Metrics for Octave 3.8, jcobi/2

analyze47.0ms (0.4%)

Memory

-27.2MiB live, 92.3MiB 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)

sample2.3s (17%)

Memory

-81.6MiB live, 2 509.5MiB allocated

Samples

794.0ms	6 556×	0	valid
245.0ms	1 245×	1	valid
149.0ms	437×	2	valid
16.0ms	18×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 933.0ms

ival-add: 259.0ms (27.8% of total)

ival-div: 257.0ms (27.5% of total)

ival-mult: 177.0ms (19% of total)

ival-sub: 75.0ms (8% of total)

adjust: 69.0ms (7.4% of total)

ival->: 59.0ms (6.3% of total)

exact: 19.0ms (2% of total)

ival-and: 16.0ms (1.7% of total)

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

Bogosity

preprocess448.0ms (3.3%)

Memory

-23.0MiB live, 829.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 848×	`lower-fma.f64`
16 848×	`lower-fma.f32`
3 846×	`lower-+.f32`
3 838×	`lower-+.f64`
3 552×	`lower-*.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
0	25	29
1	43	29
2	118	29
3	486	29
4	2368	29
5	3813	29
6	5109	29
0	8083	26

Stop Event

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

Calls

Call 1

Inputs

(/.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))

Outputs

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

explain284.0ms (2.1%)

Memory

27.2MiB live, 449.5MiB 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

42.0ms	400×	0	valid
16.0ms	46×	2	valid
11.0ms	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: 44.0ms

ival-add: 14.0ms (31.7% of total)

ival-div: 13.0ms (29.5% of total)

ival-mult: 8.0ms (18.1% of total)

adjust: 5.0ms (11.3% of total)

ival-sub: 3.0ms (6.8% of total)

exact: 1.0ms (2.3% of total)

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

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

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB 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)

simplify398.0ms (2.9%)

Memory

-28.2MiB live, 650.0MiB 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

16 848×	`lower-fma.f64`
16 848×	`lower-fma.f32`
3 846×	`lower-+.f32`
3 838×	`lower-+.f64`
3 552×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	133
0	25	133
1	43	133
2	118	133
3	486	133
4	2368	133
5	3813	133
6	5109	133
0	8083	122

Stop Event

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

Calls

Call 1

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

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

localize83.0ms (0.6%)

Memory

27.4MiB live, 105.3MiB 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

50.0ms	200×	0	valid
7.0ms	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: 51.0ms

ival-add: 36.0ms (71.2% of total)

ival-div: 6.0ms (11.9% of total)

ival-mult: 4.0ms (7.9% of total)

adjust: 3.0ms (5.9% of total)

ival-sub: 2.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series81.0ms (0.6%)

Memory

-24.9MiB live, 82.2MiB allocated

Counts

5 → 180

Calls

Call 1

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

Calls

45 calls:

Time	Variable		Point	Expression
34.0ms	beta	@	inf	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))
4.0ms	i	@	inf	(/ (+ (/ (/ (* (+ 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	alpha	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))
2.0ms	beta	@	0	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2))

rewrite632.0ms (4.7%)

Memory

-12.6MiB live, 493.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 612×	`lower-/.f32`
5 606×	`lower-/.f64`
5 576×	`lower-*.f32`
5 572×	`lower-*.f64`
3 560×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	103
0	25	103
1	125	103
2	1197	103
0	8707	93

Stop Event

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

Counts

5 → 303

Calls

Call 1

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

simplify591.0ms (4.4%)

Memory

31.4MiB live, 510.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6 196×	`lower-*.f64`
6 196×	`lower-*.f32`
6 142×	`lower-fma.f64`
6 142×	`lower-fma.f32`
5 244×	`lower-+.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 → 174

Calls

Call 1

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

eval192.0ms (1.4%)

Memory: -2.6MiB live, 178.5MiB allocated
Compiler: Compiled 30 454 to 2 369 computations (92.2% saved)

prune197.0ms (1.5%)

Memory

1.9MiB live, 205.2MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	540	13	553
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	541	13	554

Accuracy

99.9%

Counts

554 → 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))
▶	79.0%	(/.f64 (fma.f64 (/.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 alpha (fma.f64 #s(literal 2 binary64) i beta)))) #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)

simplify560.0ms (4.1%)

Memory

-21.2MiB live, 544.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

13 258×	`lower-fma.f32`
13 248×	`lower-fma.f64`
3 730×	`lower-*.f32`
3 722×	`lower-*.f64`
3 088×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	333
0	59	329
1	126	329
2	278	329
3	779	329
4	2594	329
5	6367	329
0	8113	328

Stop Event

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

Calls

Call 1

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

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

localize173.0ms (1.3%)

Memory

42.9MiB live, 433.4MiB allocated

Localize:

Found 16 expressions of interest:

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

44.0ms	177×	0	valid
29.0ms	34×	2	valid
18.0ms	33×	1	valid
14.0ms	12×	3	valid

Compiler

Compiled 363 to 37 computations (89.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-add: 19.0ms (28.4% of total)

ival-div: 17.0ms (25.4% of total)

ival-mult: 16.0ms (23.9% of total)

adjust: 10.0ms (14.9% of total)

ival-sub: 2.0ms (3% of total)

exact: 1.0ms (1.5% of total)

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

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

series75.0ms (0.6%)

Memory

-8.9MiB live, 162.1MiB allocated

Counts

20 → 612

Calls

Call 1

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

153 calls:

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

rewrite372.0ms (2.8%)

Memory

-9.2MiB live, 778.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 390×	`lower-/.f32`
5 378×	`lower-/.f64`
3 038×	`lower-*.f32`
3 030×	`lower-*.f64`
2 564×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	243
0	59	239
1	314	239
2	3197	239
0	8735	238

Stop Event

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

Counts

20 → 926

Calls

Call 1

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

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

simplify641.0ms (4.7%)

Memory

34.5MiB live, 974.6MiB allocated

Algorithm

1×	egg-herbie

Rules

5 590×	`lower-*.f64`
5 590×	`lower-*.f32`
5 458×	`lower-fma.f64`
5 458×	`lower-fma.f32`
4 398×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1854	24945
1	6076	24249
0	8041	22220

Stop Event

1×	iter limit
1×	node limit

Counts

612 → 589

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))))))))
(+ (* 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 (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))))
(+ (* 1/2 (* 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)))))) (* 1/2 (+ 1 (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))))
(+ (* 1/2 (+ 1 (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))) (* alpha (+ (* -1/2 (* alpha (+ (/ 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))))))) (* 1/2 (- (+ (* -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))))))))
(+ (* 1/2 (+ 1 (/ (pow beta 2) (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i)))))) (* alpha (+ (* 1/2 (- (+ (* -1 (/ beta (* (+ 2 (+ beta (* 2 i))) (+ beta (* 2 i))))) (/ 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))))) (* alpha (+ (* -1/2 (+ (/ 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)))))) (* 1/2 (* 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 (* -1 beta)) (* -1 (+ 2 (+ (* 2 beta) (* 4 i))))) alpha))
(/ (+ (* 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 (/ (+ (* (+ 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 (/ (+ (* -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 (/ 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)))))
(+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
(+ 1 (+ (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* beta (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* beta (- (+ (* beta (- (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 3) (pow (+ alpha (* 2 i)) 3)))) (+ (* -1 (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (+ (/ alpha (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))) (/ 1 (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (+ (* -1 (/ (pow alpha 2) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ (* -1 (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2)))))) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))))))) (/ alpha (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))) (* -1 (/ (* (pow alpha 2) (+ 2 (+ (* 2 alpha) (* 4 i)))) (* (pow (+ 2 (+ alpha (* 2 i))) 2) (pow (+ alpha (* 2 i)) 2))))))))
2
(- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (* 2 (/ 1 beta)))))
(- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))
(- (+ 2 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (+ (* (+ 2 (+ alpha (* 2 i))) (* (+ alpha (* 2 i)) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i)))))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (* -1 (pow alpha 2)) (+ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))))))) (pow beta 3))) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta))))) (+ (* 2 (/ alpha beta)) (+ (* 4 (/ i beta)) (+ (* 2 (/ 1 beta)) (+ (/ (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i))) (pow beta 2)) (/ (* (+ 2 (+ (* 2 alpha) (* 4 i))) (- (+ alpha (* -1 alpha)) (+ 2 (+ (* 2 alpha) (* 4 i))))) (pow beta 2)))))))
2
(- (+ 2 (+ (* -1 (/ alpha beta)) (/ alpha beta))) (* -1 (/ (+ (* -1 (+ 2 (+ alpha (* 2 i)))) (* -1 (+ alpha (* 2 i)))) beta)))
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(- (* 1/2 (/ (- beta (* -1 (+ 2 beta))) alpha)) 1/2)
(- (+ (* -1/2 (/ (* (+ 2 beta) (- beta (* -1 (+ 2 beta)))) (pow alpha 2))) (* 1/2 (/ (- beta (* -1 (+ 2 beta))) alpha))) 1/2)
(- (+ (* -1/2 (/ (* (+ 2 beta) (- beta (* -1 (+ 2 beta)))) (pow alpha 2))) (+ (* 1/2 (/ (* (pow (+ 2 beta) 2) (- beta (* -1 (+ 2 beta)))) (pow alpha 3))) (* 1/2 (/ (- beta (* -1 (+ 2 beta))) alpha)))) 1/2)
-1/2
(- (* -1/2 (/ (- (* -1 beta) (+ 2 beta)) alpha)) 1/2)
(- (* -1 (/ (+ (* -1/2 (/ (* (+ 2 beta) (- (* -1 beta) (+ 2 beta))) alpha)) (* 1/2 (- (* -1 beta) (+ 2 beta)))) alpha)) 1/2)
(- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow (+ 2 beta) 2) (- (* -1 beta) (+ 2 beta))) alpha)) (* 1/2 (* (+ 2 beta) (- (* -1 beta) (+ 2 beta))))) alpha)) (* 1/2 (- (* -1 beta) (+ 2 beta)))) alpha)) 1/2)
(* -1 (/ alpha (+ 2 alpha)))
(+ (* -1 (/ alpha (+ 2 alpha))) (* beta (- (/ 1 (+ 2 alpha)) (* -1 (/ alpha (pow (+ 2 alpha) 2))))))
(+ (* -1 (/ alpha (+ 2 alpha))) (* beta (- (+ (* beta (- (* -1 (/ alpha (pow (+ 2 alpha) 3))) (/ 1 (pow (+ 2 alpha) 2)))) (/ 1 (+ 2 alpha))) (* -1 (/ alpha (pow (+ 2 alpha) 2))))))
(+ (* -1 (/ alpha (+ 2 alpha))) (* beta (- (+ (* beta (- (+ (* -1 (/ alpha (pow (+ 2 alpha) 3))) (* beta (- (/ 1 (pow (+ 2 alpha) 3)) (* -1 (/ alpha (pow (+ 2 alpha) 4)))))) (/ 1 (pow (+ 2 alpha) 2)))) (/ 1 (+ 2 alpha))) (* -1 (/ alpha (pow (+ 2 alpha) 2))))))
1
(- (+ 1 (* -1 (/ alpha beta))) (+ (* 2 (/ 1 beta)) (/ alpha beta)))
(- (+ 1 (+ (* -1 (/ alpha beta)) (* -1 (/ (* (+ 2 alpha) (- (* -1 alpha) (+ 2 alpha))) (pow beta 2))))) (+ (* 2 (/ 1 beta)) (/ alpha beta)))
(- (+ 1 (+ (* -1 (/ alpha beta)) (/ (* (pow (+ 2 alpha) 2) (- (* -1 alpha) (+ 2 alpha))) (pow beta 3)))) (+ (* 2 (/ 1 beta)) (+ (/ alpha beta) (/ (* (+ 2 alpha) (- (* -1 alpha) (+ 2 alpha))) (pow beta 2)))))
1
(- (+ 1 (* -1 (/ alpha beta))) (+ (* 2 (/ 1 beta)) (/ alpha beta)))
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 alpha) (+ 2 alpha))) (/ (* (+ 2 alpha) (- (* -1 alpha) (+ 2 alpha))) beta)) beta)))
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 alpha) (+ 2 alpha))) (* -1 (/ (+ (* -1 (* (+ 2 alpha) (- (* -1 alpha) (+ 2 alpha)))) (/ (* (pow (+ 2 alpha) 2) (- (* -1 alpha) (+ 2 alpha))) beta)) beta))) beta)))
(/ beta (+ 2 beta))
(+ (* -1 (* alpha (+ (/ 1 (+ 2 beta)) (/ beta (pow (+ 2 beta) 2))))) (/ beta (+ 2 beta)))
(+ (* alpha (- (/ (* alpha (+ (/ 1 (+ 2 beta)) (/ beta (pow (+ 2 beta) 2)))) (+ 2 beta)) (+ (/ 1 (+ 2 beta)) (/ beta (pow (+ 2 beta) 2))))) (/ beta (+ 2 beta)))
(+ (* alpha (- (* alpha (- (* -1 (* alpha (+ (/ 1 (pow (+ 2 beta) 3)) (/ beta (pow (+ 2 beta) 4))))) (* -1 (/ (+ (/ 1 (+ 2 beta)) (/ beta (pow (+ 2 beta) 2))) (+ 2 beta))))) (+ (/ 1 (+ 2 beta)) (/ beta (pow (+ 2 beta) 2))))) (/ beta (+ 2 beta)))
-1
(- (/ beta alpha) (+ 1 (* -1 (/ (+ 2 beta) alpha))))
(- (+ (* -1 (/ (* (+ 2 beta) (- beta (* -1 (+ 2 beta)))) (pow alpha 2))) (/ beta alpha)) (+ 1 (* -1 (/ (+ 2 beta) alpha))))
(- (+ (/ beta alpha) (/ (* (pow (+ 2 beta) 2) (- beta (* -1 (+ 2 beta)))) (pow alpha 3))) (+ 1 (+ (* -1 (/ (+ 2 beta) alpha)) (/ (* (+ 2 beta) (- beta (* -1 (+ 2 beta)))) (pow alpha 2)))))
-1
(- (* -1 (/ (- (* -1 beta) (+ 2 beta)) alpha)) 1)
(- (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (* (+ 2 beta) (- (* -1 beta) (+ 2 beta))) alpha))) (+ 2 beta)) alpha)) 1)
(- (* -1 (/ (- (+ (* -1 beta) (* -1 (/ (- (* -1 (/ (* (pow (+ 2 beta) 2) (- (* -1 beta) (+ 2 beta))) alpha)) (* -1 (* (+ 2 beta) (- (* -1 beta) (+ 2 beta))))) alpha))) (+ 2 beta)) alpha)) 1)
(+ 1/2 (* -1/8 (/ (pow alpha 2) (pow i 2))))
(+ 1/2 (+ (* -1/8 (/ (pow alpha 2) (pow i 2))) (* 1/8 (* beta (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))))))
(+ 1/2 (+ (* -1/8 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* 1/8 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))) (* 1/8 (/ beta (pow i 2)))))))
(+ 1/2 (+ (* -1/8 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* 1/8 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))) (* 1/8 (/ beta (pow i 2)))))))
(* 1/8 (/ (pow beta 2) (pow i 2)))
(* (pow beta 2) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow beta 2) (+ (* -1/8 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (+ (/ 1/2 (pow beta 2)) (* 1/8 (/ 1 (pow i 2)))))))
(* (pow beta 2) (+ (* -1/8 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (+ (/ 1/2 (pow beta 2)) (* 1/8 (/ 1 (pow i 2)))))))
(* 1/8 (/ (pow beta 2) (pow i 2)))
(* (pow beta 2) (+ (* 1/8 (/ (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/8 (/ (pow alpha 2) (pow i 2)))) beta)) (* -1/8 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/8 (/ (pow alpha 2) (pow i 2)))) beta)) (* -1/8 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2))))) beta)) (* 1/8 (/ 1 (pow i 2)))))
(+ 1/2 (* 1/8 (/ (pow beta 2) (pow i 2))))
(+ 1/2 (+ (* 1/8 (* alpha (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) (* 1/8 (/ (pow beta 2) (pow i 2)))))
(+ 1/2 (+ (* 1/8 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ alpha (pow i 2))) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))))))
(+ 1/2 (+ (* 1/8 (/ (pow beta 2) (pow i 2))) (* alpha (+ (* -1/8 (/ alpha (pow i 2))) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))))))
(* -1/8 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (* 1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (+ (* 1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (+ (* 1/8 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/2 (pow alpha 2)))) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (+ (* 1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (+ (* 1/8 (/ (pow beta 2) (* (pow alpha 2) (pow i 2)))) (/ 1/2 (pow alpha 2)))) (* 1/8 (/ 1 (pow i 2)))))
(* -1/8 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (* -1/8 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/8 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/8 (/ (pow beta 2) (pow i 2)))) alpha)) (* 1/8 (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) alpha)) (* 1/8 (/ 1 (pow i 2)))))
(* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))
(/ (+ (* 1/8 (* (+ alpha beta) (- beta alpha))) (* 1/2 (pow i 2))) (pow i 2))
(/ (+ (* 1/8 (* (+ alpha beta) (- beta alpha))) (* 1/2 (pow i 2))) (pow i 2))
(/ (+ (* 1/8 (* (+ alpha beta) (- beta alpha))) (* 1/2 (pow i 2))) (pow i 2))
1/2
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
1/2
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(* -1 (/ (pow alpha 2) (pow i 2)))
(+ (* -1 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))))
(+ (* -1 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1 (/ alpha (pow i 2))) (+ (/ alpha (pow i 2)) (/ beta (pow i 2))))))
(+ (* -1 (/ (pow alpha 2) (pow i 2))) (* beta (+ (* -1 (/ alpha (pow i 2))) (+ (/ alpha (pow i 2)) (/ beta (pow i 2))))))
(/ (pow beta 2) (pow i 2))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2))))))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (* -1 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2)))))))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (* -1 (/ (pow alpha 2) (* (pow beta 2) (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2)))))))
(/ (pow beta 2) (pow i 2))
(* (pow beta 2) (+ (* -1 (/ alpha (* beta (pow i 2)))) (+ (/ 1 (pow i 2)) (/ alpha (* beta (pow i 2))))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))) (/ (pow alpha 2) (* beta (pow i 2)))) beta)) (/ 1 (pow i 2))))
(* (pow beta 2) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ alpha (pow i 2))) (/ alpha (pow i 2)))) (/ (pow alpha 2) (* beta (pow i 2)))) beta)) (/ 1 (pow i 2))))
(/ (pow beta 2) (pow i 2))
(+ (* alpha (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2)))) (/ (pow beta 2) (pow i 2)))
(+ (* alpha (+ (* -1 (/ alpha (pow i 2))) (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) (/ (pow beta 2) (pow i 2)))
(+ (* alpha (+ (* -1 (/ alpha (pow i 2))) (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))))) (/ (pow beta 2) (pow i 2)))
(* -1 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (+ (* -1 (/ beta (* alpha (pow i 2)))) (/ beta (* alpha (pow i 2)))) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (+ (* -1 (/ beta (* alpha (pow i 2)))) (+ (/ beta (* alpha (pow i 2))) (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (+ (* -1 (/ beta (* alpha (pow i 2)))) (+ (/ beta (* alpha (pow i 2))) (/ (pow beta 2) (* (pow alpha 2) (pow i 2))))) (/ 1 (pow i 2))))
(* -1 (/ (pow alpha 2) (pow i 2)))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ beta (pow i 2))) (/ beta (pow i 2))) alpha)) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ beta (pow i 2))) (+ (* -1 (/ (pow beta 2) (* alpha (pow i 2)))) (/ beta (pow i 2)))) alpha)) (/ 1 (pow i 2))))
(* (pow alpha 2) (- (* -1 (/ (+ (* -1 (/ beta (pow i 2))) (+ (* -1 (/ (pow beta 2) (* alpha (pow i 2)))) (/ beta (pow i 2)))) alpha)) (/ 1 (pow i 2))))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(/ (* (+ alpha beta) (- beta alpha)) (pow i 2))
(* -1 (pow alpha 2))
(+ (* -1 (pow alpha 2)) (* beta (+ alpha (* -1 alpha))))
(+ (* -1 (pow alpha 2)) (* beta (+ alpha (+ beta (* -1 alpha)))))
(+ (* -1 (pow alpha 2)) (* beta (+ alpha (+ beta (* -1 alpha)))))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (/ alpha beta))))
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))))
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (+ (* -1 (/ (pow alpha 2) (pow beta 2))) (/ alpha beta)))))
(pow beta 2)
(* (pow beta 2) (+ 1 (+ (* -1 (/ alpha beta)) (/ alpha beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha (* -1 alpha))) (/ (pow alpha 2) beta)) beta))))
(* (pow beta 2) (+ 1 (* -1 (/ (+ (* -1 (+ alpha (* -1 alpha))) (/ (pow alpha 2) beta)) beta))))
(pow beta 2)
(+ (* alpha (+ beta (* -1 beta))) (pow beta 2))
(+ (* alpha (+ beta (+ (* -1 alpha) (* -1 beta)))) (pow beta 2))
(+ (* alpha (+ beta (+ (* -1 alpha) (* -1 beta)))) (pow beta 2))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (+ (* -1 (/ beta alpha)) (/ beta alpha)) 1))
(* (pow alpha 2) (- (+ (* -1 (/ beta alpha)) (+ (/ beta alpha) (/ (pow beta 2) (pow alpha 2)))) 1))
(* (pow alpha 2) (- (+ (* -1 (/ beta alpha)) (+ (/ beta alpha) (/ (pow beta 2) (pow alpha 2)))) 1))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (* -1 (/ (+ beta (* -1 beta)) alpha)) 1))
(* (pow alpha 2) (- (* -1 (/ (+ beta (+ (* -1 beta) (* -1 (/ (pow beta 2) alpha)))) alpha)) 1))
(* (pow alpha 2) (- (* -1 (/ (+ beta (+ (* -1 beta) (* -1 (/ (pow beta 2) alpha)))) alpha)) 1))
(+ 1 (/ (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))))))
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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)))))
(+ 1/2 (+ (* -1/2 (/ (+ (* -1/64 (* (+ alpha beta) (* (pow (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) 2) (- beta alpha)))) (* 1/16 (* (+ 2 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- beta alpha))))) (pow i 4))) (+ (* -1/32 (/ (* (+ alpha beta) (* (+ (* 2 (+ 2 (+ alpha beta))) (* 2 (+ alpha beta))) (- beta alpha))) (pow i 3))) (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))))
1/2
(+ 1/2 (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2))))
(+ 1/2 (+ (* 1/32 (/ (* (+ alpha beta) (* (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) (- beta alpha))) (pow i 3))) (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))
(+ 1/2 (+ (* -1 (/ (+ (* -1/32 (* (+ alpha beta) (* (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) (- beta alpha)))) (* 1/2 (/ (+ (* -1/64 (* (+ alpha beta) (* (pow (+ (* -2 (+ 2 (+ alpha beta))) (* -2 (+ alpha beta))) 2) (- beta alpha)))) (* 1/16 (* (+ 2 (+ alpha beta)) (* (pow (+ alpha beta) 2) (- beta alpha))))) i))) (pow i 3))) (* 1/8 (/ (* (+ alpha beta) (- beta alpha)) (pow i 2)))))
(/ 1 (+ 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))
(+ 2 (+ beta (* 2 i)))
(+ 2 (+ alpha (+ beta (* 2 i))))
(+ 2 (+ alpha (+ beta (* 2 i))))
(+ 2 (+ alpha (+ beta (* 2 i))))
alpha
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (+ (* 2 (/ 1 alpha)) (/ beta alpha)))))
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (+ (* 2 (/ 1 alpha)) (/ beta alpha)))))
(* alpha (+ 1 (+ (* 2 (/ i alpha)) (+ (* 2 (/ 1 alpha)) (/ beta alpha)))))
alpha
(* -1 (* alpha (- (* -1 (/ (+ 2 (+ beta (* 2 i))) alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ (+ 2 (+ beta (* 2 i))) alpha)) 1)))
(* -1 (* alpha (- (* -1 (/ (+ 2 (+ beta (* 2 i))) alpha)) 1)))
(+ 2 (+ alpha (* 2 i)))
(+ 2 (+ alpha (+ beta (* 2 i))))
(+ 2 (+ alpha (+ beta (* 2 i))))
(+ 2 (+ alpha (+ beta (* 2 i))))
beta
(* beta (+ 1 (+ (* 2 (/ i beta)) (+ (* 2 (/ 1 beta)) (/ alpha beta)))))
(* beta (+ 1 (+ (* 2 (/ i beta)) (+ (* 2 (/ 1 beta)) (/ alpha beta)))))
(* beta (+ 1 (+ (* 2 (/ i beta)) (+ (* 2 (/ 1 beta)) (/ alpha beta)))))
beta
(* -1 (* beta (- (* -1 (/ (+ 2 (+ alpha (* 2 i))) beta)) 1)))
(* -1 (* beta (- (* -1 (/ (+ 2 (+ alpha (* 2 i))) beta)) 1)))
(* -1 (* beta (- (* -1 (/ (+ 2 (+ alpha (* 2 i))) beta)) 1)))
(+ 2 (+ alpha beta))
(+ 2 (+ alpha (+ beta (* 2 i))))
(+ 2 (+ alpha (+ beta (* 2 i))))
(+ 2 (+ alpha (+ beta (* 2 i))))
(* 2 i)
(* i (+ 2 (+ (* 2 (/ 1 i)) (+ (/ alpha i) (/ beta i)))))
(* i (+ 2 (+ (* 2 (/ 1 i)) (+ (/ alpha i) (/ beta i)))))
(* i (+ 2 (+ (* 2 (/ 1 i)) (+ (/ alpha i) (/ beta i)))))
(* 2 i)
(* -1 (* i (- (* -1 (/ (+ 2 (+ alpha beta)) i)) 2)))
(* -1 (* i (- (* -1 (/ (+ 2 (+ alpha beta)) i)) 2)))
(* -1 (* i (- (* -1 (/ (+ 2 (+ alpha beta)) i)) 2)))
(/ 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)))
(/ (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
(* 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))))))
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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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#s(literal -1 binary64)
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beta
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beta
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beta
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1
#s(literal 1 binary64)
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#s(literal 1 binary64)
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(/ (+ (* -1/2 (/ (* (+ 2 beta) (- beta (* -1 (+ 2 beta)))) alpha)) (+ (* 1/2 (- beta (* -1 (+ 2 beta)))) (* 1/2 (/ (* (pow (+ 2 beta) 2) (- beta (* -1 (+ 2 beta)))) (pow alpha 2))))) alpha)
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(/ (+ (* -1/2 (/ (* (+ 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)
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(+ (* -1/2 (/ alpha (+ 2 alpha))) (* 1/2 (* beta (- (/ 1 (+ 2 alpha)) (* -1 (/ alpha (pow (+ 2 alpha) 2)))))))
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ (- (* -1 alpha) (+ 2 alpha)) beta)))
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(* 1/2 (/ beta (+ 2 beta)))
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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
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ alpha beta))) (+ (* 2 (/ 1 beta)) (/ alpha beta)))
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(/ beta (+ 2 beta))
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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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(* 1/2 (+ 1 (* -1 (/ (pow alpha 2) (* (+ 2 (+ alpha (* 2 i))) (+ alpha (* 2 i)))))))
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(.f64 alpha (-.f64 (fma.f64 #s(literal 0 binary64) (/.f64 beta alpha) (/.f64 (.f64 beta beta) (.f64 alpha alpha))) (+.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) i beta) (/.f64 (-.f64 (-.f64 beta beta) (neg.f64 (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) (-.f64 (-.f64 beta beta) (neg.f64 (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 (-.f64 (-.f64 beta beta) (neg.f64 (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)) (neg.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)))))
(.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 (neg.f64 (fma.f64 #s(literal 2 binary64) i beta)) (-.f64 (neg.f64 (-.f64 beta beta)) (neg.f64 (fma.f64 #s(literal 2 binary64) i beta))))) alpha)) (neg.f64 (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 (-.f64 (neg.f64 (.f64 beta beta)) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) i beta) (-.f64 (neg.f64 (.f64 beta beta)) (.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) i beta)) (-.f64 (neg.f64 (-.f64 beta beta)) (neg.f64 (fma.f64 #s(literal 2 binary64) i beta)))))) alpha)) (.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) i beta)) (-.f64 (neg.f64 (-.f64 beta beta)) (neg.f64 (fma.f64 #s(literal 2 binary64) i beta))))) alpha)) (neg.f64 (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)) (neg.f64 (/.f64 (neg.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 (neg.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 (neg.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)))))
(.f64 beta (+.f64 #s(literal 1 binary64) (-.f64 (-.f64 (-.f64 (neg.f64 (/.f64 alpha beta)) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) i alpha) (-.f64 (neg.f64 (.f64 alpha alpha)) (.f64 (fma.f64 #s(literal 2 binary64) i alpha) (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha))))) (.f64 beta (.f64 beta 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 (* beta (- (* -1 (/ (+ alpha (* -1 alpha)) beta)) (+ 1 (* -1 (/ (+ alpha (* 2 i)) beta))))))
(*.f64 (neg.f64 beta) (-.f64 (neg.f64 (/.f64 (-.f64 alpha alpha) 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)))
(.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (-.f64 (neg.f64 (-.f64 alpha alpha)) (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha)))) (/.f64 (-.f64 (neg.f64 (.f64 alpha alpha)) (*.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha)) (-.f64 (neg.f64 (-.f64 alpha alpha)) (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha))))) beta)) beta)) #s(literal -1 binary64)))
(* -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)))
(.f64 (neg.f64 beta) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (-.f64 (neg.f64 (-.f64 alpha alpha)) (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha)))) (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) i alpha) (/.f64 (-.f64 (neg.f64 (.f64 alpha alpha)) (.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha)) (-.f64 (neg.f64 (-.f64 alpha alpha)) (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha))))) beta) (neg.f64 (-.f64 (neg.f64 (.f64 alpha alpha)) (*.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha)) (-.f64 (neg.f64 (-.f64 alpha alpha)) (neg.f64 (fma.f64 #s(literal 2 binary64) i alpha))))))) beta)) beta)) #s(literal -1 binary64)))
(- 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 alpha beta)) 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 alpha beta) (+.f64 alpha beta))) (*.f64 #s(literal -2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta)))) beta) alpha)
(- (+ beta (* i (- (* i (- (* -8 (/ (* i (- beta alpha)) (pow (+ alpha beta) 3))) (* -4 (/ (- beta alpha) (pow (+ alpha beta) 2))))) (* 2 (/ (- beta alpha) (+ alpha beta)))))) alpha)
(-.f64 (fma.f64 i (fma.f64 i (fma.f64 (/.f64 (.f64 i (-.f64 beta alpha)) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) #s(literal -8 binary64) (.f64 #s(literal 4 binary64) (/.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) (.f64 #s(literal -2 binary64) (/.f64 (-.f64 beta alpha) (+.f64 alpha beta)))) beta) alpha)
(* 1/2 (/ (* (+ alpha beta) (- beta alpha)) i))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) (-.f64 beta alpha)) i)
(/ (+ (* -1/4 (/ (* (pow (+ alpha beta) 2) (- beta alpha)) i)) (* 1/2 (* (+ alpha beta) (- beta alpha)))) i)
(/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) i) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) (-.f64 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)
(/.f64 (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (.f64 i i)) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) (-.f64 beta alpha))) (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (-.f64 beta alpha) (*.f64 (+.f64 alpha beta) (+.f64 alpha beta))) 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 (-.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (-.f64 beta alpha) (pow.f64 (+.f64 alpha beta) #s(literal 4 binary64))) (.f64 i (.f64 i i))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) i) (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) (.f64 i i))))) i)
(* 1/2 (/ (* (+ alpha beta) (- beta alpha)) i))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 alpha beta)) (-.f64 beta alpha)) i)
(* -1 (/ (+ (* -1/2 (* (+ alpha beta) (- beta alpha))) (* 1/4 (/ (* (pow (+ alpha beta) 2) (- beta alpha)) i))) i))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))) (-.f64 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))
(neg.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 alpha beta)) (-.f64 beta alpha)) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))) i) (.f64 #s(literal -1/4 binary64) (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) i)) 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))
(neg.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 alpha beta)) (-.f64 beta alpha)) (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (+.f64 alpha beta) #s(literal 4 binary64)) (/.f64 (-.f64 beta alpha) i)) (.f64 #s(literal -1/8 binary64) (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (.f64 (+.f64 alpha beta) (+.f64 alpha beta)))))) i)) (.f64 #s(literal -1/4 binary64) (.f64 (-.f64 beta alpha) (.f64 (+.f64 alpha beta) (+.f64 alpha beta))))) i)) i))

eval348.0ms (2.6%)

Memory: 20.3MiB live, 673.0MiB allocated
Compiler: Compiled 85 436 to 6 563 computations (92.3% saved)

prune287.0ms (2.1%)

Memory

-14.8MiB live, 571.6MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	1 990	13	2 003
Fresh	2	6	8
Picked	4	1	5
Done	0	0	0
Total	1 996	20	2 016

Accuracy

99.9%

Counts

2 016 → 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 alpha beta) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) #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)
	19.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) 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)
▶	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 446 computations (40.8% saved)

simplify320.0ms (2.4%)

Memory

-11.6MiB live, 422.4MiB 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	512	(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

12 270×	`lower-fma.f32`
12 262×	`lower-fma.f64`
3 274×	`lower-*.f32`
3 262×	`lower-*.f64`
2 190×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	177
0	52	177
1	97	177
2	217	177
3	540	166
4	1810	157
5	7415	157
0	8152	149

Stop Event

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

Calls

Call 1

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

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

localize141.0ms (1%)

Memory

30.9MiB live, 145.7MiB 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

85.0ms

256×

valid

Compiler

Compiled 187 to 35 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-sub: 27.0ms (48.6% of total)

ival-mult: 14.0ms (25.2% of total)

ival-div: 8.0ms (14.4% of total)

ival-add: 6.0ms (10.8% of total)

exact: 1.0ms (1.8% of total)

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

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

series59.0ms (0.4%)

Memory

-26.7MiB live, 46.8MiB allocated

Counts

18 → 336

Calls

Call 1

Inputs
#<alt (fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))>
#<alt (/.f64 beta (+.f64 #s(literal 2 binary64) beta))>
#<alt (+.f64 #s(literal 2 binary64) beta)>
#<alt (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 beta beta)) (*.f64 i i))>
#<alt (.f64 #s(literal 1/8 binary64) (.f64 beta beta))>
#<alt (*.f64 beta beta)>
#<alt (*.f64 i i)>
#<alt (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))>
#<alt (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64))))>
#<alt (/.f64 (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))) beta)>
#<alt (fma.f64 #s(literal 2 binary64) alpha (*.f64 i #s(literal 4 binary64)))>
#<alt (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))))>
#<alt (*.f64 #s(literal 1/2 binary64) (-.f64 beta (-.f64 #s(literal -2 binary64) beta)))>
#<alt (/.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)>
#<alt (/.f64 (*.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) beta))) alpha)>
#<alt (*.f64 i #s(literal 4 binary64))>
#<alt (-.f64 beta (-.f64 #s(literal -2 binary64) beta))>
#<alt (*.f64 (+.f64 #s(literal 2 binary64) beta) (-.f64 beta (-.f64 #s(literal -2 binary64) 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		Point	Expression
7.0ms	beta	@	inf	(* (+ 2 beta) (- beta (- -2 beta)))
6.0ms	beta	@	0	(/ (* 1/8 (* beta beta)) (* i i))
1.0ms	i	@	0	(/ (* 1/8 (* beta beta)) (* i i))
1.0ms	beta	@	inf	(/ (* 1/8 (* beta beta)) (* i i))
1.0ms	alpha	@	0	(+ (* -1/2 (/ (* (+ 2 beta) (- beta (- -2 beta))) alpha)) (* 1/2 (- beta (- -2 beta))))

rewrite724.0ms (5.4%)

Memory

3.8MiB live, 524.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 358×	`lower-/.f32`
4 348×	`lower-/.f64`
4 106×	`lower-*.f32`
4 094×	`lower-*.f64`
4 002×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	150
0	52	150
1	222	150
2	1814	148
0	8266	148

Stop Event

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

Counts

18 → 647

Calls

Call 1

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

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

simplify579.0ms (4.3%)

Memory

2.8MiB live, 526.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 964×	`lower-fma.f64`
11 964×	`lower-fma.f32`
4 850×	`lower-*.f64`
4 850×	`lower-*.f32`
4 152×	`lower-+.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 → 332

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)))
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(+.f64 (/.f64 beta alpha) (fma.f64 beta (/.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))
(- (+ (* 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))))

eval192.0ms (1.4%)

Memory: 39.5MiB live, 340.2MiB allocated
Compiler: Compiled 32 205 to 3 209 computations (90% saved)

prune194.0ms (1.4%)

Memory

-69.8MiB live, 329.9MiB allocated

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	1 067	7	1 074
Fresh	1	13	14
Picked	4	1	5
Done	0	1	1
Total	1 072	22	1 094

Accuracy

100.0%

Counts

1 094 → 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 alpha beta) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) #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)
	17.7%	(/.f64 #s(literal 1 binary64) (/.f64 alpha (fma.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 beta #s(literal 2 binary64))) (+.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 462 computations (41.1% saved)

simplify333.0ms (2.5%)

Memory

11.2MiB live, 609.1MiB 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×	`lower-fma.f32`
11 662×	`lower-fma.f64`
2 926×	`lower-*.f32`
2 914×	`lower-*.f64`
2 552×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	158
0	55	154
1	110	153
2	256	153
3	551	153
4	1089	153
5	2120	153
6	2995	153
7	4402	153
8	7710	153
0	8271	152

Stop Event

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

Calls

Call 1

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

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

localize134.0ms (1%)

Memory

6.4MiB live, 348.8MiB 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

41.0ms	177×	0	valid
16.0ms	29×	2	valid
14.0ms	32×	1	valid
14.0ms	18×	3	valid

Compiler

Compiled 174 to 36 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 21.0ms (34.5% of total)

ival-add: 20.0ms (32.8% of total)

ival-div: 8.0ms (13.1% of total)

adjust: 7.0ms (11.5% of total)

ival-sub: 3.0ms (4.9% of total)

exact: 1.0ms (1.6% of total)

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

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

series43.0ms (0.3%)

Memory

15.4MiB live, 106.5MiB allocated

Counts

17 → 336

Calls

Call 1

Inputs
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) #s(literal 1/2 binary64))>
#<alt (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))>
#<alt (-.f64 beta alpha)>
#<alt (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha)))>
#<alt (+.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))>
#<alt (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 i #s(literal -4 binary64)) beta) #s(literal 1 binary64))>
#<alt (/.f64 (*.f64 i #s(literal -4 binary64)) beta)>
#<alt (*.f64 i #s(literal -4 binary64))>
#<alt (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 alpha alpha) (.f64 i i)) #s(literal 1/2 binary64))>
#<alt (/.f64 (.f64 alpha alpha) (.f64 i i))>
#<alt (*.f64 alpha alpha)>
#<alt (*.f64 i i)>
#<alt (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))>
#<alt (/.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))))>
#<alt (*.f64 beta beta)>
#<alt (*.f64 (fma.f64 #s(literal 2 binary64) i beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta)))>
#<alt (+.f64 #s(literal 2 binary64) (+.f64 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
10.0ms	beta	@	0	(/ (* beta beta) (* (+ (* 2 i) beta) (+ 2 (+ (* 2 i) beta))))
5.0ms	beta	@	0	(/ 1 (+ 2 (+ beta alpha)))
3.0ms	beta	@	-inf	(+ (* 1/2 (/ (* i -4) beta)) 1)
1.0ms	i	@	0	(+ (* (/ (* beta beta) (* (+ (* 2 i) beta) (+ 2 (+ (* 2 i) beta)))) 1/2) 1/2)
1.0ms	beta	@	-inf	(+ (* (/ (* beta beta) (* (+ (* 2 i) beta) (+ 2 (+ (* 2 i) beta)))) 1/2) 1/2)

rewrite380.0ms (2.8%)

Memory

-25.6MiB live, 774.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 588×	`lower-/.f32`
4 580×	`lower-/.f64`
4 256×	`lower-*.f32`
4 244×	`lower-*.f64`
4 150×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	125
0	55	121
1	235	116
2	1838	116
0	8683	116

Stop Event

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

Counts

17 → 585

Calls

Call 1

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

simplify402.0ms (3%)

Memory

6.6MiB live, 568.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 748×	`lower-fma.f64`
8 748×	`lower-fma.f32`
7 298×	`lower-*.f64`
7 298×	`lower-*.f32`
4 992×	`lower-+.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 → 329

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)))

eval132.0ms (1%)

Memory: 12.3MiB live, 284.4MiB allocated
Compiler: Compiled 28 219 to 2 887 computations (89.8% saved)

prune213.0ms (1.6%)

Memory

-11.1MiB live, 227.1MiB allocated

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	905	9	914
Fresh	3	12	15
Picked	3	2	5
Done	0	2	2
Total	911	25	936

Accuracy

100.0%

Counts

936 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.7%	(fma.f64 (/.f64 (*.f64 beta beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1/2 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 alpha beta) (*.f64 #s(literal 2 binary64) 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)
	17.7%	(/.f64 #s(literal 1 binary64) (/.f64 alpha (fma.f64 #s(literal 1/2 binary64) (+.f64 beta (+.f64 beta #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 beta #s(literal 2 binary64))) (+.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)

regimes108.0ms (0.8%)

Memory

-3.8MiB live, 129.0MiB 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) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1/2 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 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) #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 (.f64 #s(literal -1/2 binary64) (+.f64 beta #s(literal 2 binary64))) (+.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 #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 alpha (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 #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 #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 alpha (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1 binary64)) #s(literal 2 binary64))

Calls

7 calls:

33.0ms	(+.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))
15.0ms	i
13.0ms	alpha
12.0ms	(*.f64 #s(literal 2 binary64) i)
12.0ms	beta

Results

Accuracy	Segments	Branch
89.8%	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)

regimes56.0ms (0.4%)

Memory

5.1MiB live, 43.0MiB allocated

Counts

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

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

3 calls:

36.0ms

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

9.0ms

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

9.0ms

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

Results

Accuracy	Segments	Branch
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)))`

Compiler

Compiled 90 to 41 computations (54.4% saved)

regimes32.0ms (0.2%)

Memory

0.8MiB live, 42.5MiB 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) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1/2 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 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 alpha (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i alpha))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) (/.f64 (*.f64 beta beta) (fma.f64 #s(literal 2 binary64) i beta)) #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 (.f64 #s(literal -1/2 binary64) (+.f64 beta #s(literal 2 binary64))) (+.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:

13.0ms

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

9.0ms

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

8.0ms

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

Results

Accuracy	Segments	Branch
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)

regimes33.0ms (0.2%)

Memory

1.3MiB live, 40.3MiB 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) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1/2 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) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) i beta)) #s(literal 1/2 binary64))

#s(literal 1 binary64)

Calls

3 calls:

16.0ms

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

8.0ms

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

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)

regimes34.0ms (0.3%)

Memory

3.9MiB live, 42.1MiB 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:

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))

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 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.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)

regimes44.0ms (0.3%)

Memory

-1.0MiB live, 36.4MiB 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:

28.0ms

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

7.0ms

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

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
94.6%	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)

regimes47.0ms (0.3%)

Memory

-0.4MiB live, 39.4MiB 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:

28.0ms	(/.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)

regimes19.0ms (0.1%)

Memory

-11.5MiB live, 26.2MiB 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:

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 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.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 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.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)

regimes15.0ms (0.1%)

Memory

25.2MiB live, 25.2MiB 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:

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

4.0ms

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

Results

Accuracy	Segments	Branch
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)

regimes12.0ms (0.1%)

Memory

-20.8MiB live, 17.0MiB 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:

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))

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)

regimes18.0ms (0.1%)

Memory

32.1MiB live, 32.1MiB 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	(*.f64 #s(literal 2 binary64) i)
3.0ms	alpha
3.0ms	beta
3.0ms	i
2.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64)))

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)

regimes11.0ms (0.1%)

Memory

-13.5MiB live, 23.4MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(literal 1/2 binary64)

Calls

4 calls:

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)))
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)

regimes9.0ms (0.1%)

Memory

21.4MiB live, 21.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
3.5%	1	`alpha`
3.5%	1	`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)

bsearch28.0ms (0.2%)

Memory

-39.5MiB live, 1.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999972100088	-0.9999999971671104

Compiler

Compiled 35 to 22 computations (37.1% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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

1.0MiB live, 1.0MiB 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)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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

0.9MiB live, 0.9MiB 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

0.8MiB live, 0.8MiB 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

0.9MiB live, 0.9MiB 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

0.5MiB live, 0.5MiB 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

0.7MiB live, 0.7MiB 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

0.5MiB live, 0.5MiB 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

0.4MiB live, 0.4MiB 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)

simplify13.0ms (0.1%)

Memory

25.4MiB live, 25.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	797
1	107	797
2	111	797
3	113	797
4	114	797

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

Outputs
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -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) (/.f64 (fma.f64 (/.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 alpha (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -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) (/.f64 (fma.f64 (/.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 alpha (fma.f64 #s(literal 2 binary64) i beta)))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (*.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (/.f64 (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 #s(literal 2 binary64) i #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -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 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #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 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 9007126675982015/9007199254740992 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (.f64 (+.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)))) #s(literal 1 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 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1/2 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 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 9007126675982015/9007199254740992 binary64)) (fma.f64 (/.f64 (*.f64 beta beta) (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) i beta))) (/.f64 #s(literal 1/2 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 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 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))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 2 binary64) (fma.f64 beta #s(literal 2 binary64) (.f64 i #s(literal 4 binary64)))) #s(literal 1/2 binary64)) alpha) (if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal 5444517870735015/10889035741470030830827987437816582766592 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (+.f64 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 (+.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))))
(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 5444517870735015/10889035741470030830827987437816582766592 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (+.f64 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 (+.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 #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) (+.f64 beta alpha))) (-.f64 beta alpha) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -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 5444517870735015/10889035741470030830827987437816582766592 binary64)) #s(literal 1/2 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 alpha beta) #s(literal 2 binary64))) (-.f64 beta alpha) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -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 (+.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 #s(literal 1/2 binary64) (/.f64 beta (+.f64 #s(literal 2 binary64) beta)) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)))) #s(literal -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 5444517870735015/10889035741470030830827987437816582766592 binary64)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 beta (+.f64 beta #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 #s(literal 2 binary64) i)) #s(literal 2 binary64))) #s(literal -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 (+.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 -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)

soundness1.4s (10.4%)

Memory

-11.6MiB live, 979.9MiB allocated

Rules

11 964×	`lower-fma.f64`
11 964×	`lower-fma.f32`
6 196×	`lower-*.f64`
6 196×	`lower-*.f32`
6 142×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	360	3596
1	1102	3344
2	2955	3205
0	8654	2960
0	1854	24945
1	6076	24249
0	8041	22220
0	29	125
0	55	121
1	235	116
2	1838	116
0	8683	116
0	933	12926
1	3169	11301
0	8840	10167
0	15	103
0	25	103
1	125	103
2	1197	103
0	8707	93
0	31	243
0	59	239
1	314	239
2	3197	239
0	8735	238

Stop Event

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

Compiler

Compiled 1 274 to 427 computations (66.5% saved)

preprocess71.0ms (0.5%)

Memory: 14.2MiB live, 167.3MiB allocated
Compiler: Compiled 1 664 to 196 computations (88.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze47.0ms (0.4%)

sample2.3s (17%)

preprocess448.0ms (3.3%)

explain284.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify398.0ms (2.9%)

localize83.0ms (0.6%)

series81.0ms (0.6%)

rewrite632.0ms (4.7%)

simplify591.0ms (4.4%)

eval192.0ms (1.4%)

prune197.0ms (1.5%)

simplify560.0ms (4.1%)

localize173.0ms (1.3%)

series75.0ms (0.6%)

rewrite372.0ms (2.8%)

simplify641.0ms (4.7%)

eval348.0ms (2.6%)

prune287.0ms (2.1%)

simplify320.0ms (2.4%)

localize141.0ms (1%)

series59.0ms (0.4%)

rewrite724.0ms (5.4%)

simplify579.0ms (4.3%)

eval192.0ms (1.4%)

prune194.0ms (1.4%)

simplify333.0ms (2.5%)

localize134.0ms (1%)

series43.0ms (0.3%)

rewrite380.0ms (2.8%)

simplify402.0ms (3%)

eval132.0ms (1%)

prune213.0ms (1.6%)

regimes108.0ms (0.8%)

regimes56.0ms (0.4%)

regimes32.0ms (0.2%)

regimes33.0ms (0.2%)

regimes34.0ms (0.3%)

regimes44.0ms (0.3%)

regimes47.0ms (0.3%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes18.0ms (0.1%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

bsearch28.0ms (0.2%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify13.0ms (0.1%)

soundness1.4s (10.4%)

preprocess71.0ms (0.5%)

end0.0ms (0%)

Profiling