Metrics for Octave 3.8, jcobi/2

analyze45.0ms (0.4%)

Memory

-2.1MiB live, 117.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 23 computations (43.9% saved)

sample1.6s (12.6%)

Memory

27.2MiB live, 2 632.7MiB allocated

Samples

726.0ms	6 657×	0	valid
253.0ms	1 222×	1	valid
116.0ms	356×	2	valid
9.0ms	21×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 819.0ms

ival-add: 240.0ms (29.3% of total)

ival-div: 232.0ms (28.3% of total)

ival-mult: 134.0ms (16.4% of total)

adjust: 63.0ms (7.7% of total)

ival->: 60.0ms (7.3% of total)

ival-sub: 52.0ms (6.3% of total)

exact: 19.0ms (2.3% of total)

ival-and: 16.0ms (2% of total)

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

Bogosity

preprocess871.0ms (7%)

Memory

33.2MiB live, 794.2MiB allocated

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	298
1	205	292
2	721	292
3	3654	290
0	15	29
1	33	29
2	108	29
3	478	29
4	2378	29
5	3830	29
6	5123	29
0	8033	26

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Call 2

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

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

explain314.0ms (2.5%)

Memory

-2.0MiB live, 516.3MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))`	o/n	89	0
↳	`(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))`	overflow	89
`+.f64`	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`	cancellation	63	0

Confusion

	Predicted +	Predicted -
+	109	0
-	0	147

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	109	0	0
-	0	0	147

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	147
1	66
2	43

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms	398×	0	valid
17.0ms	86×	1	valid
6.0ms	22×	2	valid
2.0ms	6×	3	valid

Compiler

Compiled 334 to 64 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-div: 12.0ms (29.6% of total)

ival-add: 12.0ms (29.6% of total)

ival-mult: 8.0ms (19.7% of total)

adjust: 4.0ms (9.9% of total)

ival-sub: 3.0ms (7.4% of total)

exact: 1.0ms (2.5% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.0%	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))

Status

Accuracy

Program

▶

59.0%

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

Compiler

Compiled 32 to 15 computations (53.1% saved)

simplify407.0ms (3.3%)

Memory

-0.2MiB live, 744.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize80.0ms (0.6%)

Memory

6.7MiB live, 124.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) i)
✓	accuracy	99.9%	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))
✓	accuracy	78.2%	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))
✓	accuracy	64.9%	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))

Samples

30.0ms	11×	2	valid
19.0ms	199×	0	valid
10.0ms	43×	1	valid
1.0ms	3×	3	valid

Compiler

Compiled 135 to 17 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-add: 7.0ms (32% of total)

ival-div: 6.0ms (27.4% of total)

ival-mult: 4.0ms (18.3% of total)

adjust: 2.0ms (9.1% of total)

ival-sub: 2.0ms (9.1% of total)

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

exact: 0.0ms (0% of total)

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

series56.0ms (0.5%)

Memory

-37.3MiB live, 103.4MiB allocated

Counts

6 → 192

Calls

Call 1

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

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

Calls

48 calls:

Time	Variable		Point	Expression
9.0ms	alpha	@	inf	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
4.0ms	beta	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))
3.0ms	i	@	inf	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
2.0ms	alpha	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))
2.0ms	i	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))

rewrite345.0ms (2.8%)

Memory

4.8MiB live, 621.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	106
1	115	106
2	1187	106
0	8698	96

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 305

Calls

Call 1

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

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

simplify498.0ms (4%)

Memory

9.2MiB live, 755.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 196×	`-lowering-.f32`
6 196×	`-lowering-.f64`
6 142×	`accelerator-lowering-fma.f32`
6 142×	`accelerator-lowering-fma.f64`
5 244×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	933	12962
1	3169	11337
0	8840	10203

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

eval110.0ms (0.9%)

Memory: 15.5MiB live, 167.9MiB allocated
Compiler: Compiled 31 480 to 2 396 computations (92.4% saved)

prune84.0ms (0.7%)

Memory

5.1MiB live, 203.2MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	582	9	591
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	583	9	592

Accuracy

99.9%

Counts

592 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.5%	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
▶	78.2%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64))
	23.6%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
▶	3.4%	(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	26.0%	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
▶	21.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
	64.8%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
	33.8%	#s(literal 1 binary64)
▶	58.3%	#s(literal 1/2 binary64)

Compiler

Compiled 398 to 216 computations (45.7% saved)

simplify357.0ms (2.9%)

Memory

-13.8MiB live, 579.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
✓	cost-diff	128	(+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))))
✓	cost-diff	320	(-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))))
✓	cost-diff	320	(.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha)))
✓	cost-diff	0	(fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))
✓	cost-diff	0	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
✓	cost-diff	128	(+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))))
✓	cost-diff	512	(.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64))
✓	cost-diff	192	(+.f64 #s(literal -1 binary64) #s(literal 1 binary64))
✓	cost-diff	704	(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64))

Rules

9 846×	`accelerator-lowering-fma.f32`
9 846×	`accelerator-lowering-fma.f64`
3 706×	`+-lowering-+.f64`
3 706×	`+-lowering-+.f32`
3 454×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	495
1	104	495
2	320	491
3	1432	473
4	6183	473
0	8203	400

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize220.0ms (1.8%)

Memory

25.9MiB live, 380.5MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	95.5%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
✓	accuracy	93.0%	(/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha)
✓	accuracy	81.5%	(-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))))
✓	accuracy	62.1%	(fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64))))
✓	accuracy	100.0%	(*.f64 i #s(literal 4 binary64))
✓	accuracy	100.0%	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
✓	accuracy	99.7%	(.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal -1 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 alpha beta)
✓	accuracy	100.0%	(/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	78.2%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64))

Samples

74.0ms	199×	0	valid
25.0ms	43×	1	valid
8.0ms	11×	2	valid
3.0ms	3×	3	valid

Compiler

Compiled 447 to 42 computations (90.6% saved)

Precisions

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

ival-mult: 31.0ms (40.8% of total)

ival-add: 16.0ms (21% of total)

ival-div: 14.0ms (18.4% of total)

adjust: 7.0ms (9.2% of total)

ival-sub: 7.0ms (9.2% of total)

exact: 1.0ms (1.3% of total)

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

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

series88.0ms (0.7%)

Memory

14.2MiB live, 196.2MiB allocated

Counts

18 → 468

Calls

Call 1

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

Outputs
#<alt (+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))>
#<alt (+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))>
#<alt (+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))>
#<alt (+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (+ (* beta (- (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 3) (pow (+ alpha (* 2 i)) 3)))) (+ (* -1 (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (+ (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))) (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))>
#<alt 2>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (* -1 (pow alpha 2)) (+ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))))))) (pow beta 3))) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta))))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))>
#<alt 2>
#<alt (- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (* -1 (/ (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) beta)))>
#<alt (+ 2 (* -1 (/ (- (+ (* -1 (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) (/ (pow alpha 2) beta)) (+ (* -1 (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) beta)) (/ (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) beta))) beta)))>
#<alt (+ 2 (* -1 (/ (+ (* -1 (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) (* -1 (/ (+ (* -1 (- (pow alpha 2) (+ (* -1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))))))))) (* -1 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))))))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (pow alpha 2) (+ (* -1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))))))) beta))) beta))) beta)))>
#<alt (+ 1 (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))>
#<alt (+ 1 (+ (* alpha (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))))>
#<alt (+ 1 (+ (* alpha (- (+ (* -1 (* alpha (+ (/ 1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (/ (pow beta 2) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))))) (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))))>
#<alt (+ 1 (+ (* alpha (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (+ (* alpha (- (* alpha (- (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 3) (pow (+ beta (* 2 i)) 3))) (+ (* -1 (/ beta (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2)))) (+ (* -1 (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (+ (/ 1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (/ (pow beta 2) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2)))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))))) (+ (/ 1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (/ (pow beta 2) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))))) (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))) (/ (* (pow beta 2) (+ 2 (+ (* 2 beta) (* 4 i)))) (* (pow (+ 2 (+ beta (* 2 i))) 2) (pow (+ beta (* 2 i)) 2))))) (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))))>
#<alt (/ (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))) alpha)>
#<alt (/ (- (+ beta (+ (* -1 beta) (/ (pow beta 2) alpha))) (+ (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))) (+ (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))) alpha)) (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))) alpha)))) alpha)>
#<alt (/ (- (+ beta (+ (* -1 beta) (+ (* -1 (/ (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))))))) (pow alpha 2))) (/ (pow beta 2) alpha)))) (+ (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))) (+ (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))) alpha)) (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))) alpha)))) alpha)>
#<alt (/ (- (+ beta (+ (* -1 beta) (+ (* -1 (/ (+ (* -1 (* (+ 2 (+ (* 2 beta) (* 4 i))) (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))))))))) (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))))))) (pow alpha 3))) (/ (pow beta 2) alpha)))) (+ (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))) (+ (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))) alpha)) (+ (/ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))) (pow alpha 2)) (+ (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i)))))) alpha) (/ (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ 2 (+ (* 2 beta) (* 4 i))) (- (+ beta (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))))))) (pow alpha 2))))))) alpha)>
#<alt (* -1 (/ (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))) alpha))>
#<alt (* -1 (/ (- (+ beta (+ (* -1 beta) (* -1 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i))))))))) alpha)))) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))) alpha))>
#<alt (* -1 (/ (- (+ beta (+ (* -1 beta) (* -1 (/ (- (+ (/ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))) alpha) (+ (/ (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))))) alpha) (pow beta 2))) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i))))))))) alpha)))) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))) alpha))>
#<alt (* -1 (/ (- (+ beta (+ (* -1 beta) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))))))) alpha)) (/ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i))))))))))) alpha)) (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))))))) alpha)) (pow beta 2)) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i))))))))) alpha)))) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))) alpha))>
#<alt (- (+ 1 (/ beta (+ 2 (+ alpha beta)))) (/ alpha (+ 2 (+ alpha beta))))>
#<alt (- (+ 1 (+ (* -1 (/ (* i (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha))) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))) (/ beta (+ 2 (+ alpha beta))))) (/ alpha (+ 2 (+ alpha beta))))>
#<alt (- (+ 1 (+ (* i (- (* -1 (* i (+ (* -1 (/ (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* 4 (/ (- beta alpha) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta))))))) (/ (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta))))) (/ beta (+ 2 (+ alpha beta))))) (/ alpha (+ 2 (+ alpha beta))))>
#<alt (- (+ 1 (+ (* i (- (* i (- (* -1 (* i (+ (* -4 (/ (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* -1 (/ (* (+ (* -1 (/ (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* 4 (/ (- beta alpha) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta))))) (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta)))) (* (+ 2 (+ alpha beta)) (+ alpha beta))))))) (+ (* -1 (/ (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* 4 (/ (- beta alpha) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta))))))) (/ (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta))))) (/ beta (+ 2 (+ alpha beta))))) (/ alpha (+ 2 (+ alpha beta))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))>
#<alt (+ 1 (+ (* -1/16 (/ (* (+ alpha beta) (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha))) (pow i 3))) (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))>
#<alt (- (+ 1 (+ (* -1 (/ (+ (* -1/64 (* (+ alpha beta) (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)))) (* 1/16 (* (+ 2 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- beta alpha))))) (pow i 4))) (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))) (* 1/16 (/ (* (+ alpha beta) (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha))) (pow i 3))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))>
#<alt (+ 1 (+ (* 1/16 (/ (* (+ alpha beta) (* (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) (- beta alpha))) (pow i 3))) (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))>
#<alt (+ 1 (+ (* -1 (/ (- (+ (* -1/64 (/ (* (+ alpha beta) (* (pow (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) 2) (- beta alpha))) i)) (* 1/16 (/ (* (+ 2 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- beta alpha))) i))) (* 1/16 (* (+ alpha beta) (* (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) (- beta alpha))))) (pow i 3))) (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))>
#<alt (* 1/2 (+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))>
#<alt (+ (* 1/2 (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))) (* 1/2 (+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))))>
#<alt (+ (* 1/2 (+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* beta (+ (* 1/2 (* beta (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))) (* 1/2 (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))))))>
#<alt (+ (* 1/2 (+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* beta (+ (* 1/2 (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* beta (+ (* 1/2 (* beta (- (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 3) (pow (+ alpha (* 2 i)) 3)))) (+ (* -1 (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (+ (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))))) (* 1/2 (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))) beta)))>
#<alt (+ 1 (+ (* 1/2 (/ (- (* -1 (pow alpha 2)) (+ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))))) (pow beta 2))) (* 1/2 (/ (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))) beta))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (* -1 (pow alpha 2)) (+ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))))))) (pow beta 3))) (+ (* 1/2 (/ (- (* -1 (pow alpha 2)) (+ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))))) (pow beta 2))) (* 1/2 (/ (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))) beta)))))>
#<alt 1>
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#<alt (/ alpha (+ 2 (+ alpha (* 2 i))))>
#<alt (+ (* beta (- (/ 1 (+ 2 (+ alpha (* 2 i)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))>
#<alt (+ (* beta (- (+ (* beta (- (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))>
#<alt (+ (* beta (- (+ (* beta (- (+ (* beta (- (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 4)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3))) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ 2 (* 2 i)) beta)))>
#<alt (- (+ 1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta))))>
#<alt (- (+ 1 (* -1 (/ (* (+ 2 (* 2 i)) (pow (+ 2 (+ alpha (* 2 i))) 2)) (pow beta 3)))) (+ (* -1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))>
#<alt (+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))>
#<alt (+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 (+ alpha (* 2 i))) 2) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta)) (* -1 (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))>
#<alt (/ (+ alpha beta) (+ 2 (+ alpha beta)))>
#<alt (+ (* -2 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 2))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))>
#<alt (+ (* i (- (* 4 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 3))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))>
#<alt (+ (* i (- (* i (- (* -8 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 4))) (* -4 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 3))))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))>
#<alt (* 1/2 (/ (+ alpha beta) i))>
#<alt (/ (+ (* -1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)) (* 1/2 (+ alpha beta))) i)>
#<alt (/ (- (+ (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/2 (+ alpha beta))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i)>
#<alt (/ (- (+ (* -1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) (pow i 3))) (* 1/2 (+ alpha beta))) (+ (* -1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)))) i)>
#<alt (* 1/2 (/ (+ alpha beta) i))>
#<alt (* -1 (/ (+ (* -1/2 (+ alpha beta)) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) i)) (* 1/8 (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))>
#<alt beta>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt alpha>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt (* alpha (+ 1 (/ beta alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt (* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))>
#<alt alpha>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt (+ alpha beta)>
#<alt beta>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt (* beta (+ 1 (/ alpha beta)))>
#<alt beta>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* -1 (* beta (- (* -1 (/ alpha beta)) 1)))>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (* 4 i)>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2))>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) (pow (+ 2 (* 4 i)) 2)))>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))>
#<alt (+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))>
#<alt (* 3 (pow beta 2))>
#<alt (* (pow beta 2) (+ 3 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta)))))>
#<alt (* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))>
#<alt (* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))>
#<alt (* 3 (pow beta 2))>
#<alt (* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) beta))))>
#<alt (* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))>
#<alt (* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) (pow (+ 2 (* 2 beta)) 2)))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))>
#<alt (+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))>
#<alt (* 12 (pow i 2))>
#<alt (* (pow i 2) (+ 12 (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (* 8 (/ (+ 2 (* 2 beta)) i)))))>
#<alt (* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))>
#<alt (* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))>
#<alt (* 12 (pow i 2))>
#<alt (* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) i))))>
#<alt (* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))>
#<alt (* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))>
#<alt (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha))>
#<alt (+ (* -1 (/ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) alpha)) (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)))>
#<alt (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))>
#<alt (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))>
#<alt (* -2 (/ (pow beta 2) alpha))>
#<alt (* (pow beta 2) (- (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta))) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))>
#<alt (* -2 (/ (pow beta 2) alpha))>
#<alt (* (pow beta 2) (- (+ (* -4 (/ (+ 2 (* 4 i)) (* alpha beta))) (+ (* 4 (/ i (* alpha beta))) (* 2 (/ 1 (* alpha beta))))) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))>
#<alt (* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))>
#<alt (/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) alpha)>
#<alt (- (+ (* -1 (/ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) alpha)) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))>
#<alt (- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))>
#<alt (- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))>
#<alt (* -12 (/ (pow i 2) alpha))>
#<alt (* (pow i 2) (- (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (* 12 (/ 1 alpha))))>
#<alt (* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))>
#<alt (* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))>
#<alt (* -12 (/ (pow i 2) alpha))>
#<alt (* (pow i 2) (- (+ (* -8 (/ (+ 2 (* 2 beta)) (* alpha i))) (+ (* 2 (/ beta (* alpha i))) (* 2 (/ (+ 2 beta) (* alpha i))))) (* 12 (/ 1 alpha))))>
#<alt (* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))>
#<alt (* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>
#<alt (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)>

Calls

117 calls:

Time	Variable		Point	Expression
8.0ms	alpha	@	0	(/ (+ alpha beta) (+ alpha (+ beta (+ (* 2 i) 2))))
6.0ms	alpha	@	inf	(* 1/2 (+ (+ 2 (+ (* beta 2) (* i 4))) (/ (- (* beta beta) (+ (* (+ 2 (+ (* beta 2) (* i 4))) (+ 2 (+ (* beta 2) (* i 4)))) (* (+ (* 2 i) beta) (- -2 (+ (* 2 i) beta))))) alpha)))
6.0ms	i	@	0	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ (+ alpha beta) (+ alpha (+ beta (+ (* 2 i) 2))))) 1)
4.0ms	beta	@	0	(* 1/2 (+ (+ 2 (+ (* beta 2) (* i 4))) (/ (- (* beta beta) (+ (* (+ 2 (+ (* beta 2) (* i 4))) (+ 2 (+ (* beta 2) (* i 4)))) (* (+ (* 2 i) beta) (- -2 (+ (* 2 i) beta))))) alpha)))
3.0ms	i	@	inf	(/ (- beta alpha) (+ alpha (+ (* 2 i) beta)))

rewrite424.0ms (3.4%)

Memory

-20.2MiB live, 749.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 474×	`/-lowering-/.f32`
4 474×	`/-lowering-/.f64`
3 476×	`-lowering-.f32`
3 476×	`-lowering-.f64`
2 866×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	304
1	297	304
2	3395	304
0	8641	260

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 491

Calls

Call 1

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

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

simplify488.0ms (3.9%)

Memory

9.3MiB live, 815.0MiB allocated

Algorithm

1×	egg-herbie

Rules

5 472×	`-lowering-.f32`
5 472×	`-lowering-.f64`
5 166×	`accelerator-lowering-fma.f32`
5 166×	`accelerator-lowering-fma.f64`
4 010×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1523	17704
1	5027	16230
0	8148	14651

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

Calls

Call 1

Inputs
(+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (+ (* beta (- (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 3) (pow (+ alpha (* 2 i)) 3)))) (+ (* -1 (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (+ (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))) (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
2
(- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))
(- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (* -1 (pow alpha 2)) (+ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))))))) (pow beta 3))) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta))))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))
2
(- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (* -1 (/ (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) beta)))
(+ 2 (* -1 (/ (- (+ (* -1 (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) (/ (pow alpha 2) beta)) (+ (* -1 (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) beta)) (/ (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) beta))) beta)))
(+ 2 (* -1 (/ (+ (* -1 (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))) (* -1 (/ (+ (* -1 (- (pow alpha 2) (+ (* -1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))))))))) (* -1 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))))))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (pow alpha 2) (+ (* -1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (* (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) (- (+ alpha (* -1 alpha)) (* -1 (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i))))))))))) beta))) beta))) beta)))
(+ 1 (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))
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(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))))))) (* 1/2 (/ (+ (* -1 (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (+ (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i))))))))))))) (* (+ 2 (+ beta (* 2 i))) (* (+ beta (* 2 i)) (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))))))) alpha))) alpha)) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (* (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))) (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i))))))))))) alpha)) (* 1/2 (- (+ beta (* -1 beta)) (* -1 (+ (* -1 (+ 2 (+ beta (* 2 i)))) (* -1 (+ beta (* 2 i)))))))) alpha))
(* 1/2 (- (+ 1 (/ beta (+ 2 (+ alpha beta)))) (/ alpha (+ 2 (+ alpha beta)))))
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(+ (* 1/2 (- (+ 1 (/ beta (+ 2 (+ alpha beta)))) (/ alpha (+ 2 (+ alpha beta))))) (* i (+ (* -1/2 (* i (+ (* -1 (/ (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* 4 (/ (- beta alpha) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta))))))) (* -1/2 (/ (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))))))
(+ (* 1/2 (- (+ 1 (/ beta (+ 2 (+ alpha beta)))) (/ alpha (+ 2 (+ alpha beta))))) (* i (+ (* -1/2 (/ (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))) (* i (+ (* -1/2 (* i (+ (* -4 (/ (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* -1 (/ (* (+ (* -1 (/ (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* 4 (/ (- beta alpha) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta))))) (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta)))) (* (+ 2 (+ alpha beta)) (+ alpha beta))))))) (* -1/2 (+ (* -1 (/ (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)) (* (pow (+ 2 (+ alpha beta)) 3) (pow (+ alpha beta) 2)))) (* 4 (/ (- beta alpha) (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))))))))))
1/2
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (+ (* -1/32 (/ (* (+ alpha beta) (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha))) (pow i 3))) (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))
(+ 1/2 (+ (* -1/2 (/ (+ (* -1/64 (* (+ alpha beta) (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)))) (* 1/16 (* (+ 2 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- beta alpha))))) (pow i 4))) (+ (* -1/32 (/ (* (+ alpha beta) (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha))) (pow i 3))) (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))))
1/2
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (+ (* 1/32 (/ (* (+ alpha beta) (* (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) (- beta alpha))) (pow i 3))) (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))
(+ 1/2 (+ (* -1 (/ (+ (* -1/32 (* (+ alpha beta) (* (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) (- beta alpha)))) (* 1/2 (/ (+ (* -1/64 (* (+ alpha beta) (* (pow (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) 2) (- beta alpha)))) (* 1/16 (* (+ 2 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- beta alpha))))) i))) (pow i 3))) (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))
(* -1 (/ alpha (+ alpha (* 2 i))))
(+ (* -1 (/ alpha (+ alpha (* 2 i)))) (* beta (- (/ 1 (+ alpha (* 2 i))) (* -1 (/ alpha (pow (+ alpha (* 2 i)) 2))))))
(+ (* -1 (/ alpha (+ alpha (* 2 i)))) (* beta (- (+ (* beta (- (* -1 (/ alpha (pow (+ alpha (* 2 i)) 3))) (/ 1 (pow (+ alpha (* 2 i)) 2)))) (/ 1 (+ alpha (* 2 i)))) (* -1 (/ alpha (pow (+ alpha (* 2 i)) 2))))))
(+ (* -1 (/ alpha (+ alpha (* 2 i)))) (* beta (- (+ (* beta (- (+ (* -1 (/ alpha (pow (+ alpha (* 2 i)) 3))) (* beta (- (/ 1 (pow (+ alpha (* 2 i)) 3)) (* -1 (/ alpha (pow (+ alpha (* 2 i)) 4)))))) (/ 1 (pow (+ alpha (* 2 i)) 2)))) (/ 1 (+ alpha (* 2 i)))) (* -1 (/ alpha (pow (+ alpha (* 2 i)) 2))))))
1
(- (+ 1 (* -1 (/ alpha beta))) (+ (* 2 (/ i beta)) (/ alpha beta)))
(- (+ 1 (+ (* -1 (/ alpha beta)) (* -1 (/ (* (+ alpha (* 2 i)) (- (* -1 alpha) (+ alpha (* 2 i)))) (pow beta 2))))) (+ (* 2 (/ i beta)) (/ alpha beta)))
(- (+ 1 (+ (* -1 (/ alpha beta)) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* -1 alpha) (+ alpha (* 2 i)))) (pow beta 3)))) (+ (* 2 (/ i beta)) (+ (/ alpha beta) (/ (* (+ alpha (* 2 i)) (- (* -1 alpha) (+ alpha (* 2 i)))) (pow beta 2)))))
1
(- (+ 1 (* -1 (/ alpha beta))) (+ (* 2 (/ i beta)) (/ alpha beta)))
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 alpha) (+ alpha (* 2 i)))) (/ (* (+ alpha (* 2 i)) (- (* -1 alpha) (+ alpha (* 2 i)))) beta)) beta)))
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 alpha) (+ alpha (* 2 i)))) (* -1 (/ (+ (* -1 (* (+ alpha (* 2 i)) (- (* -1 alpha) (+ alpha (* 2 i))))) (/ (* (pow (+ alpha (* 2 i)) 2) (- (* -1 alpha) (+ alpha (* 2 i)))) beta)) beta))) beta)))
(/ beta (+ beta (* 2 i)))
(+ (* -1 (* alpha (+ (/ 1 (+ beta (* 2 i))) (/ beta (pow (+ beta (* 2 i)) 2))))) (/ beta (+ beta (* 2 i))))
(+ (* alpha (- (/ (* alpha (+ (/ 1 (+ beta (* 2 i))) (/ beta (pow (+ beta (* 2 i)) 2)))) (+ beta (* 2 i))) (+ (/ 1 (+ beta (* 2 i))) (/ beta (pow (+ beta (* 2 i)) 2))))) (/ beta (+ beta (* 2 i))))
(+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (/ 1 (pow (+ beta (* 2 i)) 3)) (/ beta (pow (+ beta (* 2 i)) 4))))) (* -1 (/ (+ (/ 1 (+ beta (* 2 i))) (/ beta (pow (+ beta (* 2 i)) 2))) (+ beta (* 2 i)))))) (+ (/ 1 (+ beta (* 2 i))) (/ beta (pow (+ beta (* 2 i)) 2))))) (/ beta (+ beta (* 2 i))))
-1
(- (/ beta alpha) (+ 1 (* -1 (/ (+ beta (* 2 i)) alpha))))
(- (+ (* -1 (/ (* (+ beta (* 2 i)) (- beta (* -1 (+ beta (* 2 i))))) (pow alpha 2))) (/ beta alpha)) (+ 1 (* -1 (/ (+ beta (* 2 i)) alpha))))
(- (+ (/ beta alpha) (/ (* (pow (+ beta (* 2 i)) 2) (- beta (* -1 (+ beta (* 2 i))))) (pow alpha 3))) (+ 1 (+ (* -1 (/ (+ beta (* 2 i)) alpha)) (/ (* (+ beta (* 2 i)) (- beta (* -1 (+ beta (* 2 i))))) (pow alpha 2)))))
-1
(- (* -1 (/ (- (* -1 beta) (+ beta (* 2 i))) alpha)) 1)
(- (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (* (+ beta (* 2 i)) (- (* -1 beta) (+ beta (* 2 i)))) alpha))) (+ beta (* 2 i))) alpha)) 1)
(- (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (- (* -1 (/ (* (pow (+ beta (* 2 i)) 2) (- (* -1 beta) (+ beta (* 2 i)))) alpha)) (* -1 (* (+ beta (* 2 i)) (- (* -1 beta) (+ beta (* 2 i)))))) alpha))) (+ beta (* 2 i))) alpha)) 1)
(/ (- beta alpha) (+ alpha beta))
(- (+ (* -2 (/ (* i (- beta alpha)) (pow (+ alpha beta) 2))) (/ beta (+ alpha beta))) (/ alpha (+ alpha beta)))
(- (+ (* i (- (* 4 (/ (* i (- beta alpha)) (pow (+ alpha beta) 3))) (* 2 (/ (- beta alpha) (pow (+ alpha beta) 2))))) (/ beta (+ alpha beta))) (/ alpha (+ alpha beta)))
(- (+ (* i (- (* i (- (* -8 (/ (* i (- beta alpha)) (pow (+ alpha beta) 4))) (* -4 (/ (- beta alpha) (pow (+ alpha beta) 3))))) (* 2 (/ (- beta alpha) (pow (+ alpha beta) 2))))) (/ beta (+ alpha beta))) (/ alpha (+ alpha beta)))
(* 1/2 (/ (- beta alpha) i))
(/ (+ (* -1/4 (/ (* (+ alpha beta) (- beta alpha)) i)) (* 1/2 (- beta alpha))) i)
(/ (- (+ (* 1/8 (/ (* (pow (+ alpha beta) 2) (- beta alpha)) (pow i 2))) (* 1/2 (- beta alpha))) (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) i))) i)
(/ (- (+ (* -1/16 (/ (* (pow (+ alpha beta) 3) (- beta alpha)) (pow i 3))) (* 1/2 (- beta alpha))) (+ (* -1/8 (/ (* (pow (+ alpha beta) 2) (- beta alpha)) (pow i 2))) (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) i)))) i)
(* 1/2 (/ (- beta alpha) i))
(* -1 (/ (+ (* -1/2 (- beta alpha)) (* 1/4 (/ (* (+ alpha beta) (- beta alpha)) i))) i))
(* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ (* (pow (+ alpha beta) 2) (- beta alpha)) i)) (* 1/4 (* (+ alpha beta) (- beta alpha)))) i)) (* -1/2 (- beta alpha))) i))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (* (pow (+ alpha beta) 3) (- beta alpha)) i)) (* 1/8 (* (pow (+ alpha beta) 2) (- beta alpha)))) i)) (* 1/4 (* (+ alpha beta) (- beta alpha)))) i)) (* -1/2 (- beta alpha))) i))
(* -1 alpha)
(- beta alpha)
(- beta alpha)
(- beta alpha)
beta
(* beta (+ 1 (* -1 (/ alpha beta))))
(* beta (+ 1 (* -1 (/ alpha beta))))
(* beta (+ 1 (* -1 (/ alpha beta))))
beta
(* -1 (* beta (- (/ alpha beta) 1)))
(* -1 (* beta (- (/ alpha beta) 1)))
(* -1 (* beta (- (/ alpha beta) 1)))
beta
(+ beta (* -1 alpha))
(+ beta (* -1 alpha))
(+ beta (* -1 alpha))
(* -1 alpha)
(* alpha (- (/ beta alpha) 1))
(* alpha (- (/ beta alpha) 1))
(* alpha (- (/ beta alpha) 1))
(* -1 alpha)
(* -1 (* alpha (+ 1 (* -1 (/ beta alpha)))))
(* -1 (* alpha (+ 1 (* -1 (/ beta alpha)))))
(* -1 (* alpha (+ 1 (* -1 (/ beta alpha)))))
(* 1/2 (+ 2 (* 4 i)))
(+ beta (* 1/2 (+ 2 (* 4 i))))
(+ beta (* 1/2 (+ 2 (* 4 i))))
(+ beta (* 1/2 (+ 2 (* 4 i))))
beta
(* beta (+ 1 (* 1/2 (/ (+ 2 (* 4 i)) beta))))
(* beta (+ 1 (* 1/2 (/ (+ 2 (* 4 i)) beta))))
(* beta (+ 1 (* 1/2 (/ (+ 2 (* 4 i)) beta))))
beta
(* -1 (* beta (- (* -1/2 (/ (+ 2 (* 4 i)) beta)) 1)))
(* -1 (* beta (- (* -1/2 (/ (+ 2 (* 4 i)) beta)) 1)))
(* -1 (* beta (- (* -1/2 (/ (+ 2 (* 4 i)) beta)) 1)))
(* 1/2 (+ 2 (* 2 beta)))
(+ (* 1/2 (+ 2 (* 2 beta))) (* 2 i))
(+ (* 1/2 (+ 2 (* 2 beta))) (* 2 i))
(+ (* 1/2 (+ 2 (* 2 beta))) (* 2 i))
(* 2 i)
(* i (+ 2 (* 1/2 (/ (+ 2 (* 2 beta)) i))))
(* i (+ 2 (* 1/2 (/ (+ 2 (* 2 beta)) i))))
(* i (+ 2 (* 1/2 (/ (+ 2 (* 2 beta)) i))))
(* 2 i)
(* -1 (* i (- (* -1/2 (/ (+ 2 (* 2 beta)) i)) 2)))
(* -1 (* i (- (* -1/2 (/ (+ 2 (* 2 beta)) i)) 2)))
(* -1 (* i (- (* -1/2 (/ (+ 2 (* 2 beta)) i)) 2)))
(+ 2 (* 4 i))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(* 2 beta)
(* beta (+ 2 (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(* beta (+ 2 (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(* beta (+ 2 (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(* 2 beta)
(* -1 (* beta (- (* -1 (/ (+ 2 (* 4 i)) beta)) 2)))
(* -1 (* beta (- (* -1 (/ (+ 2 (* 4 i)) beta)) 2)))
(* -1 (* beta (- (* -1 (/ (+ 2 (* 4 i)) beta)) 2)))
(+ 2 (* 2 beta))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(+ 2 (+ (* 2 beta) (* 4 i)))
(* 4 i)
(* i (+ 4 (+ (* 2 (/ beta i)) (* 2 (/ 1 i)))))
(* i (+ 4 (+ (* 2 (/ beta i)) (* 2 (/ 1 i)))))
(* i (+ 4 (+ (* 2 (/ beta i)) (* 2 (/ 1 i)))))
(* 4 i)
(* -1 (* i (- (* -1 (/ (+ 2 (* 2 beta)) i)) 4)))
(* -1 (* i (- (* -1 (/ (+ 2 (* 2 beta)) i)) 4)))
(* -1 (* i (- (* -1 (/ (+ 2 (* 2 beta)) i)) 4)))
(* 1/2 (/ (+ 2 (* 4 i)) alpha))
(+ (* 1/2 (/ (+ 2 (* 4 i)) alpha)) (/ beta alpha))
(+ (* 1/2 (/ (+ 2 (* 4 i)) alpha)) (/ beta alpha))
(+ (* 1/2 (/ (+ 2 (* 4 i)) alpha)) (/ beta alpha))
(/ beta alpha)
(* beta (+ (* 1/2 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) beta)) (/ 1 alpha)))
(* beta (+ (* 1/2 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) beta)) (/ 1 alpha)))
(* beta (+ (* 1/2 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) beta)) (/ 1 alpha)))
(/ beta alpha)
(* -1 (* beta (- (* -1/2 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) beta)) (/ 1 alpha))))
(* -1 (* beta (- (* -1/2 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) beta)) (/ 1 alpha))))
(* -1 (* beta (- (* -1/2 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) beta)) (/ 1 alpha))))
(* 1/2 (/ (+ 2 (* 2 beta)) alpha))
(+ (* 1/2 (/ (+ 2 (* 2 beta)) alpha)) (* 2 (/ i alpha)))
(+ (* 1/2 (/ (+ 2 (* 2 beta)) alpha)) (* 2 (/ i alpha)))
(+ (* 1/2 (/ (+ 2 (* 2 beta)) alpha)) (* 2 (/ i alpha)))
(* 2 (/ i alpha))
(* i (+ (* 1/2 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ 1 alpha))) i)) (* 2 (/ 1 alpha))))
(* i (+ (* 1/2 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ 1 alpha))) i)) (* 2 (/ 1 alpha))))
(* i (+ (* 1/2 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ 1 alpha))) i)) (* 2 (/ 1 alpha))))
(* 2 (/ i alpha))
(* -1 (* i (- (* -1/2 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ 1 alpha))) i)) (* 2 (/ 1 alpha)))))
(* -1 (* i (- (* -1/2 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ 1 alpha))) i)) (* 2 (/ 1 alpha)))))
(* -1 (* i (- (* -1/2 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ 1 alpha))) i)) (* 2 (/ 1 alpha)))))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* 4 i)
(+ (* 2 beta) (* 4 i))
(+ (* 2 beta) (* 4 i))
(+ (* 2 beta) (* 4 i))
(* 2 beta)
(* beta (+ 2 (* 4 (/ i beta))))
(* beta (+ 2 (* 4 (/ i beta))))
(* beta (+ 2 (* 4 (/ i beta))))
(* 2 beta)
(* -1 (* beta (- (* -4 (/ i beta)) 2)))
(* -1 (* beta (- (* -4 (/ i beta)) 2)))
(* -1 (* beta (- (* -4 (/ i beta)) 2)))
(* 2 beta)
(+ (* 2 beta) (* 4 i))
(+ (* 2 beta) (* 4 i))
(+ (* 2 beta) (* 4 i))
(* 4 i)
(* i (+ 4 (* 2 (/ beta i))))
(* i (+ 4 (* 2 (/ beta i))))
(* i (+ 4 (* 2 (/ beta i))))
(* 4 i)
(* -1 (* i (- (* -2 (/ beta i)) 4)))
(* -1 (* i (- (* -2 (/ beta i)) 4)))
(* -1 (* i (- (* -2 (/ beta i)) 4)))
(* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))))
(+ (* 1/2 (* beta (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))))) (* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha)))))
(+ (* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha)))) (* beta (+ (* -1 (/ beta alpha)) (* 1/2 (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha))))))))
(+ (* 1/2 (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha)))) (* beta (+ (* -1 (/ beta alpha)) (* 1/2 (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha))))))))
(* -1 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (* 1/2 (/ (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))) beta)) (/ 1 alpha)))
(* (pow beta 2) (- (+ (* 1/2 (/ (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))) beta)) (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) (pow beta 2)))) (/ 1 alpha)))
(* (pow beta 2) (- (+ (* 1/2 (/ (- 2 (+ (* -1 (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha)))) (* 4 (/ (+ 2 (* 4 i)) alpha)))) beta)) (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) (pow beta 2)))) (/ 1 alpha)))
(* -1 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (* 1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) beta)) (/ 1 alpha)))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha)))))) (* -1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) beta))) beta)) (/ 1 alpha)))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha)))))) (* -1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) beta))) beta)) (/ 1 alpha)))
(* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))))
(+ (* 1/2 (* i (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))))) (* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))))
(+ (* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))) (* i (+ (* -6 (/ i alpha)) (* 1/2 (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha))))))))
(+ (* 1/2 (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))) (* i (+ (* -6 (/ i alpha)) (* 1/2 (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha))))))))
(* -6 (/ (pow i 2) alpha))
(* (pow i 2) (- (* 1/2 (/ (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))) i)) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (+ (* 1/2 (/ (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))) i)) (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) (pow i 2)))) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (+ (* 1/2 (/ (- 4 (+ (* -1 (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))) (* 8 (/ (+ 2 (* 2 beta)) alpha)))) i)) (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) (pow i 2)))) (* 6 (/ 1 alpha))))
(* -6 (/ (pow i 2) alpha))
(* (pow i 2) (- (* 1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) i)) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))))) (* -1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 6 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha)))))) (* -1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 6 (/ 1 alpha))))
(* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) alpha)
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) alpha)
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) alpha)
(* 1/2 (+ 2 (+ (* 2 beta) (* 4 i))))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(* 1/2 (+ 2 (+ (* 2 beta) (* 4 i))))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)))
(* -1 (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(- (* -1 (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))))) (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(- (* beta (- (* -2 beta) (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))))) (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(- (* beta (- (* -2 beta) (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))))) (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)))
(* -2 (pow beta 2))
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) beta)) 2))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (pow beta 2))) (+ 2 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta))))))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (pow beta 2))) (+ 2 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta))))))
(* -2 (pow beta 2))
(* (pow beta 2) (- (+ (* -4 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))) 2))
(* (pow beta 2) (- (* -1 (/ (- (+ (* -2 (/ (* i (+ 2 (* 2 i))) beta)) (/ (pow (+ 2 (* 4 i)) 2) beta)) (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i)))) beta)) 2))
(* (pow beta 2) (- (* -1 (/ (- (+ (* -2 (/ (* i (+ 2 (* 2 i))) beta)) (/ (pow (+ 2 (* 4 i)) 2) beta)) (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i)))) beta)) 2))
(- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(- (+ (* -1 (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))))) (pow beta 2)) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(- (+ (* i (- (* -12 i) (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))))) (pow beta 2)) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(- (+ (* i (- (* -12 i) (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))))) (pow beta 2)) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)))
(* -12 (pow i 2))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) i)) 12))
(* (pow i 2) (- (/ (pow beta 2) (pow i 2)) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2))))))))
(* (pow i 2) (- (/ (pow beta 2) (pow i 2)) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2))))))))
(* -12 (pow i 2))
(* (pow i 2) (- (+ (* -8 (/ (+ 2 (* 2 beta)) i)) (+ (* 2 (/ beta i)) (* 2 (/ (+ 2 beta) i)))) 12))
(* (pow i 2) (- (* -1 (/ (- (* -1 (/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) i)) (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta))))) i)) 12))
(* (pow i 2) (- (* -1 (/ (- (* -1 (/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) i)) (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta))))) i)) 12))
(* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha))
(+ (* 1/2 (* beta (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))))) (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha)))
(+ (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha)) (* beta (+ (* -1 (/ beta (pow alpha 2))) (* 1/2 (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2)))))))))
(+ (* 1/2 (/ (- (+ 2 (* 4 i)) (+ (* -2 (/ (* i (+ 2 (* 2 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) alpha))) alpha)) (* beta (+ (* -1 (/ beta (pow alpha 2))) (* 1/2 (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2)))))))))
(* -1 (/ (pow beta 2) (pow alpha 2)))
(* (pow beta 2) (- (* 1/2 (/ (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))) beta)) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (+ (* 1/2 (/ (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))) beta)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) (pow beta 2)))) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (+ (* 1/2 (/ (- (* 2 (/ 1 alpha)) (+ (* -1 (/ (+ (* 4 (/ i alpha)) (* 2 (/ 1 alpha))) alpha)) (* 4 (/ (+ 2 (* 4 i)) (pow alpha 2))))) beta)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) (pow beta 2)))) (/ 1 (pow alpha 2))))
(* -1 (/ (pow beta 2) (pow alpha 2)))
(* (pow beta 2) (- (* 1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) (* alpha beta))) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) beta))) beta)) (/ 1 (pow alpha 2))))
(* (pow beta 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (+ (* -4 (/ (+ 2 (* 4 i)) alpha)) (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (* 4 (/ i alpha))) (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow alpha 2))) (/ (pow (+ 2 (* 4 i)) 2) (pow alpha 2)))) beta))) beta)) (/ 1 (pow alpha 2))))
(* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha))
(+ (* 1/2 (* i (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))))) (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha)))
(+ (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha)) (* i (+ (* -6 (/ i (pow alpha 2))) (* 1/2 (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2)))))))))
(+ (* 1/2 (/ (- (+ 2 (+ (* 2 beta) (/ (pow beta 2) alpha))) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) alpha)) (* i (+ (* -6 (/ i (pow alpha 2))) (* 1/2 (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2)))))))))
(* -6 (/ (pow i 2) (pow alpha 2)))
(* (pow i 2) (- (* 1/2 (/ (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))) i)) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (+ (* 1/2 (/ (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))) i)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) (pow i 2)))) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (+ (* 1/2 (/ (- (* 4 (/ 1 alpha)) (+ (* -1 (/ (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))) alpha)) (* 8 (/ (+ 2 (* 2 beta)) (pow alpha 2))))) i)) (* 1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) (pow i 2)))) (* 6 (/ 1 (pow alpha 2)))))
(* -6 (/ (pow i 2) (pow alpha 2)))
(* (pow i 2) (- (* 1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) (* alpha i))) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) i))) i)) (* 6 (/ 1 (pow alpha 2)))))
(* (pow i 2) (- (* -1 (/ (+ (* -1/2 (/ (+ 4 (+ (* -8 (/ (+ 2 (* 2 beta)) alpha)) (+ (* 2 (/ beta alpha)) (* 2 (/ (+ 2 beta) alpha))))) alpha)) (* -1/2 (/ (- (+ (* 2 (/ 1 alpha)) (+ (* 2 (/ beta alpha)) (/ (pow beta 2) (pow alpha 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (pow alpha 2))) (/ (pow (+ 2 (* 2 beta)) 2) (pow alpha 2)))) i))) i)) (* 6 (/ 1 (pow alpha 2)))))
(* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) (pow alpha 2)))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))
(/ (+ (* 1/2 (* alpha (+ 2 (+ (* 2 beta) (* 4 i))))) (* 1/2 (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))))) (pow alpha 2))
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)
(/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)
(/ (+ (* 1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* 1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha)
(* 1/2 (/ (+ 2 (+ (* 2 beta) (* 4 i))) alpha))
(* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))
(* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))
(* -1 (/ (+ (* -1/2 (+ 2 (+ (* 2 beta) (* 4 i)))) (* -1/2 (/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha))) alpha))
(/ beta (+ 2 (+ beta (* 2 i))))
(+ (* alpha (- (/ 1 (+ 2 (+ beta (* 2 i)))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))
(+ (* alpha (- (+ (* alpha (- (/ beta (pow (+ 2 (+ beta (* 2 i))) 3)) (/ 1 (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ 1 (+ 2 (+ beta (* 2 i))))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))
(+ (* alpha (- (+ (* alpha (- (+ (* alpha (- (/ 1 (pow (+ 2 (+ beta (* 2 i))) 3)) (/ beta (pow (+ 2 (+ beta (* 2 i))) 4)))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 3))) (/ 1 (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ 1 (+ 2 (+ beta (* 2 i))))) (/ beta (pow (+ 2 (+ beta (* 2 i))) 2)))) (/ beta (+ 2 (+ beta (* 2 i)))))
1
(+ 1 (* -1 (/ (+ 2 (* 2 i)) alpha)))
(- (+ 1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ beta (* 2 i)))) (pow alpha 2))) (+ (* 2 (/ i alpha)) (* 2 (/ 1 alpha))))
(- (+ 1 (* -1 (/ (* (+ 2 (* 2 i)) (pow (+ 2 (+ beta (* 2 i))) 2)) (pow alpha 3)))) (+ (* -1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ beta (* 2 i)))) (pow alpha 2))) (+ (* 2 (/ i alpha)) (* 2 (/ 1 alpha)))))
1
(+ 1 (* -1 (/ (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))
(+ 1 (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (* (+ 2 (+ beta (* 2 i))) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))) alpha))) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))
(+ 1 (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 (+ beta (* 2 i))) 2) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))) alpha)) (* -1 (* (+ 2 (+ beta (* 2 i))) (- (* -1 beta) (* -1 (+ 2 (+ beta (* 2 i)))))))) alpha))) (* -1 (+ 2 (+ beta (* 2 i))))) alpha)))
(/ alpha (+ 2 (+ alpha (* 2 i))))
(+ (* beta (- (/ 1 (+ 2 (+ alpha (* 2 i)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))
(+ (* beta (- (+ (* beta (- (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))
(+ (* beta (- (+ (* beta (- (+ (* beta (- (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 3)) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 4)))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 3))) (/ 1 (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ 1 (+ 2 (+ alpha (* 2 i))))) (/ alpha (pow (+ 2 (+ alpha (* 2 i))) 2)))) (/ alpha (+ 2 (+ alpha (* 2 i)))))
1
(+ 1 (* -1 (/ (+ 2 (* 2 i)) beta)))
(- (+ 1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta))))
(- (+ 1 (* -1 (/ (* (+ 2 (* 2 i)) (pow (+ 2 (+ alpha (* 2 i))) 2)) (pow beta 3)))) (+ (* -1 (/ (* (+ 2 (* 2 i)) (+ 2 (+ alpha (* 2 i)))) (pow beta 2))) (+ (* 2 (/ i beta)) (* 2 (/ 1 beta)))))
1
(+ 1 (* -1 (/ (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))
(+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))
(+ 1 (* -1 (/ (- (+ (* -1 alpha) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 (+ alpha (* 2 i))) 2) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))) beta)) (* -1 (* (+ 2 (+ alpha (* 2 i))) (- (* -1 alpha) (* -1 (+ 2 (+ alpha (* 2 i)))))))) beta))) (* -1 (+ 2 (+ alpha (* 2 i))))) beta)))
(/ (+ alpha beta) (+ 2 (+ alpha beta)))
(+ (* -2 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 2))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))
(+ (* i (- (* 4 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 3))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))
(+ (* i (- (* i (- (* -8 (/ (* i (+ alpha beta)) (pow (+ 2 (+ alpha beta)) 4))) (* -4 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 3))))) (* 2 (/ (+ alpha beta) (pow (+ 2 (+ alpha beta)) 2))))) (+ (/ alpha (+ 2 (+ alpha beta))) (/ beta (+ 2 (+ alpha beta)))))
(* 1/2 (/ (+ alpha beta) i))
(/ (+ (* -1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)) (* 1/2 (+ alpha beta))) i)
(/ (- (+ (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/2 (+ alpha beta))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i)
(/ (- (+ (* -1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) (pow i 3))) (* 1/2 (+ alpha beta))) (+ (* -1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) (pow i 2))) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i)))) i)
(* 1/2 (/ (+ alpha beta) i))
(* -1 (/ (+ (* -1/2 (+ alpha beta)) (* 1/4 (/ (* (+ 2 (+ alpha beta)) (+ alpha beta)) i))) i))
(* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (* (pow (+ 2 (+ alpha beta)) 3) (+ alpha beta)) i)) (* 1/8 (* (pow (+ 2 (+ alpha beta)) 2) (+ alpha beta)))) i)) (* 1/4 (* (+ 2 (+ alpha beta)) (+ alpha beta)))) i)) (* -1/2 (+ alpha beta))) i))
beta
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
alpha
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
(* alpha (+ 1 (/ beta alpha)))
alpha
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ beta alpha)) 1)))
alpha
(+ alpha beta)
(+ alpha beta)
(+ alpha beta)
beta
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
(* beta (+ 1 (/ alpha beta)))
beta
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* -1 (* beta (- (* -1 (/ alpha beta)) 1)))
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(* 4 i)
(+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2))
(+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) (pow (+ 2 (* 4 i)) 2)))
(+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))
(+ (* -2 (* i (+ 2 (* 2 i)))) (+ (* beta (+ (* -1 (+ 2 (* 4 i))) (+ (* 3 beta) (* 4 (+ 2 (* 4 i)))))) (pow (+ 2 (* 4 i)) 2)))
(* 3 (pow beta 2))
(* (pow beta 2) (+ 3 (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (* 4 (/ (+ 2 (* 4 i)) beta)))))
(* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))
(* (pow beta 2) (+ 3 (+ (* -2 (/ (* i (+ 2 (* 2 i))) (pow beta 2))) (+ (* -1 (/ (+ 2 (* 4 i)) beta)) (+ (* 4 (/ (+ 2 (* 4 i)) beta)) (/ (pow (+ 2 (* 4 i)) 2) (pow beta 2)))))))
(* 3 (pow beta 2))
(* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) beta))))
(* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))
(* (pow beta 2) (+ 3 (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) beta)) (* 4 i)))) beta))))
(+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))
(+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) (pow (+ 2 (* 2 beta)) 2)))
(+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))
(+ (* -1 (* beta (+ 2 beta))) (+ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (+ (* 8 (+ 2 (* 2 beta))) (* 12 i)))) (pow (+ 2 (* 2 beta)) 2)))
(* 12 (pow i 2))
(* (pow i 2) (+ 12 (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (* 8 (/ (+ 2 (* 2 beta)) i)))))
(* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))
(* (pow i 2) (+ 12 (+ (* -1 (/ (* beta (+ 2 beta)) (pow i 2))) (+ (* -1 (/ (+ (* 2 beta) (* 2 (+ 2 beta))) i)) (+ (* 8 (/ (+ 2 (* 2 beta)) i)) (/ (pow (+ 2 (* 2 beta)) 2) (pow i 2)))))))
(* 12 (pow i 2))
(* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) i))))
(* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))
(* (pow i 2) (+ 12 (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* -1 (/ (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2)) i)) (+ (* 2 beta) (* 2 (+ 2 beta))))) i))))
(* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha))
(+ (* -1 (/ (* beta (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i))))) alpha)) (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)))
(+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))
(+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) alpha)) (* beta (+ (* -2 (/ beta alpha)) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) alpha)))))
(* -2 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta))) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (+ (* -1 (/ (+ (* -2 (* i (+ 2 (* 2 i)))) (pow (+ 2 (* 4 i)) 2)) (* alpha (pow beta 2)))) (* -1 (/ (+ (* -1 (+ 2 (* 4 i))) (* 4 (+ 2 (* 4 i)))) (* alpha beta)))) (* 2 (/ 1 alpha))))
(* -2 (/ (pow beta 2) alpha))
(* (pow beta 2) (- (+ (* -4 (/ (+ 2 (* 4 i)) (* alpha beta))) (+ (* 4 (/ i (* alpha beta))) (* 2 (/ 1 (* alpha beta))))) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))
(* (pow beta 2) (- (* -1 (/ (+ (* -2 (/ (* i (+ 2 (* 2 i))) (* alpha beta))) (+ (* -1 (/ (+ 2 (+ (* -4 (+ 2 (* 4 i))) (* 4 i))) alpha)) (/ (pow (+ 2 (* 4 i)) 2) (* alpha beta)))) beta)) (* 2 (/ 1 alpha))))
(/ (- (pow beta 2) (+ (* -1 (* beta (+ 2 beta))) (pow (+ 2 (* 2 beta)) 2))) alpha)
(- (+ (* -1 (/ (* i (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta))))) alpha)) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))
(- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))
(- (+ (* i (+ (* -12 (/ i alpha)) (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) alpha)))) (/ (pow beta 2) alpha)) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha)))
(* -12 (/ (pow i 2) alpha))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (* 12 (/ 1 alpha))))
(* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))
(* (pow i 2) (- (+ (* -1 (/ (+ (* -1 (+ (* 2 beta) (* 2 (+ 2 beta)))) (* 8 (+ 2 (* 2 beta)))) (* alpha i))) (/ (pow beta 2) (* alpha (pow i 2)))) (+ (* -1 (/ (* beta (+ 2 beta)) (* alpha (pow i 2)))) (+ (* 12 (/ 1 alpha)) (/ (pow (+ 2 (* 2 beta)) 2) (* alpha (pow i 2)))))))
(* -12 (/ (pow i 2) alpha))
(* (pow i 2) (- (+ (* -8 (/ (+ 2 (* 2 beta)) (* alpha i))) (+ (* 2 (/ beta (* alpha i))) (* 2 (/ (+ 2 beta) (* alpha i))))) (* 12 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))
(* (pow i 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -8 (+ 2 (* 2 beta))) (+ (* 2 beta) (* 2 (+ 2 beta)))) alpha)) (* -1 (/ (- (/ (pow beta 2) alpha) (+ (* -1 (/ (* beta (+ 2 beta)) alpha)) (/ (pow (+ 2 (* 2 beta)) 2) alpha))) i))) i)) (* 12 (/ 1 alpha))))
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)
(/ (- (pow beta 2) (+ (* -1 (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))) (pow (+ 2 (+ (* 2 beta) (* 4 i))) 2))) alpha)

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

eval258.0ms (2.1%)

Memory: 20.8MiB live, 474.2MiB allocated
Compiler: Compiled 68 992 to 4 976 computations (92.8% saved)

prune216.0ms (1.7%)

Memory

3.6MiB live, 373.3MiB allocated

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1 344	14	1 358
Fresh	0	4	4
Picked	4	1	5
Done	0	0	0
Total	1 348	19	1 367

Accuracy

99.9%

Counts

1 367 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.5%	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	26.0%	(fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha)))
	40.8%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 (+.f64 alpha beta) #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	77.0%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	62.7%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
	23.6%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	19.8%	(/.f64 (*.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha)
▶	19.3%	(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha)
	10.7%	(/.f64 (*.f64 #s(literal 2 binary64) i) alpha)
	8.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64)))) (-.f64 (.f64 beta beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64))))))))) (*.f64 alpha alpha))
	23.3%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (fma.f64 beta beta (.f64 beta (+.f64 #s(literal 2 binary64) beta))) (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)))) alpha))) alpha)
	23.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 beta beta) #s(literal -2 binary64)) alpha))) alpha)
	10.3%	(/.f64 beta alpha)
	64.8%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
	25.9%	(*.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) alpha))
	25.7%	(*.f64 beta (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 #s(literal 2 binary64) alpha)) beta) (/.f64 #s(literal 1 binary64) alpha)))
	33.8%	#s(literal 1 binary64)
✓	58.3%	#s(literal 1/2 binary64)
▶	3.4%	#s(literal 0 binary64)

Compiler

Compiled 738 to 426 computations (42.3% saved)

simplify368.0ms (3%)

Memory

-16.2MiB live, 636.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(*.f64 (-.f64 beta alpha) (+.f64 beta alpha))
✓	cost-diff	0	(/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i))
✓	cost-diff	0	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha)
✓	cost-diff	512	(*.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))

Rules

13 074×	`accelerator-lowering-fma.f32`
13 074×	`accelerator-lowering-fma.f64`
6 320×	`-lowering-.f32`
6 320×	`-lowering-.f64`
2 052×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	268
1	87	268
2	196	264
3	455	260
4	1261	260
5	4932	260
0	8506	235

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1) 2)
(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)
(/ (- beta alpha) (+ alpha (+ (* 2 i) beta)))
(- beta alpha)
beta
alpha
(+ alpha (+ (* 2 i) beta))
(+ (* 2 i) beta)
2
i
(/ beta (+ 2 (+ (* 2 i) beta)))
(+ 2 (+ (* 2 i) beta))
1
0
(/ (* (+ (* 2 beta) 2) 1/2) alpha)
(* (+ (* 2 beta) 2) 1/2)
(+ (* 2 beta) 2)
2
beta
1/2
alpha
(+ (* (/ (* (- beta alpha) (+ beta alpha)) (* i i)) 1/8) 1/2)
(/ (* (- beta alpha) (+ beta alpha)) (* i i))
(* (- beta alpha) (+ beta alpha))
(- beta alpha)
beta
alpha
(+ beta alpha)
(* i i)
i
1/8
1/2
(/ (+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ alpha (+ 2 (+ (* 2 i) alpha)))) 1) 2)
(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ alpha (+ 2 (+ (* 2 i) alpha)))) 1)
(/ (- beta alpha) (+ alpha (+ (* 2 i) beta)))
(- beta alpha)
beta
alpha
(+ alpha (+ (* 2 i) beta))
(+ (* 2 i) beta)
2
i
(/ alpha (+ 2 (+ (* 2 i) alpha)))
(+ 2 (+ (* 2 i) alpha))
(+ (* 2 i) alpha)
1

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

localize175.0ms (1.4%)

Memory

-10.1MiB live, 292.1MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))
✓	accuracy	100.0%	(/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	78.2%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 beta alpha)
✓	accuracy	100.0%	(*.f64 (-.f64 beta alpha) (+.f64 beta alpha))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	82.0%	(/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i))
✓	accuracy	100.0%	(fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha)
✓	accuracy	100.0%	(+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	93.9%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))

Samples

86.0ms	200×	0	valid
25.0ms	41×	1	valid
10.0ms	15×	2	valid

Compiler

Compiled 243 to 36 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

ival-add: 40.0ms (40.6% of total)

ival-div: 38.0ms (38.6% of total)

ival-mult: 14.0ms (14.2% of total)

adjust: 4.0ms (4.1% of total)

ival-sub: 2.0ms (2% of total)

exact: 1.0ms (1% of total)

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

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

series96.0ms (0.8%)

Memory

12.8MiB live, 221.7MiB allocated

Counts

18 → 492

Calls

Call 1

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

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

Calls

123 calls:

Time	Variable		Point	Expression
15.0ms	i	@	inf	(/ (+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ alpha (+ 2 (+ (* 2 i) alpha)))) 1) 2)
13.0ms	alpha	@	-inf	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ alpha (+ 2 (+ (* 2 i) alpha)))) 1)
7.0ms	alpha	@	-inf	(+ (* (/ (* (- beta alpha) (+ beta alpha)) (* i i)) 1/8) 1/2)
6.0ms	i	@	inf	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)
2.0ms	alpha	@	inf	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ alpha (+ 2 (+ (* 2 i) alpha)))) 1)

rewrite342.0ms (2.8%)

Memory

16.5MiB live, 762.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 546×	`/-lowering-/.f32`
5 546×	`/-lowering-/.f64`
3 666×	`-lowering-.f32`
3 666×	`-lowering-.f64`
2 756×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	200
1	250	200
2	2505	200
0	8143	179

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 816

Calls

Call 1

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

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

simplify446.0ms (3.6%)

Memory

-1.0MiB live, 800.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6 504×	`-lowering-.f32`
6 504×	`-lowering-.f64`
5 456×	`accelerator-lowering-fma.f32`
5 456×	`accelerator-lowering-fma.f64`
3 536×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1528	14493
1	5180	13868
0	8191	12668

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

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

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

eval345.0ms (2.8%)

Memory: -17.7MiB live, 349.2MiB allocated
Compiler: Compiled 58 817 to 5 099 computations (91.3% saved)

prune336.0ms (2.7%)

Memory

-3.1MiB live, 316.4MiB allocated

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	1 621	8	1 629
Fresh	2	11	13
Picked	4	1	5
Done	0	1	1
Total	1 627	21	1 648

Accuracy

100.0%

Counts

1 648 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.5%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 (+.f64 beta alpha) #s(literal 1/8 binary64)) i) #s(literal 1/2 binary64))
	38.8%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	26.0%	(fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha)))
▶	77.0%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	76.7%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	58.8%	(/.f64 (fma.f64 (neg.f64 (/.f64 alpha (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
	23.6%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	19.3%	(/.f64 (+.f64 #s(literal 1 binary64) beta) alpha)
	19.8%	(/.f64 (*.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha)
▶	10.7%	(/.f64 (*.f64 #s(literal 2 binary64) i) alpha)
	8.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64)))) (-.f64 (.f64 beta beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64))))))))) (*.f64 alpha alpha))
	23.3%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (fma.f64 beta beta (.f64 beta (+.f64 #s(literal 2 binary64) beta))) (.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)))) alpha))) alpha)
	23.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 beta beta) #s(literal -2 binary64)) alpha))) alpha)
	10.3%	(/.f64 beta alpha)
	13.1%	(/.f64 #s(literal 1 binary64) alpha)
▶	64.8%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
	19.3%	(*.f64 (fma.f64 beta #s(literal 2 binary64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) alpha))
	25.7%	(*.f64 beta (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 #s(literal 2 binary64) alpha)) beta) (/.f64 #s(literal 1 binary64) alpha)))
▶	33.8%	#s(literal 1 binary64)
✓	58.3%	#s(literal 1/2 binary64)
✓	3.4%	#s(literal 0 binary64)

Compiler

Compiled 748 to 432 computations (42.2% saved)

simplify370.0ms (3%)

Memory

4.5MiB live, 258.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) i beta)
✓	cost-diff	0	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))))
✓	cost-diff	128	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) i)
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 2 binary64) i) alpha)
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))
✓	cost-diff	256	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64))

Rules

9 936×	`accelerator-lowering-fma.f32`
9 936×	`accelerator-lowering-fma.f64`
3 172×	`-lowering-.f32`
3 172×	`-lowering-.f64`
2 280×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	232
1	75	232
2	130	232
3	217	232
4	503	232
5	1488	232
6	3014	232
7	4800	232
8	7611	232
0	8312	209

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize169.0ms (1.4%)

Memory

-13.9MiB live, 183.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (+.f64 beta alpha))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))
✓	accuracy	71.9%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
✓	accuracy	100.0%	(/.f64 (*.f64 #s(literal 2 binary64) i) alpha)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) i)
✓	accuracy	100.0%	(+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))
✓	accuracy	100.0%	(+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))
✓	accuracy	100.0%	(/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)))
✓	accuracy	94.0%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64))

Samples

52.0ms	180×	0	valid
22.0ms	29×	2	valid
19.0ms	21×	3	valid
11.0ms	26×	1	valid

Compiler

Compiled 212 to 32 computations (84.9% saved)

Precisions

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

ival-div: 19.0ms (32.3% of total)

ival-add: 18.0ms (30.6% of total)

adjust: 10.0ms (17% of total)

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

ival-sub: 2.0ms (3.4% of total)

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

exact: 0.0ms (0% of total)

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

series58.0ms (0.5%)

Memory

9.2MiB live, 45.7MiB allocated

Counts

19 → 504

Calls

Call 1

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

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

Calls

126 calls:

Time	Variable		Point	Expression
19.0ms	i	@	inf	(/ (+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1) 2)
1.0ms	i	@	0	(+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)
1.0ms	beta	@	-inf	(+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)
1.0ms	i	@	0	(/ (+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1) 2)
1.0ms	beta	@	inf	(+ (* (/ beta (+ (* 2 i) beta)) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)

rewrite474.0ms (3.8%)

Memory

-9.0MiB live, 553.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 094×	`/-lowering-/.f32`
6 094×	`/-lowering-/.f64`
3 784×	`-lowering-.f32`
3 784×	`-lowering-.f64`
3 080×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	199
1	258	199
2	2577	199
0	8775	178

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 839

Calls

Call 1

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

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

simplify551.0ms (4.5%)

Memory

-1.1MiB live, 555.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 370×	`-lowering-.f32`
6 370×	`-lowering-.f64`
5 178×	`accelerator-lowering-fma.f32`
5 178×	`accelerator-lowering-fma.f64`
3 518×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1606	12088
1	5269	11765
0	8097	10906

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 504

Calls

Call 1

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

eval427.0ms (3.5%)

Memory: 19.6MiB live, 482.2MiB allocated
Compiler: Compiled 49 738 to 5 028 computations (89.9% saved)

prune297.0ms (2.4%)

Memory

-12.3MiB live, 592.8MiB allocated

Pruning

25 alts after pruning (20 fresh and 5 done)

	Pruned	Kept	Total
New	1 438	8	1 446
Fresh	2	12	14
Picked	2	3	5
Done	0	2	2
Total	1 442	25	1 467

Accuracy

100.0%

Counts

1 467 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.8%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	40.5%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 (+.f64 beta alpha) #s(literal 1/8 binary64)) i) #s(literal 1/2 binary64))
	38.8%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	26.0%	(fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha)))
	68.9%	(fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 beta #s(literal 2 binary64))) #s(literal 1/2 binary64))
	49.8%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	62.2%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) beta) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
	44.0%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (*.f64 beta #s(literal 1/2 binary64)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	76.7%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	77.0%	(/.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i (+.f64 beta alpha))) (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 2 binary64))
	58.8%	(/.f64 (fma.f64 (neg.f64 (/.f64 alpha (fma.f64 #s(literal 2 binary64) i alpha))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
	16.3%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 beta #s(literal 2 binary64)) (+.f64 beta (+.f64 beta #s(literal 2 binary64)))) alpha) (.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))))) alpha)
	23.6%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	19.3%	(/.f64 (+.f64 #s(literal 1 binary64) beta) alpha)
	19.8%	(/.f64 (*.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha)
✓	10.7%	(/.f64 (*.f64 #s(literal 2 binary64) i) alpha)
	8.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64)))) (-.f64 (.f64 beta beta) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) beta (.f64 i #s(literal 4 binary64))))))))) (*.f64 alpha alpha))
	10.3%	(/.f64 beta alpha)
	13.1%	(/.f64 #s(literal 1 binary64) alpha)
	58.5%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (.f64 (neg.f64 alpha) (+.f64 (/.f64 (-.f64 #s(literal -2 binary64) beta) alpha) #s(literal -1 binary64))))))
	19.3%	(*.f64 (fma.f64 beta #s(literal 2 binary64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) alpha))
	25.7%	(*.f64 beta (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (/.f64 i alpha) (/.f64 #s(literal 2 binary64) alpha)) beta) (/.f64 #s(literal 1 binary64) alpha)))
✓	33.8%	#s(literal 1 binary64)
✓	58.3%	#s(literal 1/2 binary64)
✓	3.4%	#s(literal 0 binary64)

Compiler

Compiled 1 081 to 431 computations (60.1% saved)

regimes81.0ms (0.7%)

Memory

7.3MiB live, 213.1MiB allocated

Counts

40 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

12.0ms	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
12.0ms	(*.f64 #s(literal 2 binary64) i)
12.0ms	beta
11.0ms	alpha
11.0ms	i

Results

Accuracy	Segments	Branch
90.4%	2	`alpha`
78.2%	1	`beta`
78.2%	1	`i`
96.8%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
96.8%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
96.8%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`
78.2%	1	`(*.f64 #s(literal 2 binary64) i)`

Compiler

Compiled 108 to 55 computations (49.1% saved)

regimes27.0ms (0.2%)

Memory

-8.5MiB live, 72.0MiB allocated

Counts

34 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

9.0ms

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

9.0ms

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

8.0ms

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

Results

Accuracy	Segments	Branch
96.5%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
96.5%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
96.5%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes21.0ms (0.2%)

Memory

18.3MiB live, 57.8MiB allocated

Counts

26 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

Calls

3 calls:

7.0ms

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

7.0ms

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

6.0ms

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

Results

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

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes20.0ms (0.2%)

Memory

-17.3MiB live, 61.6MiB allocated

Counts

23 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

#s(literal 1 binary64)

Calls

3 calls:

7.0ms

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

6.0ms

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

5.0ms

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

Results

Accuracy	Segments	Branch
94.2%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
94.2%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
94.2%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes17.0ms (0.1%)

Memory

14.0MiB live, 55.5MiB allocated

Counts

19 → 3

Calls

Call 1

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

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

Calls

3 calls:

5.0ms

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

5.0ms

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

5.0ms

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

Results

Accuracy	Segments	Branch
94.2%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
94.2%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
94.2%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes15.0ms (0.1%)

Memory

9.4MiB live, 49.1MiB allocated

Counts

17 → 3

Calls

Call 1

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

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

Calls

3 calls:

5.0ms

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

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
94.1%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
94.1%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
94.1%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes21.0ms (0.2%)

Memory

-28.3MiB live, 49.4MiB allocated

Counts

15 → 3

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
77.5%	2	`alpha`
87.9%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
87.9%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
87.9%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 94 to 44 computations (53.2% saved)

regimes11.0ms (0.1%)

Memory

38.0MiB live, 38.0MiB allocated

Counts

12 → 3

Calls

Call 1

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

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

Calls

3 calls:

4.0ms

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

3.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
87.2%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
87.2%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
87.2%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes19.0ms (0.1%)

Memory

-29.1MiB live, 51.3MiB allocated

Counts

6 → 3

Calls

Call 1

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

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

Calls

6 calls:

4.0ms	(*.f64 #s(literal 2 binary64) i)
3.0ms	beta
3.0ms	i
2.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))
2.0ms	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
58.3%	1	`i`
58.3%	1	`(*.f64 #s(literal 2 binary64) i)`
70.6%	2	`beta`
80.9%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
80.9%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
80.9%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 104 to 52 computations (50% saved)

regimes7.0ms (0.1%)

Memory

19.9MiB live, 19.9MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
58.3%	1	`alpha`
74.4%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
74.4%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
74.4%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 94 to 44 computations (53.2% saved)

regimes11.0ms (0.1%)

Memory

-10.5MiB live, 28.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(literal 1/2 binary64)

Calls

6 calls:

3.0ms	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
2.0ms	(*.f64 #s(literal 2 binary64) i)
2.0ms	i
2.0ms	beta
1.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
58.3%	1	`i`
58.3%	1	`(*.f64 #s(literal 2 binary64) i)`
58.3%	1	`beta`
58.3%	1	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
58.3%	1	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
58.3%	1	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 104 to 52 computations (50% saved)

regimes11.0ms (0.1%)

Memory

-11.8MiB live, 27.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

7 calls:

3.0ms	beta
1.0ms	(*.f64 #s(literal 2 binary64) i)
1.0ms	alpha
1.0ms	i
1.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
3.4%	1	`alpha`
3.4%	1	`beta`
3.4%	1	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
3.4%	1	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
3.4%	1	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`
3.4%	1	`i`
3.4%	1	`(*.f64 #s(literal 2 binary64) i)`

Compiler

Compiled 108 to 55 computations (49.1% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.2241257282975696e-14	0.9999999999999999
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.2241257282975696e-14	0.9999999999999999
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.2241257282975696e-14	0.9999999999999999
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.2241257282975696e-14	0.9999999999999999
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.2241257282975696e-14	0.9999999999999999
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.2241257282975696e-14	0.9999999999999999
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.2241257282975696e-14	0.9999999999999999
0.0ms	-0.9999999988726775	-0.314806637225756

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch15.0ms (0.1%)

Memory

-9.1MiB live, 34.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	2.2241257282975696e-14	0.9999999999999999

Samples

9.0ms

160×

valid

Compiler

Compiled 135 to 122 computations (9.6% saved)

Precisions

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

ival-div: 1.0ms (43.6% of total)

ival-add: 1.0ms (43.6% of total)

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

exact: 0.0ms (0% of total)

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

simplify16.0ms (0.1%)

Memory

1.0MiB live, 39.8MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative_binary64`
16×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	645
1	93	645
2	97	645
3	99	645
4	100	645

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) beta) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) beta) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)

Outputs
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) beta) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) beta) (/.f64 beta (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 i alpha) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) beta #s(literal 2 binary64)) alpha))) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64))))) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (.f64 (fma.f64 beta #s(literal 2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) alpha)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64))) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) beta) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (+.f64 beta #s(literal 1 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/158456325028528675187087900672 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)

soundness1.1s (9.1%)

Memory

17.0MiB live, 1 616.7MiB allocated

Rules

6 504×	`-lowering-.f32`
6 504×	`-lowering-.f64`
6 370×	`-lowering-.f32`
6 370×	`-lowering-.f64`
6 196×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	304
1	297	304
2	3395	304
0	8641	260
0	1523	17704
1	5027	16230
0	8148	14651
0	33	200
1	250	200
2	2505	200
0	8143	179
0	1528	14493
1	5180	13868
0	8191	12668
0	933	12962
1	3169	11337
0	8840	10203
0	1606	12088
1	5269	11765
0	8097	10906
0	15	106
1	115	106
2	1187	106
0	8698	96

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 1 109 to 405 computations (63.5% saved)

preprocess68.0ms (0.6%)

Memory: 4.4MiB live, 160.0MiB allocated
Compiler: Compiled 1 360 to 174 computations (87.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze45.0ms (0.4%)

sample1.6s (12.6%)

preprocess871.0ms (7%)

explain314.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify407.0ms (3.3%)

localize80.0ms (0.6%)

series56.0ms (0.5%)

rewrite345.0ms (2.8%)

simplify498.0ms (4%)

eval110.0ms (0.9%)

prune84.0ms (0.7%)

simplify357.0ms (2.9%)

localize220.0ms (1.8%)

series88.0ms (0.7%)

rewrite424.0ms (3.4%)

simplify488.0ms (3.9%)

eval258.0ms (2.1%)

prune216.0ms (1.7%)

simplify368.0ms (3%)

localize175.0ms (1.4%)

series96.0ms (0.8%)

rewrite342.0ms (2.8%)

simplify446.0ms (3.6%)

eval345.0ms (2.8%)

prune336.0ms (2.7%)

simplify370.0ms (3%)

localize169.0ms (1.4%)

series58.0ms (0.5%)

rewrite474.0ms (3.8%)

simplify551.0ms (4.5%)

eval427.0ms (3.5%)

prune297.0ms (2.4%)

regimes81.0ms (0.7%)

regimes27.0ms (0.2%)

regimes21.0ms (0.2%)

regimes20.0ms (0.2%)

regimes17.0ms (0.1%)

regimes15.0ms (0.1%)

regimes21.0ms (0.2%)

regimes11.0ms (0.1%)

regimes19.0ms (0.1%)

regimes7.0ms (0.1%)

regimes11.0ms (0.1%)

regimes11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch15.0ms (0.1%)

simplify16.0ms (0.1%)

soundness1.1s (9.1%)

preprocess68.0ms (0.6%)

end0.0ms (0%)

Profiling