Metrics for Octave 3.8, jcobi/2

analyze44.0ms (0.3%)

Memory

6.7MiB live, 84.6MiB 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)

sample2.4s (18.1%)

Memory

8.7MiB live, 2 262.5MiB allocated

Samples

897.0ms	6 556×	0	valid
655.0ms	1 245×	1	valid
251.0ms	437×	2	valid
9.0ms	18×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-div: 409.0ms (29.1% of total)

ival-add: 363.0ms (25.9% of total)

adjust: 238.0ms (17% of total)

ival-mult: 209.0ms (14.9% of total)

ival->: 99.0ms (7.1% of total)

ival-sub: 48.0ms (3.4% of total)

exact: 18.0ms (1.3% of total)

ival-and: 16.0ms (1.1% of total)

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

Bogosity

preprocess434.0ms (3.3%)

Memory

37.9MiB live, 796.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

explain214.0ms (1.6%)

Memory

-7.1MiB live, 594.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
90	-	1	(-1.6244416638513172e-155 2.416514343637401e-190 2.5743084679193863e-49)	`(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))`
59	-	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	81	0
↳	`(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))`	overflow	81
`+.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	59	0

Confusion

	Predicted +	Predicted -
+	104	0
-	0	152

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	104	0	0
-	0	0	152

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	152
1	68
2	36

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

41.0ms	400×	0	valid
13.0ms	46×	2	valid
13.0ms	54×	1	valid
5.0ms	12×	3	valid

Compiler

Compiled 334 to 64 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-div: 14.0ms (30.5% of total)

ival-add: 12.0ms (26.1% of total)

ival-mult: 10.0ms (21.8% of total)

adjust: 5.0ms (10.9% of total)

ival-sub: 3.0ms (6.5% of total)

exact: 1.0ms (2.2% of total)

ival-true: 1.0ms (2.2% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.1%	(/.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))

Status

Accuracy

Program

▶

61.1%

(/.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))

Compiler

Compiled 32 to 15 computations (53.1% saved)

simplify440.0ms (3.3%)

Memory

16.9MiB live, 782.9MiB 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 (0.4%)

Memory

3.1MiB live, 120.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (+.f64 alpha beta) (*.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	79.3%	(+.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))
✓	accuracy	67.3%	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))

Samples

18.0ms	200×	0	valid
9.0ms	23×	2	valid
5.0ms	27×	1	valid
2.0ms	6×	3	valid

Compiler

Compiled 135 to 17 computations (87.4% saved)

Precisions

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

ival-div: 6.0ms (28.9% of total)

ival-add: 6.0ms (28.9% of total)

ival-mult: 4.0ms (19.3% of total)

adjust: 3.0ms (14.5% of total)

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

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

exact: 0.0ms (0% of total)

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

series51.0ms (0.4%)

Memory

21.8MiB live, 97.4MiB allocated

Counts

5 → 180

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)))>

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

Calls

45 calls:

Time	Variable		Point	Expression
5.0ms	i	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))
3.0ms	i	@	0	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
3.0ms	alpha	@	inf	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
2.0ms	i	@	inf	(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2)) 1) 2)
2.0ms	alpha	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))

rewrite411.0ms (3.1%)

Memory

-29.7MiB live, 564.4MiB 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	103
1	115	103
2	1187	103
0	8698	93

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 303

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)))

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

simplify407.0ms (3.1%)

Memory

-3.2MiB live, 693.9MiB 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	12926
1	3169	11301
0	8840	10167

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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))

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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(* 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))

eval130.0ms (1%)

Memory: 3.2MiB live, 200.1MiB allocated
Compiler: Compiled 30 668 to 2 386 computations (92.2% saved)

prune87.0ms (0.7%)

Memory

25.7MiB live, 227.0MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	550	13	563
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	551	13	564

Accuracy

99.9%

Counts

564 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.3%	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
	63.2%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	22.5%	(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))
▶	79.3%	(/.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))
▶	61.1%	(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64))
	22.4%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	3.5%	(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
	24.8%	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
	21.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
▶	64.7%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
	68.1%	(.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
	32.4%	#s(literal 1 binary64)
▶	60.9%	#s(literal 1/2 binary64)

Compiler

Compiled 592 to 332 computations (43.9% saved)

simplify394.0ms (3%)

Memory

-17.2MiB live, 504.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
✓	cost-diff	0	(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	cost-diff	384	(/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1 binary64) (+.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	704	(fma.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(*.f64 (-.f64 beta alpha) (+.f64 beta alpha))
✓	cost-diff	0	(/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i))
✓	cost-diff	0	(fma.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 i i)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(-.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	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))
✓	cost-diff	384	(/.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))

Rules

11 356×	`accelerator-lowering-fma.f32`
11 356×	`accelerator-lowering-fma.f64`
3 800×	`-lowering-.f32`
3 800×	`-lowering-.f64`
2 084×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	353
1	101	353
2	238	353
3	634	353
4	2049	353
5	4184	353
0	8106	325

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

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

localize442.0ms (3.4%)

Memory

-7.0MiB live, 344.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))
✓	accuracy	79.1%	(fma.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64))
✓	accuracy	67.3%	(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	100.0%	(+.f64 beta alpha)
✓	accuracy	100.0%	(*.f64 (-.f64 beta alpha) (+.f64 beta alpha))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	79.5%	(/.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	70.7%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
✓	accuracy	100.0%	(+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))
✓	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	79.3%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64))

Samples

235.0ms	34×	2	valid
71.0ms	12×	3	valid
52.0ms	177×	0	valid
20.0ms	33×	1	valid

Compiler

Compiled 332 to 38 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 346.0ms

ival-add: 225.0ms (65.1% of total)

ival-sub: 62.0ms (17.9% of total)

ival-mult: 25.0ms (7.2% of total)

ival-div: 24.0ms (6.9% of total)

adjust: 9.0ms (2.6% of total)

exact: 1.0ms (0.3% of total)

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

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

series68.0ms (0.5%)

Memory

-33.1MiB live, 117.7MiB allocated

Counts

20 → 600

Calls

Call 1

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

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

Calls

150 calls:

Time	Variable		Point	Expression
11.0ms	beta	@	0	(/ (+ alpha beta) (+ alpha (+ beta (+ (* 2 i) 2))))
5.0ms	alpha	@	inf	(+ 1/2 (* 1/2 (/ (- beta alpha) (+ 2 (+ beta alpha)))))
4.0ms	beta	@	0	(+ 1/2 (* 1/2 (/ (- beta alpha) (+ 2 (+ beta alpha)))))
1.0ms	i	@	0	(+ (* (/ (* (- beta alpha) (+ beta alpha)) (* i i)) 1/8) 1/2)
1.0ms	alpha	@	-inf	(+ 1/2 (* 1/2 (/ (- beta alpha) (+ 2 (+ beta alpha)))))

rewrite481.0ms (3.7%)

Memory

30.1MiB live, 653.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 432×	`/-lowering-/.f32`
5 432×	`/-lowering-/.f64`
3 100×	`-lowering-.f32`
3 100×	`-lowering-.f64`
2 604×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	256
1	299	256
2	3284	256
0	8909	237

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 913

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -2 binary64)))
(-.f64 (/.f64 (/.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64))) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) (.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64)))))
(neg.f64 (/.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #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 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #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 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64))))))
(/.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64))) #s(literal -2 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (+.f64 beta alpha) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (.f64 (-.f64 beta alpha) (.f64 (-.f64 beta alpha) (-.f64 beta alpha)))) (.f64 (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))))))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i 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 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (+.f64 beta alpha) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (.f64 (-.f64 beta alpha) (.f64 (-.f64 beta alpha) (-.f64 beta alpha)))) (.f64 (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)))))))) (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))))))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) #s(literal -1 binary64))) (neg.f64 (.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (+.f64 beta alpha) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (.f64 (-.f64 beta alpha) (.f64 (-.f64 beta alpha) (-.f64 beta alpha)))) (.f64 (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))))))) #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))))))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (+.f64 beta alpha) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (.f64 (-.f64 beta alpha) (.f64 (-.f64 beta alpha) (-.f64 beta alpha)))) (.f64 (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (.f64 (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha))))))) #s(literal 1/2 binary64))) (neg.f64 (+.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (.f64 (+.f64 (/.f64 (.f64 (.f64 (-.f64 beta alpha) (+.f64 beta alpha)) (.f64 (-.f64 beta alpha) (+.f64 beta alpha))) (.f64 (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64))))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal -1 binary64))))
(pow.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (*.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 beta alpha) (/.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) (+.f64 (+.f64 beta (fma.f64 #s(literal 2 binary64) i alpha)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
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simplify585.0ms (4.5%)

Memory

1.8MiB live, 948.6MiB allocated

Algorithm

1×	egg-herbie

Rules

5 682×	`accelerator-lowering-fma.f32`
5 682×	`accelerator-lowering-fma.f64`
5 522×	`-lowering-.f32`
5 522×	`-lowering-.f64`
4 254×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1834	24852
1	6005	23944
0	8239	21767

Stop Event

1×	iter limit
1×	node limit

Counts

600 → 600

Calls

Call 1

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

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

eval307.0ms (2.3%)

Memory: 33.2MiB live, 659.0MiB allocated
Compiler: Compiled 75 227 to 5 846 computations (92.2% saved)

prune296.0ms (2.3%)

Memory

-19.4MiB live, 627.1MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	1 798	13	1 811
Fresh	2	6	8
Picked	4	1	5
Done	0	0	0
Total	1 804	20	1 824

Accuracy

99.9%

Counts

1 824 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.7%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	44.3%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
	63.2%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	64.8%	(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
▶	22.5%	(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))
▶	72.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))
	43.2%	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
	50.2%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	44.5%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
	64.3%	(/.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))
	63.7%	(/.f64 (fma.f64 (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64))
▶	17.6%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta)))) alpha)
	22.4%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	24.8%	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
	21.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
	19.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
▶	3.4%	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
	3.5%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
▶	32.4%	#s(literal 1 binary64)
✓	60.9%	#s(literal 1/2 binary64)

Compiler

Compiled 754 to 444 computations (41.1% saved)

simplify463.0ms (3.5%)

Memory

32.0MiB live, 590.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (*.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
✓	cost-diff	0	(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta)))) alpha)
✓	cost-diff	512	(*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta)))
✓	cost-diff	576	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))))
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta)
✓	cost-diff	128	(-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64))))
✓	cost-diff	384	(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))
✓	cost-diff	0	(*.f64 i i)
✓	cost-diff	0	(*.f64 beta beta)
✓	cost-diff	0	(.f64 #s(literal 1/8 binary64) (.f64 beta beta))
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) beta)
✓	cost-diff	0	(/.f64 beta (+.f64 #s(literal 2 binary64) beta))
✓	cost-diff	0	(fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))

Rules

14 304×	`accelerator-lowering-fma.f32`
14 304×	`accelerator-lowering-fma.f64`
3 694×	`-lowering-.f32`
3 694×	`-lowering-.f64`
2 458×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	181
1	83	181
2	212	177
3	585	164
4	1430	157
5	3588	153
6	7395	153
0	8471	143

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize93.0ms (0.7%)

Memory

3.8MiB live, 239.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta)))
✓	accuracy	100.0%	(+.f64 beta (+.f64 #s(literal 2 binary64) beta))
✓	accuracy	98.8%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta)))) alpha)
✓	accuracy	97.7%	(/.f64 (*.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
✓	accuracy	100.0%	(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))
✓	accuracy	100.0%	(-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64))))
✓	accuracy	100.0%	(*.f64 i #s(literal 4 binary64))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta)
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	100.0%	(.f64 #s(literal 1/8 binary64) (.f64 beta beta))
✓	accuracy	77.2%	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) beta)
✓	accuracy	100.0%	(/.f64 beta (+.f64 #s(literal 2 binary64) beta))

Samples

55.0ms

256×

valid

Compiler

Compiled 175 to 34 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 14.0ms (39.4% of total)

ival-add: 10.0ms (28.1% of total)

ival-div: 9.0ms (25.3% of total)

ival-sub: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

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

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

series33.0ms (0.3%)

Memory

-5.1MiB live, 70.4MiB allocated

Counts

18 → 336

Calls

Call 1

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

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

Calls

84 calls:

Time	Variable		Expression
6.0ms	beta	@	(/ (* 1/8 (* beta beta)) (* i i))
2.0ms	beta	@	(+ (* 1/2 (/ beta (+ 2 beta))) 1/2)
1.0ms	i	@	(/ (* 1/8 (* beta beta)) (* i i))
1.0ms	alpha	@	(+ (* -1/2 (/ (* (+ 2 beta) (+ beta (+ 2 beta))) alpha)) (* 1/2 (+ beta (+ 2 beta))))
1.0ms	i	@	(+ (* 1/2 (/ (- -2 (+ (* 2 alpha) (* i 4))) beta)) 1)

rewrite444.0ms (3.4%)

Memory

-7.0MiB live, 718.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 480×	`/-lowering-/.f32`
4 480×	`/-lowering-/.f64`
4 248×	`-lowering-.f32`
4 248×	`-lowering-.f64`
4 058×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	158
1	200	158
2	1769	156
0	8402	148

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 703

Calls

Call 1

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

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

simplify493.0ms (3.8%)

Memory

-6.7MiB live, 796.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 964×	`accelerator-lowering-fma.f32`
11 964×	`accelerator-lowering-fma.f64`
4 850×	`-lowering-.f32`
4 850×	`-lowering-.f64`
4 152×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	360	3596
1	1102	3344
2	2955	3205
0	8654	2960

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

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

eval321.0ms (2.4%)

Memory: 16.7MiB live, 356.8MiB allocated
Compiler: Compiled 38 091 to 3 674 computations (90.4% saved)

prune257.0ms (2%)

Memory

4.6MiB live, 298.0MiB allocated

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	1 182	7	1 189
Fresh	1	13	14
Picked	4	1	5
Done	0	1	1
Total	1 187	22	1 209

Accuracy

100.0%

Counts

1 209 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.7%	(fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	44.3%	(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
▶	63.2%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
▶	64.8%	(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
▶	24.8%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
	51.6%	(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
▶	43.2%	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
	50.2%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	44.5%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
	64.3%	(/.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))
	63.7%	(/.f64 (fma.f64 (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64))
	9.9%	(/.f64 (fma.f64 (+.f64 beta #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) beta) (fma.f64 beta alpha alpha)) (*.f64 alpha alpha))
	22.4%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	19.8%	(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
	15.1%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) alpha)) alpha)
	24.8%	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
	21.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
	18.6%	(/.f64 #s(literal 1 binary64) (/.f64 alpha (fma.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 beta #s(literal 2 binary64))) (/.f64 (+.f64 beta (+.f64 beta #s(literal 2 binary64))) alpha)))))
▶	3.5%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
	3.8%	(.f64 (.f64 beta #s(literal 1/8 binary64)) (/.f64 beta (*.f64 i i)))
✓	32.4%	#s(literal 1 binary64)
✓	60.9%	#s(literal 1/2 binary64)

Compiler

Compiled 784 to 464 computations (40.8% saved)

simplify424.0ms (3.2%)

Memory

-13.5MiB live, 547.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))
✓	cost-diff	0	(*.f64 beta beta)
✓	cost-diff	0	(/.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))))
✓	cost-diff	0	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 i i)
✓	cost-diff	0	(*.f64 alpha alpha)
✓	cost-diff	0	(/.f64 (.f64 alpha alpha) (.f64 i i))
✓	cost-diff	0	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 i #s(literal -4 binary64))
✓	cost-diff	0	(/.f64 (*.f64 i #s(literal -4 binary64)) beta)
✓	cost-diff	320	(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
✓	cost-diff	192	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))
✓	cost-diff	0	(-.f64 beta alpha)
✓	cost-diff	0	(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64))

Rules

11 672×	`accelerator-lowering-fma.f32`
11 672×	`accelerator-lowering-fma.f64`
2 926×	`-lowering-.f32`
2 926×	`-lowering-.f64`
2 552×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	166
1	90	164
2	236	164
3	534	164
4	1073	164
5	2129	164
6	3022	164
7	4446	164
8	7722	164
0	8277	152

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize227.0ms (1.7%)

Memory

11.6MiB live, 209.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 beta beta)
✓	accuracy	100.0%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))
✓	accuracy	74.6%	(/.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))))
✓	accuracy	100.0%	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 i i)
✓	accuracy	100.0%	(*.f64 alpha alpha)
✓	accuracy	74.3%	(/.f64 (.f64 alpha alpha) (.f64 i i))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 (*.f64 i #s(literal -4 binary64)) beta)
✓	accuracy	100.0%	(*.f64 i #s(literal -4 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (+.f64 beta alpha))
✓	accuracy	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))
✓	accuracy	70.4%	(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))

Samples

67.0ms	32×	1	valid
48.0ms	177×	0	valid
15.0ms	29×	2	valid
13.0ms	18×	3	valid

Compiler

Compiled 162 to 36 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-add: 26.0ms (30.6% of total)

ival-sub: 23.0ms (27% of total)

ival-mult: 19.0ms (22.3% of total)

ival-div: 8.0ms (9.4% of total)

adjust: 7.0ms (8.2% of total)

exact: 1.0ms (1.2% of total)

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

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

series33.0ms (0.3%)

Memory

5.3MiB live, 82.1MiB allocated

Counts

17 → 336

Calls

Call 1

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

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

Calls

84 calls:

Time	Variable		Point	Expression
4.0ms	beta	@	-inf	(/ 1 (+ 2 (+ beta alpha)))
3.0ms	i	@	0	(+ (* (/ (* beta beta) (* (+ (* 2 i) beta) (+ 2 (+ (* 2 i) beta)))) 1/2) 1/2)
2.0ms	beta	@	-inf	(+ (* (- beta alpha) (* (/ 1 (+ 2 (+ beta alpha))) 1/2)) 1/2)
1.0ms	beta	@	-inf	(+ (* (/ (* beta beta) (* (+ (* 2 i) beta) (+ 2 (+ (* 2 i) beta)))) 1/2) 1/2)
1.0ms	beta	@	0	(+ (* (/ (* beta beta) (* (+ (* 2 i) beta) (+ 2 (+ (* 2 i) beta)))) 1/2) 1/2)

rewrite417.0ms (3.2%)

Memory

11.2MiB live, 681.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 588×	`/-lowering-/.f32`
4 588×	`/-lowering-/.f64`
4 256×	`-lowering-.f32`
4 256×	`-lowering-.f64`
4 150×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	131
1	215	125
2	1818	125
0	8664	116

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 585

Calls

Call 1

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

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

simplify459.0ms (3.5%)

Memory

-46.8MiB live, 732.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 748×	`accelerator-lowering-fma.f32`
8 748×	`accelerator-lowering-fma.f64`
7 298×	`-lowering-.f32`
7 298×	`-lowering-.f64`
4 992×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	809	5290
1	2649	5146
0	8336	4831

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

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

eval229.0ms (1.7%)

Memory: -0.4MiB live, 242.1MiB allocated
Compiler: Compiled 28 295 to 2 887 computations (89.8% saved)

prune186.0ms (1.4%)

Memory

-4.5MiB live, 313.2MiB allocated

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	912	9	921
Fresh	3	12	15
Picked	3	2	5
Done	0	2	2
Total	918	25	943

Accuracy

100.0%

Counts

943 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.7%	(fma.f64 (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1/2 binary64))
✓	63.2%	(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
	50.2%	(fma.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) i) (/.f64 alpha i) #s(literal 1/2 binary64))
	64.8%	(fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 beta alpha) #s(literal 1/2 binary64))
	44.2%	(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) alpha)) #s(literal 1/2 binary64))
	4.3%	(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) alpha) #s(literal 1/2 binary64))
	51.6%	(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
✓	43.2%	(fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))
	50.2%	(fma.f64 #s(literal -1/2 binary64) (/.f64 alpha (+.f64 alpha #s(literal 2 binary64))) #s(literal 1/2 binary64))
	24.8%	(fma.f64 #s(literal -2 binary64) (/.f64 i beta) #s(literal 1 binary64))
	44.5%	(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) i) #s(literal 1 binary64)) #s(literal 2 binary64))
	64.3%	(/.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))
	9.9%	(/.f64 (fma.f64 (+.f64 beta #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) beta) (fma.f64 beta alpha alpha)) (*.f64 alpha alpha))
	22.4%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 beta beta) alpha)) (-.f64 (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) alpha) (.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 (fma.f64 #s(literal 2 binary64) i beta) alpha))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))))) alpha) #s(literal 2 binary64))
	44.2%	(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 beta alpha) #s(literal -1/2 binary64))) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 beta alpha) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 beta alpha) #s(literal -1/2 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 beta alpha) #s(literal -1/2 binary64))))
	43.4%	(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (-.f64 beta alpha) #s(literal 1/2 binary64)) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))))
	19.8%	(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
	15.1%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) alpha)) alpha)
	24.8%	(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha)
	21.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (/.f64 (-.f64 (.f64 beta beta) (fma.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) i beta))))) alpha))) alpha)
	18.6%	(/.f64 #s(literal 1 binary64) (/.f64 alpha (fma.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 beta #s(literal 2 binary64))) (/.f64 (+.f64 beta (+.f64 beta #s(literal 2 binary64))) alpha)))))
	3.8%	(.f64 (.f64 beta #s(literal 1/8 binary64)) (/.f64 beta (*.f64 i i)))
✓	32.4%	#s(literal 1 binary64)
✓	60.9%	#s(literal 1/2 binary64)
	3.5%	#s(literal 0 binary64)

Compiler

Compiled 1 221 to 444 computations (63.6% saved)

regimes123.0ms (0.9%)

Memory

16.1MiB live, 184.1MiB allocated

Counts

43 → 2

Calls

Call 1

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

(/.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:

39.0ms	(/.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)))
20.0ms	alpha
16.0ms	i
12.0ms	(*.f64 #s(literal 2 binary64) i)
12.0ms	beta

Results

Accuracy	Segments	Branch
89.7%	2	`alpha`
79.3%	1	`beta`
79.3%	1	`i`
96.4%	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
96.4%	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
96.4%	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`
79.3%	1	`(*.f64 #s(literal 2 binary64) i)`

Compiler

Compiled 108 to 55 computations (49.1% saved)

regimes43.0ms (0.3%)

Memory

5.4MiB live, 44.6MiB allocated

Counts

36 → 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))
(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
(fma.f64 #s(literal -2 binary64) (/.f64 i beta) #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))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) alpha)) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) alpha)) alpha)
(.f64 (.f64 beta #s(literal 1/8 binary64)) (/.f64 beta (*.f64 i i)))
(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 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))
(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))
(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) i) (/.f64 alpha i) #s(literal 1/2 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 (fma.f64 (+.f64 beta #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) beta) (fma.f64 beta alpha alpha)) (*.f64 alpha alpha))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) #s(literal 1/2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) beta) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha) (.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta)))) alpha)
(.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) 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 beta) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 #s(literal 1 binary64) (+.f64 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 alpha (fma.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 beta #s(literal 2 binary64))) (/.f64 (+.f64 beta (+.f64 beta #s(literal 2 binary64))) alpha)))))

Outputs

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

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

#s(literal 1 binary64)

Calls

3 calls:

24.0ms

(/.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))

8.0ms

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

Results

Accuracy	Segments	Branch
95.1%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
95.1%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
95.1%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes46.0ms (0.3%)

Memory

-28.7MiB live, 49.5MiB allocated

Counts

31 → 3

Calls

Call 1

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

Outputs

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

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

#s(literal 1 binary64)

Calls

3 calls:

27.0ms

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

7.0ms

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

7.0ms

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

Results

Accuracy	Segments	Branch
94.9%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
94.9%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
94.9%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes25.0ms (0.2%)

Memory

5.0MiB live, 45.8MiB 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))
(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
(fma.f64 #s(literal -2 binary64) (/.f64 i beta) #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))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) alpha)) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) alpha)) alpha)
(.f64 (.f64 beta #s(literal 1/8 binary64)) (/.f64 beta (*.f64 i i)))
(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 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))
(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))
(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) i) (/.f64 alpha i) #s(literal 1/2 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 (fma.f64 (+.f64 beta #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) beta) (fma.f64 beta alpha alpha)) (*.f64 alpha alpha))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))

Outputs

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

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

#s(literal 1 binary64)

Calls

3 calls:

9.0ms

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

7.0ms

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

7.0ms

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

Results

Accuracy	Segments	Branch
94.9%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
94.9%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
94.9%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes35.0ms (0.3%)

Memory

4.2MiB live, 43.3MiB allocated

Counts

28 → 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))
(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
(fma.f64 #s(literal -2 binary64) (/.f64 i beta) #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))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) alpha)) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) alpha)) alpha)
(.f64 (.f64 beta #s(literal 1/8 binary64)) (/.f64 beta (*.f64 i i)))
(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 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))
(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))
(fma.f64 (-.f64 beta alpha) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) alpha) i) (/.f64 alpha i) #s(literal 1/2 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 (fma.f64 (+.f64 beta #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) beta) (fma.f64 beta alpha alpha)) (*.f64 alpha alpha))
(fma.f64 (/.f64 (-.f64 beta alpha) i) (*.f64 (/.f64 (+.f64 beta alpha) i) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))

Outputs

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

#s(literal 1/2 binary64)

(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:

19.0ms

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

7.0ms

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

Results

Accuracy	Segments	Branch
94.6%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
94.6%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
94.6%	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)

regimes60.0ms (0.5%)

Memory

15.2MiB live, 54.0MiB 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))
(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
(fma.f64 #s(literal -2 binary64) (/.f64 i beta) #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))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) alpha)) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) alpha)) alpha)
(.f64 (.f64 beta #s(literal 1/8 binary64)) (/.f64 beta (*.f64 i i)))
(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 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))
(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 beta #s(literal 1 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

4 calls:

41.0ms	(/.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	alpha
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
79.1%	2	`alpha`
89.1%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
89.1%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
89.1%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 94 to 44 computations (53.2% saved)

regimes29.0ms (0.2%)

Memory

-1.7MiB live, 35.8MiB allocated

Counts

18 → 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))
(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
(fma.f64 #s(literal -2 binary64) (/.f64 i beta) #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))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 #s(literal 2 binary64) beta))) alpha)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))
(fma.f64 (-.f64 beta alpha) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) alpha)) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) alpha)) alpha)
(.f64 (.f64 beta #s(literal 1/8 binary64)) (/.f64 beta (*.f64 i i)))
(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 beta alpha) #s(literal 1/2 binary64))

Outputs

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

#s(literal 1/2 binary64)

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

Calls

3 calls:

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))

5.0ms

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

5.0ms

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

Results

Accuracy	Segments	Branch
89.1%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
89.1%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
89.1%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes32.0ms (0.2%)

Memory

-1.5MiB live, 42.1MiB allocated

Counts

17 → 3

Calls

Call 1

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

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

21.0ms

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

5.0ms

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

5.0ms

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

Results

Accuracy	Segments	Branch
89.1%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
89.1%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
89.1%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes27.0ms (0.2%)

Memory

-16.8MiB live, 22.9MiB allocated

Counts

9 → 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))
(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
(fma.f64 #s(literal -2 binary64) (/.f64 i beta) #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
(/.f64 (+.f64 beta #s(literal 1 binary64)) alpha)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

Calls

3 calls:

20.0ms

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

3.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
89.1%	3	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
89.1%	3	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
89.1%	3	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes19.0ms (0.1%)

Memory

33.7MiB live, 73.4MiB 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))
(fma.f64 #s(literal 1/4 binary64) beta #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))

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

Calls

7 calls:

3.0ms	beta
3.0ms	(*.f64 #s(literal 2 binary64) i)
3.0ms	i
3.0ms	alpha
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)))

Results

Accuracy	Segments	Branch
60.9%	1	`alpha`
60.9%	1	`i`
60.9%	1	`(*.f64 #s(literal 2 binary64) i)`
73.7%	2	`beta`
76.3%	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))`
76.3%	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))`
76.3%	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)

regimes7.0ms (0.1%)

Memory

-21.5MiB live, 18.0MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(literal 1/2 binary64)

Calls

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

Results

Accuracy	Segments	Branch
60.9%	1	`beta`
60.9%	1	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))`
60.9%	1	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64))`
60.9%	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 94 to 44 computations (53.2% saved)

regimes10.0ms (0.1%)

Memory

-10.1MiB live, 29.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

7 calls:

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

Results

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

Compiler

Compiled 108 to 55 computations (49.1% saved)

bsearch1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999971671104	-3.762319991502022e-12

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.9999919421390685	1.0
0.0ms	-0.9999999972100088	-0.9999999971671104

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.9999919421390685	1.0
0.0ms	-0.9999999971671104	-3.762319991502022e-12

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	0.9999919421390685	1.0
0.0ms	-0.9999999971671104	-3.762319991502022e-12

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	3.5064600869064354e-25	7.353749111917624e-23
0.0ms	-0.9999999971671104	-3.762319991502022e-12

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	3.5064600869064354e-25	7.353749111917624e-23
0.0ms	-0.9999999971671104	-3.762319991502022e-12

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	3.5064600869064354e-25	7.353749111917624e-23
0.0ms	-0.9999999971671104	-3.762319991502022e-12

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	3.5064600869064354e-25	7.353749111917624e-23
0.0ms	-0.9999999971671104	-3.762319991502022e-12

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.9586616440886006e-14	0.9999919421390685
0.0ms	-0.9999999971671104	-3.762319991502022e-12

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.9586616440886006e-14	0.9999919421390685

Compiler

Compiled 35 to 22 computations (37.1% saved)

simplify16.0ms (0.1%)

Memory

-1.5MiB live, 36.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	729
1	101	729
2	105	729
3	107	729
4	108	729

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -4503599614760417/4503599627370496 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 9007126675982015/9007199254740992 binary64)) (.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta)) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64)))))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 9007126675982015/9007199254740992 binary64)) (fma.f64 (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i 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 -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 9007126675982015/9007199254740992 binary64)) (fma.f64 (/.f64 (.f64 beta beta) (.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 5444517870735015/10889035741470030830827987437816582766592 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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#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 (+.f64 beta #s(literal 1 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 6338253001141147/316912650057057350374175801344 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 6338253001141147/316912650057057350374175801344 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 6338253001141147/316912650057057350374175801344 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)

soundness1.2s (9%)

Memory

16.5MiB live, 1 214.5MiB allocated

Rules

11 964×	`accelerator-lowering-fma.f32`
11 964×	`accelerator-lowering-fma.f64`
6 196×	`-lowering-.f32`
6 196×	`-lowering-.f64`
6 142×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	360	3596
1	1102	3344
2	2955	3205
0	8654	2960
0	15	103
1	115	103
2	1187	103
0	8698	93
0	36	256
1	299	256
2	3284	256
0	8909	237
0	933	12926
1	3169	11301
0	8840	10167
0	35	131
1	215	125
2	1818	125
0	8664	116
0	1834	24852
1	6005	23944
0	8239	21767

Stop Event

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

Compiler

Compiled 1 195 to 415 computations (65.3% saved)

preprocess170.0ms (1.3%)

Memory: -28.6MiB live, 169.2MiB allocated
Compiler: Compiled 1 528 to 186 computations (87.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze44.0ms (0.3%)

sample2.4s (18.1%)

preprocess434.0ms (3.3%)

explain214.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify440.0ms (3.3%)

localize59.0ms (0.4%)

series51.0ms (0.4%)

rewrite411.0ms (3.1%)

simplify407.0ms (3.1%)

eval130.0ms (1%)

prune87.0ms (0.7%)

simplify394.0ms (3%)

localize442.0ms (3.4%)

series68.0ms (0.5%)

rewrite481.0ms (3.7%)

simplify585.0ms (4.5%)

eval307.0ms (2.3%)

prune296.0ms (2.3%)

simplify463.0ms (3.5%)

localize93.0ms (0.7%)

series33.0ms (0.3%)

rewrite444.0ms (3.4%)

simplify493.0ms (3.8%)

eval321.0ms (2.4%)

prune257.0ms (2%)

simplify424.0ms (3.2%)

localize227.0ms (1.7%)

series33.0ms (0.3%)

rewrite417.0ms (3.2%)

simplify459.0ms (3.5%)

eval229.0ms (1.7%)

prune186.0ms (1.4%)

regimes123.0ms (0.9%)

regimes43.0ms (0.3%)

regimes46.0ms (0.3%)

regimes25.0ms (0.2%)

regimes35.0ms (0.3%)

regimes60.0ms (0.5%)

regimes29.0ms (0.2%)

regimes32.0ms (0.2%)

regimes27.0ms (0.2%)

regimes19.0ms (0.1%)

regimes7.0ms (0.1%)

regimes10.0ms (0.1%)

bsearch1.0ms (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%)

simplify16.0ms (0.1%)

soundness1.2s (9%)

preprocess170.0ms (1.3%)

end0.0ms (0%)

Profiling