678296064 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 (/.f64 i beta) (+.f64 i alpha)) beta))
(if (<=.f64 beta #s(literal 30000000000000001332168704667067968928271318091371336647836257566611034246247676731166325460361286831240448925672604857758253281137641325011616793212250695678296064 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 (+.f64 i alpha) (/.f64 i beta)) beta))
(if (<=.f64 beta #s(literal 68000000000000002167136926439067117588146837458254417178678317660603555363554273482275494896434918149960097688320363419541966779026551844709337505790113802566500352 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 i beta)))
(if (<=.f64 beta #s(literal 429999999999999995652167653055083225117014761716172313317513372469268128677854037666592487554618481224361137996524960865007928928623392128949175335040096178020548608 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 (/.f64 i beta) i) beta))
(if (<=.f64 beta #s(literal 429999999999999995652167653055083225117014761716172313317513372469268128677854037666592487554618481224361137996524960865007928928623392128949175335040096178020548608 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (/.f64 (.f64 i (/.f64 i beta)) beta))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (/.f64 (.f64 i (+.f64 alpha i)) (.f64 beta beta)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 beta alpha))) (+.f64 (.f64 i (+.f64 i (+.f64 beta alpha))) (.f64 beta alpha))) (.f64 (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))) (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))))) (+.f64 (.f64 (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))) (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64)))) #s(literal -1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (/.f64 (.f64 i (+.f64 i alpha)) (.f64 beta beta)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (.f64 (/.f64 (+.f64 i alpha) (.f64 beta beta)) i) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 beta alpha))) (+.f64 (.f64 i (+.f64 i (+.f64 beta alpha))) (.f64 beta alpha))) (.f64 (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))) (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))))) (+.f64 (.f64 (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))) (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64)))) #s(literal -1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (.f64 i (/.f64 (+.f64 i alpha) (.f64 beta beta))) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) #s(literal 1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (/.f64 (.f64 i i) (.f64 beta beta)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 beta alpha))) (+.f64 (.f64 i (+.f64 i (+.f64 beta alpha))) (.f64 beta alpha))) (.f64 (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))) (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))))) (+.f64 (.f64 (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64))) (+.f64 (+.f64 beta alpha) (.f64 i #s(literal 2 binary64)))) #s(literal -1 binary64))) #s(literal 4835703278458517/4835703278458516698824704 binary64)) (/.f64 (.f64 i i) (.f64 beta beta)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 beta #s(literal 8999999999999999795959558556514947537987820844012540503764914737608588057919899397837661490586579927210850224244110069857545258699750948966376934438797714900636592392265520015309047604419332509888983370023044682174364307254745004301577003075036220158027273076736 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 i i))) (.f64 alpha (/.f64 i (*.f64 beta beta))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
#s(literal 1/16 binary64)

soundness1.2s (8.7%)

Memory

29.0MiB live, 1 007.8MiB allocated

Rules

9 362×	`accelerator-lowering-fma.f32`
9 362×	`accelerator-lowering-fma.f64`
9 164×	`accelerator-lowering-fma.f32`
9 164×	`accelerator-lowering-fma.f64`
7 768×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	278
1	379	264
2	4044	263
0	9526	246
0	1089	12630
1	3841	11840
0	8260	10972
0	1985	25612
1	6874	25600
0	8006	23362
0	33	282
1	275	273
2	3070	272
0	8619	253
0	921	8445
1	3128	8101
0	8579	7555
0	2195	22025
1	7574	22021
0	8831	20149
0	33	177
1	223	172
2	2185	172
0	8509	157

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 1 188 to 590 computations (50.3% saved)

preprocess157.0ms (1.1%)

Memory: -23.4MiB live, 149.4MiB allocated
Compiler: Compiled 896 to 224 computations (75% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze27.0ms (0.2%)

sample1.4s (10.2%)

preprocess394.0ms (2.8%)

explain267.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify366.0ms (2.6%)

localize55.0ms (0.4%)

series192.0ms (1.4%)

rewrite728.0ms (5.2%)

simplify619.0ms (4.4%)

eval206.0ms (1.5%)

prune227.0ms (1.6%)

simplify365.0ms (2.6%)

localize527.0ms (3.8%)

series94.0ms (0.7%)

rewrite462.0ms (3.3%)

simplify970.0ms (6.9%)

eval598.0ms (4.3%)

prune296.0ms (2.1%)

simplify366.0ms (2.6%)

localize160.0ms (1.1%)

series91.0ms (0.7%)

rewrite401.0ms (2.9%)

simplify613.0ms (4.4%)

eval198.0ms (1.4%)

prune219.0ms (1.6%)

simplify294.0ms (2.1%)

localize95.0ms (0.7%)

series31.0ms (0.2%)

rewrite930.0ms (6.6%)

simplify515.0ms (3.7%)

eval205.0ms (1.5%)

prune426.0ms (3%)

regimes87.0ms (0.6%)

regimes16.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

regimes12.0ms (0.1%)

regimes13.0ms (0.1%)

regimes6.0ms (0%)

regimes11.0ms (0.1%)

regimes4.0ms (0%)

regimes8.0ms (0.1%)

bsearch14.0ms (0.1%)

bsearch17.0ms (0.1%)

bsearch15.0ms (0.1%)

bsearch17.0ms (0.1%)

bsearch15.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch20.0ms (0.1%)

simplify15.0ms (0.1%)

soundness1.2s (8.7%)

preprocess157.0ms (1.1%)

end0.0ms (0%)

Profiling