Metrics for Octave 3.8, jcobi/2

analyze92.0ms (0.7%)

Memory

16.0MiB live, 54.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 23 computations (43.9% saved)

sample2.1s (16.4%)

Memory

17.5MiB live, 2 793.8MiB allocated

Samples

865.0ms	6 632×	0	valid
436.0ms	1 160×	1	valid
223.0ms	441×	2	valid
7.0ms	23×	3	valid

Precisions

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

ival-add: 298.0ms (24.9% of total)

ival->: 257.0ms (21.4% of total)

ival-div: 248.0ms (20.7% of total)

ival-mult: 218.0ms (18.2% of total)

adjust: 83.0ms (6.9% of total)

ival-sub: 55.0ms (4.6% of total)

exact: 20.0ms (1.7% of total)

ival-and: 16.0ms (1.3% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

preprocess491.0ms (3.8%)

Memory

-29.3MiB live, 680.2MiB 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)

explain265.0ms (2.1%)

Memory

2.8MiB live, 481.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
90	-	2	(1.6109634971797865e-213 1.7678134526281226e-159 4.6477726415107837e-184)	`(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))`
58	-	0	-	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
0	-	0	-	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`
0	-	0	-	`beta`
0	-	0	-	`(+.f64 alpha beta)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`alpha`
0	-	0	-	`(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))`
0	-	0	-	`(+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`i`
0	-	0	-	`(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))`
0	-	0	-	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
0	-	0	-	`(-.f64 beta alpha)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) i)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))`	o/n	76	0
↳	`(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))`	overflow	76
`+.f64`	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`	cancellation	58	0

Confusion

	Predicted +	Predicted -
+	98	0
-	0	158

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	98	0	0
-	0	0	158

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	158
1	62
2	36

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms	396×	0	valid
30.0ms	20×	3	valid
12.0ms	62×	1	valid
11.0ms	34×	2	valid

Compiler

Compiled 334 to 64 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-div: 14.0ms (29.1% of total)

ival-add: 13.0ms (27% of total)

ival-mult: 13.0ms (27% of total)

adjust: 3.0ms (6.2% of total)

ival-sub: 3.0ms (6.2% of total)

exact: 1.0ms (2.1% 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

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.0%	(/.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

▶

63.0%

(/.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)

simplify388.0ms (3%)

Memory

19.6MiB live, 714.4MiB 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)

localize59.0ms (0.5%)

Memory

16.2MiB live, 131.7MiB 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	78.7%	(+.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	67.7%	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))

Samples

19.0ms	198×	0	valid
8.0ms	17×	2	valid
7.0ms	10×	3	valid
6.0ms	31×	1	valid

Compiler

Compiled 135 to 17 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-add: 7.0ms (29.2% of total)

ival-div: 6.0ms (25% of total)

ival-mult: 4.0ms (16.7% of total)

adjust: 3.0ms (12.5% of total)

ival-sub: 3.0ms (12.5% of total)

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

exact: 0.0ms (0% of total)

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

series57.0ms (0.4%)

Memory

-9.1MiB live, 106.6MiB 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)>
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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
6.0ms	beta	@	0	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1)
4.0ms	alpha	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))
3.0ms	alpha	@	inf	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
3.0ms	i	@	inf	(/ (/ (* (+ 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)

rewrite784.0ms (6.1%)

Memory

27.5MiB live, 658.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	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))

simplify594.0ms (4.6%)

Memory

-42.9MiB live, 702.9MiB 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)

eval88.0ms (0.7%)

Memory: 6.7MiB live, 213.1MiB allocated
Compiler: Compiled 31 480 to 2 396 computations (92.4% saved)

prune132.0ms (1%)

Memory

-11.6MiB live, 183.4MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	578	13	591
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	579	13	592

Accuracy

100.0%

Counts

592 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.8%	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	57.5%	(fma.f64 (/.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)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	23.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta) #s(literal 1 binary64))
▶	78.8%	(/.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))
	58.2%	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 alpha alpha) (fma.f64 i #s(literal -2 binary64) (neg.f64 alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	23.0%	(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha)) beta)) #s(literal 1 binary64)) #s(literal 2 binary64))
	3.5%	(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
	25.3%	(/.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)
	21.0%	(/.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)
▶	65.7%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
	25.3%	(*.f64 (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha) #s(literal -1/2 binary64))
	32.6%	#s(literal 1 binary64)
▶	59.7%	#s(literal 1/2 binary64)

Compiler

Compiled 492 to 302 computations (38.6% saved)

simplify321.0ms (2.5%)

Memory

23.9MiB live, 537.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha)) beta))
✓	cost-diff	0	(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha)) beta)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	192	(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha)) beta)) #s(literal 1 binary64))
✓	cost-diff	384	(-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(*.f64 (-.f64 beta alpha) (+.f64 beta alpha))
✓	cost-diff	0	(/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i))
✓	cost-diff	0	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 #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 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

9 212×	`accelerator-lowering-fma.f32`
9 212×	`accelerator-lowering-fma.f64`
3 382×	`+-lowering-+.f64`
3 382×	`+-lowering-+.f32`
3 242×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	323
1	109	299
2	290	299
3	801	299
4	2546	299
5	7611	299
0	8710	272

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize214.0ms (1.7%)

Memory

20.2MiB live, 398.8MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha)) beta))
✓	accuracy	100.0%	(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha)) beta)) #s(literal 1 binary64))
✓	accuracy	100.0%	(-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha))
✓	accuracy	100.0%	(/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i alpha)) (fma.f64 #s(literal 2 binary64) i alpha)) beta)
✓	accuracy	100.0%	(*.f64 (-.f64 beta alpha) (+.f64 beta alpha))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	99.7%	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
✓	accuracy	81.3%	(/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (+.f64 beta alpha))
✓	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 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))
✓	accuracy	70.4%	(+.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 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))
✓	accuracy	100.0%	(/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))
✓	accuracy	99.9%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	78.8%	(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

42.0ms	176×	0	valid
30.0ms	28×	1	valid
28.0ms	35×	2	valid
16.0ms	16×	3	valid
1.0ms	1×	4	valid

Compiler

Compiled 299 to 40 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-add: 25.0ms (34.5% of total)

ival-div: 19.0ms (26.2% of total)

ival-mult: 13.0ms (17.9% of total)

adjust: 8.0ms (11% of total)

ival-sub: 6.0ms (8.3% of total)

exact: 1.0ms (1.4% of total)

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

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

series80.0ms (0.6%)

Memory

-25.5MiB live, 185.4MiB allocated

Counts

19 → 564

Calls

Call 1

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

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

Calls

141 calls:

Time	Variable		Point	Expression
12.0ms	alpha	@	-inf	(/ (+ alpha beta) (+ alpha (+ beta (+ (* 2 i) 2))))
6.0ms	i	@	0	(/ (+ (+ 1 (/ (- (- -2 (+ (* 2 i) alpha)) (+ (* 2 i) alpha)) beta)) 1) 2)
4.0ms	i	@	inf	(/ (- beta alpha) (+ alpha (+ (* 2 i) beta)))
4.0ms	alpha	@	inf	(+ 1/2 (* 1/2 (/ (- beta alpha) (+ 2 (+ beta alpha)))))
3.0ms	alpha	@	-inf	(+ 1/2 (* 1/2 (/ (- beta alpha) (+ 2 (+ beta alpha)))))

rewrite440.0ms (3.4%)

Memory

-26.0MiB live, 667.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 032×	`/-lowering-/.f32`
5 032×	`/-lowering-/.f64`
3 736×	`-lowering-.f32`
3 736×	`-lowering-.f64`
3 310×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	249
1	336	225
2	3782	225
0	9008	209

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 609

Calls

Call 1

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

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

simplify477.0ms (3.7%)

Memory

38.6MiB live, 793.8MiB allocated

Algorithm

1×	egg-herbie

Rules

5 480×	`-lowering-.f32`
5 480×	`-lowering-.f64`
5 310×	`accelerator-lowering-fma.f32`
5 310×	`accelerator-lowering-fma.f64`
4 010×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1572	16605
1	5185	15034
0	8295	13863

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 564

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

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

eval273.0ms (2.1%)

Memory: -1.9MiB live, 374.6MiB allocated
Compiler: Compiled 43 707 to 4 311 computations (90.1% saved)

prune197.0ms (1.5%)

Memory

-9.6MiB live, 399.8MiB allocated

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	1 251	18	1 269
Fresh	4	4	8
Picked	4	1	5
Done	0	0	0
Total	1 259	23	1 282

Accuracy

100.0%

Counts

1 282 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.7%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
▶	43.2%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
	57.5%	(fma.f64 (/.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)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	23.7%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 (neg.f64 alpha) #s(literal -2 binary64)) alpha) beta) #s(literal 1 binary64))
	73.5%	(fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))
	42.9%	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
	49.5%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	43.5%	(/.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))
▶	78.0%	(/.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))
	63.3%	(/.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))
	17.7%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 2 binary64) beta) (/.f64 (+.f64 beta (+.f64 #s(literal 2 binary64) beta)) alpha)) (.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta)))) alpha)
	25.0%	(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta)) #s(literal 1 binary64)) #s(literal 2 binary64))
	25.3%	(/.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)
	21.0%	(/.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)
	3.3%	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
	25.3%	(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta))) alpha)
	19.4%	(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) beta)) alpha)
	2.8%	(/.f64 (*.f64 #s(literal -2 binary64) i) beta)
▶	26.9%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) beta)))
	3.5%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
	23.3%	(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) beta)))
▶	32.6%	#s(literal 1 binary64)
✓	59.7%	#s(literal 1/2 binary64)

Compiler

Compiled 734 to 462 computations (37.1% saved)

simplify334.0ms (2.6%)

Memory

14.0MiB live, 457.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) i)
✓	cost-diff	384	(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (+.f64 beta alpha))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))
✓	cost-diff	0	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) beta)
✓	cost-diff	128	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) beta))
✓	cost-diff	192	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) beta)))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))

Rules

9 836×	`accelerator-lowering-fma.f32`
9 836×	`accelerator-lowering-fma.f64`
4 306×	`-lowering-.f32`
4 306×	`-lowering-.f64`
1 656×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	203
1	83	203
2	170	203
3	370	201
4	1113	201
5	3520	201
6	6364	201
0	8087	186

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize143.0ms (1.1%)

Memory

3.8MiB live, 349.9MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) i)
✓	accuracy	100.0%	(/.f64 (+.f64 beta alpha) i)
✓	accuracy	99.8%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 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	71.1%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(-.f64 beta alpha)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) beta))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) beta)))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) beta)
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	99.9%	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	96.2%	(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

41.0ms	176×	0	valid
27.0ms	36×	2	valid
16.0ms	19×	3	valid
12.0ms	21×	1	valid
2.0ms	2×	5	exit
2.0ms	2×	4	valid

Compiler

Compiled 192 to 32 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-div: 20.0ms (31.8% of total)

ival-mult: 17.0ms (27% of total)

ival-add: 16.0ms (25.4% of total)

adjust: 6.0ms (9.5% of total)

ival-sub: 3.0ms (4.8% of total)

exact: 1.0ms (1.6% of total)

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

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

series57.0ms (0.4%)

Memory

7.7MiB live, 85.7MiB allocated

Counts

17 → 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 (+ 1/2 (* 1/2 (/ (- beta alpha) beta)))>
#<alt (* 1/2 (/ (- beta alpha) beta))>
#<alt (/ (- beta alpha) beta)>
#<alt (+ (* (/ (- beta alpha) (+ 2 (+ beta alpha))) 1/2) 1/2)>
#<alt (/ (- beta alpha) (+ 2 (+ beta alpha)))>
#<alt (+ 2 (+ beta alpha))>
#<alt (+ (* (/ (- beta alpha) i) (* (/ (+ beta alpha) i) 1/8)) 1/2)>
#<alt (/ (- beta alpha) i)>
#<alt (* (/ (+ beta alpha) i) 1/8)>
#<alt (/ beta (+ 2 (+ (* 2 i) beta)))>
#<alt (+ 2 (+ (* 2 i) beta))>
#<alt (+ beta alpha)>
#<alt (/ (+ beta alpha) i)>

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

Calls

123 calls:

Time	Variable		Point	Expression
14.0ms	i	@	inf	(* (/ (+ beta alpha) i) 1/8)
5.0ms	beta	@	-inf	(/ (- beta alpha) beta)
2.0ms	beta	@	0	(/ (+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1) 2)
1.0ms	beta	@	-inf	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)
1.0ms	i	@	0	(+ (* (/ (- beta alpha) (+ alpha (+ (* 2 i) beta))) (/ beta (+ 2 (+ (* 2 i) beta)))) 1)

rewrite372.0ms (2.9%)

Memory

-23.1MiB live, 784.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 744×	`-lowering-.f32`
5 744×	`-lowering-.f64`
5 180×	`/-lowering-/.f32`
5 180×	`/-lowering-/.f64`
3 302×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	161
1	234	161
2	2309	161
0	9412	149

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 443

Calls

Call 1

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

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

simplify410.0ms (3.2%)

Memory

5.4MiB live, 722.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 350×	`-lowering-.f32`
6 350×	`-lowering-.f64`
5 534×	`accelerator-lowering-fma.f32`
5 534×	`accelerator-lowering-fma.f64`
4 358×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1256	10117
1	4102	9659
0	8289	8982

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

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

eval240.0ms (1.9%)

Memory: 12.5MiB live, 283.8MiB allocated
Compiler: Compiled 30 185 to 3 123 computations (89.7% saved)

prune192.0ms (1.5%)

Memory

20.0MiB live, 230.0MiB allocated

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	1 107	8	1 115
Fresh	3	14	17
Picked	3	2	5
Done	0	1	1
Total	1 113	25	1 138

Accuracy

100.0%

Counts

1 138 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.7%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
▶	45.8%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
▶	26.9%	(fma.f64 (/.f64 (-.f64 beta alpha) beta) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	57.5%	(fma.f64 (/.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)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	73.5%	(fma.f64 (/.f64 beta (+.f64 beta #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	26.9%	(fma.f64 (/.f64 alpha beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
▶	65.7%	(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 alpha #s(literal 2 binary64)))) #s(literal 1/2 binary64))
	23.7%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 (neg.f64 alpha) #s(literal -2 binary64)) alpha) beta) #s(literal 1 binary64))
	42.9%	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
	49.5%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	43.5%	(/.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))
	63.3%	(/.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))
▶	77.5%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	16.9%	(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 beta #s(literal 2 binary64)) (+.f64 beta (+.f64 beta #s(literal 2 binary64)))) alpha))) alpha)
	25.0%	(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta)) #s(literal 1 binary64)) #s(literal 2 binary64))
	25.3%	(/.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)
	21.0%	(/.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)
	19.4%	(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64)))) alpha)
	3.3%	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
	25.3%	(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta))) alpha)
	2.8%	(/.f64 (*.f64 #s(literal -2 binary64) i) beta)
▶	3.5%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
	23.3%	(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) beta)))
✓	32.6%	#s(literal 1 binary64)
✓	59.7%	#s(literal 1/2 binary64)

Compiler

Compiled 749 to 474 computations (36.7% saved)

simplify378.0ms (2.9%)

Memory

-16.5MiB live, 375.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i)
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) i)
✓	cost-diff	384	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
✓	cost-diff	0	(+.f64 beta (+.f64 alpha #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 alpha #s(literal 2 binary64))))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 alpha #s(literal 2 binary64)))) #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(/.f64 (-.f64 beta alpha) beta)
✓	cost-diff	192	(fma.f64 (/.f64 (-.f64 beta alpha) beta) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	cost-diff	192	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) i beta)
✓	cost-diff	0	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))
✓	cost-diff	0	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	384	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))

Rules

10 512×	`accelerator-lowering-fma.f32`
10 512×	`accelerator-lowering-fma.f64`
3 894×	`-lowering-.f32`
3 894×	`-lowering-.f64`
1 692×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	164
1	73	164
2	142	162
3	294	162
4	686	162
5	1700	162
6	3335	162
7	5878	162
0	8077	149

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize215.0ms (1.7%)

Memory

-10.7MiB live, 207.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 beta alpha)
✓	accuracy	100.0%	(*.f64 #s(literal 1/8 binary64) alpha)
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) i)
✓	accuracy	99.1%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 beta (+.f64 alpha #s(literal 2 binary64)))
✓	accuracy	100.0%	(+.f64 alpha #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 alpha #s(literal 2 binary64))))
✓	accuracy	71.4%	(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 alpha #s(literal 2 binary64)))) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(-.f64 beta alpha)
✓	accuracy	100.0%	(fma.f64 (/.f64 (-.f64 beta alpha) beta) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 (-.f64 beta alpha) beta)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	100.0%	(fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	100.0%	(/.f64 beta (fma.f64 #s(literal 2 binary64) i beta))

Samples

74.0ms	176×	0	valid
20.0ms	38×	2	valid
11.0ms	22×	1	valid
11.0ms	16×	3	valid
4.0ms	4×	5	exit

Compiler

Compiled 155 to 33 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-add: 40.0ms (42.1% of total)

ival-mult: 28.0ms (29.5% of total)

ival-div: 19.0ms (20% of total)

adjust: 5.0ms (5.3% of total)

ival-sub: 2.0ms (2.1% of total)

exact: 1.0ms (1.1% of total)

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

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

series59.0ms (0.5%)

Memory

15.2MiB live, 54.0MiB allocated

Counts

18 → 408

Calls

Call 1

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

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

Calls

102 calls:

Time	Variable		Point	Expression
21.0ms	alpha	@	inf	(+ beta (+ alpha 2))
13.0ms	beta	@	0	(+ (* (/ (- beta alpha) i) (/ (* 1/8 alpha) i)) 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)

rewrite437.0ms (3.4%)

Memory

-12.4MiB live, 499.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 494×	`-lowering-.f32`
5 494×	`-lowering-.f64`
5 008×	`/-lowering-/.f32`
5 008×	`/-lowering-/.f64`
3 210×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	140
1	222	140
2	2110	140
0	9172	127

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 378

Calls

Call 1

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

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

simplify484.0ms (3.8%)

Memory

9.2MiB live, 574.0MiB allocated

Algorithm

1×	egg-herbie

Rules

8 706×	`accelerator-lowering-fma.f32`
8 706×	`accelerator-lowering-fma.f64`
7 596×	`-lowering-.f32`
7 596×	`-lowering-.f64`
4 822×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	952	5891
1	3026	5679
0	8649	5300

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

Calls

Call 1

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

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

eval224.0ms (1.7%)

Memory: 13.4MiB live, 287.6MiB allocated
Compiler: Compiled 21 113 to 2 382 computations (88.7% saved)

prune189.0ms (1.5%)

Memory

-25.0MiB live, 293.0MiB allocated

Pruning

26 alts after pruning (21 fresh and 5 done)

	Pruned	Kept	Total
New	909	7	916
Fresh	3	14	17
Picked	3	2	5
Done	0	3	3
Total	915	26	941

Accuracy

100.0%

Counts

941 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.3%	(fma.f64 (/.f64 (fma.f64 i #s(literal 4 binary64) #s(literal 2 binary64)) beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓	65.7%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	26.9%	(fma.f64 (/.f64 (-.f64 beta alpha) beta) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	57.5%	(fma.f64 (/.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)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	47.2%	(fma.f64 (/.f64 (neg.f64 alpha) i) (/.f64 (*.f64 #s(literal 1/8 binary64) alpha) i) #s(literal 1/2 binary64))
	73.5%	(fma.f64 (/.f64 beta (+.f64 beta #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	26.9%	(fma.f64 (/.f64 alpha beta) #s(literal -1/2 binary64) #s(literal 1 binary64))
	28.9%	(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64))
	4.6%	(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) alpha) #s(literal 1/2 binary64))
	42.9%	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
	49.5%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	17.7%	(/.f64 (fma.f64 (fma.f64 beta #s(literal -1/2 binary64) #s(literal -1 binary64)) (/.f64 (+.f64 beta (+.f64 beta #s(literal 2 binary64))) alpha) (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))))) alpha)
	43.5%	(/.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))
	63.3%	(/.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))
✓	77.5%	(/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64))
	25.0%	(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta)) #s(literal 1 binary64)) #s(literal 2 binary64))
	25.3%	(/.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)
	21.0%	(/.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)
	19.4%	(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64)))) alpha)
	3.3%	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
	25.3%	(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta))) alpha)
	2.8%	(/.f64 (*.f64 #s(literal -2 binary64) i) beta)
	26.9%	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) beta)) #s(literal 1/2 binary64))
✓	32.6%	#s(literal 1 binary64)
✓	59.7%	#s(literal 1/2 binary64)
	3.5%	#s(literal 0 binary64)

Compiler

Compiled 1 012 to 424 computations (58.1% saved)

regimes100.0ms (0.8%)

Memory

-2.8MiB live, 245.7MiB allocated

Counts

47 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

18.0ms	alpha
16.0ms	beta
15.0ms	(*.f64 #s(literal 2 binary64) i)
14.0ms	i
12.0ms	(/.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
90.0%	2	`alpha`
78.8%	1	`beta`
78.8%	1	`i`
98.8%	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))`
98.8%	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))`
98.8%	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)))`
78.8%	1	`(*.f64 #s(literal 2 binary64) i)`

Compiler

Compiled 108 to 55 computations (49.1% saved)

regimes34.0ms (0.3%)

Memory

17.8MiB live, 94.2MiB allocated

Counts

44 → 2

Calls

Call 1

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

Outputs

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

Calls

3 calls:

11.0ms

(/.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)))

11.0ms

(/.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))

10.0ms

(+.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
98.2%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
98.2%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
98.2%	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)

regimes52.0ms (0.4%)

Memory

-12.1MiB live, 143.3MiB allocated

Counts

42 → 2

Calls

Call 1

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

Outputs

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

(/.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:

21.0ms

(/.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))

18.0ms

(+.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))

12.0ms

(/.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
97.6%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
97.6%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
97.6%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes34.0ms (0.3%)

Memory

15.2MiB live, 95.2MiB allocated

Counts

39 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

3 calls:

13.0ms

(/.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)))

10.0ms

(/.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 (+.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
97.7%	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))`
97.7%	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))`
97.7%	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)

regimes29.0ms (0.2%)

Memory

0.6MiB live, 77.5MiB allocated

Counts

34 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

Calls

3 calls:

10.0ms

(/.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)))

10.0ms

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

8.0ms

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

Results

Accuracy	Segments	Branch
97.3%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
97.3%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
97.3%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes29.0ms (0.2%)

Memory

-10.2MiB live, 66.4MiB allocated

Counts

29 → 3

Calls

Call 1

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

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

Calls

3 calls:

12.0ms

(/.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)))

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))

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))

Results

Accuracy	Segments	Branch
97.3%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
97.3%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
97.3%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes28.0ms (0.2%)

Memory

-2.9MiB live, 76.3MiB allocated

Counts

25 → 3

Calls

Call 1

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

#s(literal 1/2 binary64)

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

Calls

4 calls:

8.0ms	alpha
6.0ms	(+.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 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))
6.0ms	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
80.6%	2	`alpha`
91.3%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
91.3%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
91.3%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 94 to 44 computations (53.2% saved)

regimes27.0ms (0.2%)

Memory

-5.7MiB live, 48.7MiB allocated

Counts

22 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

Calls

3 calls:

15.0ms

(/.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))

6.0ms

(/.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 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
91.3%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
91.3%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
91.3%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes18.0ms (0.1%)

Memory

2.4MiB live, 42.1MiB allocated

Counts

21 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

Calls

3 calls:

6.0ms

(+.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 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
90.8%	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))`
90.8%	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))`
90.8%	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

-6.0MiB live, 32.9MiB allocated

Counts

16 → 3

Calls

Call 1

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

Outputs

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

#s(literal 1/2 binary64)

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

4.0ms

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

4.0ms

(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.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
90.7%	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))`
90.7%	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))`
90.7%	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)

regimes33.0ms (0.3%)

Memory

-4.7MiB live, 75.9MiB allocated

Counts

14 → 2

Calls

Call 1

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

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

Calls

7 calls:

6.0ms	i
5.0ms	alpha
5.0ms	(*.f64 #s(literal 2 binary64) i)
4.0ms	beta
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)))

Results

Accuracy	Segments	Branch
73.5%	1	`i`
73.5%	1	`(*.f64 #s(literal 2 binary64) i)`
73.5%	1	`beta`
73.5%	1	`alpha`
76.6%	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))`
76.6%	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))`
76.6%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 108 to 55 computations (49.1% saved)

regimes10.0ms (0.1%)

Memory

-3.7MiB live, 35.6MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

3 calls:

3.0ms

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

3.0ms

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

2.0ms

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

Results

Accuracy	Segments	Branch
76.2%	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))`
76.2%	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))`
76.2%	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)

regimes7.0ms (0.1%)

Memory

29.3MiB live, 29.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

3 calls:

2.0ms

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

2.0ms

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

2.0ms

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

Results

Accuracy	Segments	Branch
76.1%	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))`
76.1%	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))`
76.1%	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)

regimes11.0ms (0.1%)

Memory

-4.6MiB live, 35.0MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(literal 1/2 binary64)

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
59.7%	1	`beta`
59.7%	1	`i`
59.7%	1	`(*.f64 #s(literal 2 binary64) i)`
59.7%	1	`alpha`
59.7%	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))`
59.7%	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))`
59.7%	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 108 to 55 computations (49.1% saved)

regimes9.0ms (0.1%)

Memory

-13.8MiB live, 25.8MiB 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:

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))
1.0ms	(*.f64 #s(literal 2 binary64) i)
1.0ms	beta
1.0ms	i
1.0ms	alpha

Results

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

Compiler

Compiled 108 to 55 computations (49.1% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999972248	-0.021030206393281122

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999972248	-0.021030206393281122

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999972248	-0.021030206393281122

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	8.08318681048693e-52	2.306316239625373e-50
0.0ms	-0.9999999999972248	-0.021030206393281122

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	8.08318681048693e-52	2.306316239625373e-50
0.0ms	-0.9999999999972248	-0.021030206393281122

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	8.08318681048693e-52	2.306316239625373e-50
0.0ms	-0.9999999999972248	-0.021030206393281122

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	8.08318681048693e-52	2.306316239625373e-50
0.0ms	-0.9999999999996984	-0.9999999999972248

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	8.08318681048693e-52	2.306316239625373e-50
0.0ms	-0.9999999999996984	-0.9999999999972248

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	7.933951839023949e-6	0.9789708394447268
0.0ms	-0.9999999999996984	-0.9999999999972248

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	8.08318681048693e-52	2.306316239625373e-50
0.0ms	-0.9999999999996984	-0.9999999999972248

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.08318681048693e-52	2.306316239625373e-50

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.933951839023949e-6	0.9789708394447268

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.933951839023949e-6	0.9789708394447268

Compiler

Compiled 35 to 22 computations (37.1% saved)

simplify18.0ms (0.1%)

Memory

-4.2MiB live, 36.6MiB allocated

Algorithm

1×	egg-herbie

Rules

44×	`+-commutative_binary64`
22×	`*-commutative_binary64`
20×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	871
1	125	871
2	140	871
3	148	871
4	152	871

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(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 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha) #s(literal -1/2 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)))
(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 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (/.f64 beta (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 beta (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha) #s(literal -1/2 binary64)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) (fma.f64 (/.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)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha) #s(literal -1/2 binary64)) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.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 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) 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 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
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(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 -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) 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 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) 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 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 alpha beta) #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 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)

Outputs
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(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha)) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (.f64 (/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (fma.f64 #s(literal 2 binary64) i beta)) alpha) #s(literal -1/2 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)))
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(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 -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) beta)) 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 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 alpha #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) 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 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 beta alpha)) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) beta)) 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 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) 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 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -4503599627361489/4503599627370496 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 #s(literal -2 binary64) beta) beta)) 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 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 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))))
(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 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 binary64)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)))) #s(literal 1684996666696915/1684996666696914987166688442938726917102321526408785780068975640576 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)))
(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 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 alpha beta) #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 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 alpha beta) #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 5902958103587057/590295810358705651712 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 5902958103587057/590295810358705651712 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)

soundness1.5s (11.6%)

Memory

-3.0MiB live, 1 311.6MiB allocated

Rules

8 706×	`accelerator-lowering-fma.f32`
8 706×	`accelerator-lowering-fma.f64`
7 596×	`-lowering-.f32`
7 596×	`-lowering-.f64`
6 350×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	106
1	115	106
2	1187	106
0	8698	96
0	38	249
1	336	225
2	3782	225
0	9008	209
0	952	5891
1	3026	5679
0	8649	5300
0	1572	16605
1	5185	15034
0	8295	13863
0	1256	10117
1	4102	9659
0	8289	8982
0	933	12962
1	3169	11337
0	8840	10203
0	32	140
1	222	140
2	2110	140
0	9172	127
0	30	161
1	234	161
2	2309	161
0	9412	149

Stop Event

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

Compiler

Compiled 1 489 to 529 computations (64.5% saved)

preprocess155.0ms (1.2%)

Memory: 9.1MiB live, 165.6MiB allocated
Compiler: Compiled 1 812 to 212 computations (88.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze92.0ms (0.7%)

sample2.1s (16.4%)

preprocess491.0ms (3.8%)

explain265.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify388.0ms (3%)

localize59.0ms (0.5%)

series57.0ms (0.4%)

rewrite784.0ms (6.1%)

simplify594.0ms (4.6%)

eval88.0ms (0.7%)

prune132.0ms (1%)

simplify321.0ms (2.5%)

localize214.0ms (1.7%)

series80.0ms (0.6%)

rewrite440.0ms (3.4%)

simplify477.0ms (3.7%)

eval273.0ms (2.1%)

prune197.0ms (1.5%)

simplify334.0ms (2.6%)

localize143.0ms (1.1%)

series57.0ms (0.4%)

rewrite372.0ms (2.9%)

simplify410.0ms (3.2%)

eval240.0ms (1.9%)

prune192.0ms (1.5%)

simplify378.0ms (2.9%)

localize215.0ms (1.7%)

series59.0ms (0.5%)

rewrite437.0ms (3.4%)

simplify484.0ms (3.8%)

eval224.0ms (1.7%)

prune189.0ms (1.5%)

regimes100.0ms (0.8%)

regimes34.0ms (0.3%)

regimes52.0ms (0.4%)

regimes34.0ms (0.3%)

regimes29.0ms (0.2%)

regimes29.0ms (0.2%)

regimes28.0ms (0.2%)

regimes27.0ms (0.2%)

regimes18.0ms (0.1%)

regimes15.0ms (0.1%)

regimes33.0ms (0.3%)

regimes10.0ms (0.1%)

regimes7.0ms (0.1%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

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%)

simplify18.0ms (0.1%)

soundness1.5s (11.6%)

preprocess155.0ms (1.2%)

end0.0ms (0%)

Profiling