Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.1MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze542.0ms (15.7%)

Memory

21.6MiB live, 343.5MiB allocated; 706ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	48.6%	51.4%	0%	0%	0%	0
0%	0%	48.6%	51.4%	0%	0%	0%	1
0%	0%	48.6%	51.4%	0%	0%	0%	2
0%	0%	48.6%	51.4%	0%	0%	0%	3
0%	0%	48.6%	51.4%	0%	0%	0%	4
31.3%	15.2%	33.4%	51.4%	0%	0%	0%	5
34.4%	16.7%	31.9%	51.4%	0%	0%	0%	6
51.6%	25.1%	23.6%	51.4%	0%	0%	0%	7
53.1%	25.8%	22.8%	51.4%	0%	0%	0%	8
62.5%	30.4%	18.2%	51.4%	0%	0%	0%	9
63.7%	31%	17.7%	51.4%	0%	0%	0%	10
68.6%	33.3%	15.3%	51.4%	0%	0%	0%	11
69.2%	33.7%	15%	51.4%	0%	0%	0%	12

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample1.2s (33.5%)

Memory

74.1MiB live, 1 464.6MiB allocated; 283ms collecting garbage

Samples

434.0ms	6 257×	0	valid
230.0ms	964×	2	valid
120.0ms	448×	3	valid
75.0ms	587×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 631.0ms

ival-sqrt: 215.0ms (34.1% of total)

ival-mult!: 186.0ms (29.5% of total)

adjust: 99.0ms (15.7% of total)

ival-div!: 69.0ms (10.9% of total)

ival-add!: 56.0ms (8.9% of total)

ival-fabs: 3.0ms (0.5% of total)

ival-and: 1.0ms (0.2% of total)

ival-<: 1.0ms (0.2% of total)

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

Bogosity

preprocess48.0ms (1.4%)

Memory

1.5MiB live, 46.4MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	106
1	159	104
2	475	104
3	1685	104

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.1%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Symmetry

(abs p)

Compiler

Compiled 28 to 28 computations (0% saved)

series29.0ms (0.8%)

Memory

-11.9MiB live, 33.9MiB allocated; 5ms collecting garbage

Counts

14 → 105

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
#s(literal 1 binary64)
(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
x
(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(.f64 (.f64 #s(literal 4 binary64) p) p)
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)

Outputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 1))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 2))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 x))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ x (* 2 (/ (pow p 2) x)))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (+ (* 4 (pow p 2)) (pow x 2))))
#s(approx (* (* 4 p) p) #s(hole binary64 (* 4 (pow p 2))))
#s(approx (* 4 p) #s(hole binary64 (* 4 p)))
#s(approx p #s(hole binary64 p))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 1/2))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* 2 p)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -2 p)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 -1))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	p	@	0	((sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) x (sqrt (+ (* (* 4 p) p) (* x x))) (+ (* (* 4 p) p) (* x x)) (* (* 4 p) p) (* 4 p) 4 p (* x x))
5.0ms	x	@	-inf	((sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) x (sqrt (+ (* (* 4 p) p) (* x x))) (+ (* (* 4 p) p) (* x x)) (* (* 4 p) p) (* 4 p) 4 p (* x x))
4.0ms	p	@	inf	((sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) x (sqrt (+ (* (* 4 p) p) (* x x))) (+ (* (* 4 p) p) (* x x)) (* (* 4 p) p) (* 4 p) 4 p (* x x))
3.0ms	x	@	0	((sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) x (sqrt (+ (* (* 4 p) p) (* x x))) (+ (* (* 4 p) p) (* x x)) (* (* 4 p) p) (* 4 p) 4 p (* x x))
3.0ms	x	@	inf	((sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) x (sqrt (+ (* (* 4 p) p) (* x x))) (+ (* (* 4 p) p) (* x x)) (* (* 4 p) p) (* 4 p) 4 p (* x x))

rewrite170.0ms (4.9%)

Memory

-19.7MiB live, 164.0MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	595	4704
0	610	4183
1	2409	4093
0	8065	3822

Stop Event

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

Counts

119 → 214

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
#s(literal 1 binary64)
(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
x
(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(.f64 (.f64 #s(literal 4 binary64) p) p)
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 1))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 2))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 x))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ x (* 2 (/ (pow p 2) x)))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (+ (* 4 (pow p 2)) (pow x 2))))
#s(approx (* (* 4 p) p) #s(hole binary64 (* 4 (pow p 2))))
#s(approx (* 4 p) #s(hole binary64 (* 4 p)))
#s(approx p #s(hole binary64 p))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 1/2))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* 2 p)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -2 p)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))))
#s(approx (+ (* (* 4 p) p) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 -1))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))))

Outputs
(pow.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
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(fabs.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))))
(fabs.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))))
(.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)))
(/.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p))))))
(-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p))))) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))))
(-.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p))))))
(+.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
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(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 1 binary64))
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(-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64))
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(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
#s(literal 1 binary64)
(.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p))))))
(.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))
x
(pow.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))
(sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))
(fabs.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
(fabs.f64 (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))
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(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (.f64 (.f64 p #s(literal 4 binary64)) p))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (.f64 (.f64 p #s(literal 4 binary64)) p))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (.f64 (.f64 p #s(literal 4 binary64)) p))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 (.f64 p #s(literal 4 binary64)) p))
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(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 p #s(literal 4 binary64)) p))
(fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 (neg.f64 x)) x))
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(fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))
(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 (neg.f64 (neg.f64 x)) x))
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(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))
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(fma.f64 #s(literal 4 binary64) (.f64 p p) (neg.f64 (neg.f64 (.f64 x x))))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (*.f64 p #s(literal 4 binary64)) p))
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(-.f64 (.f64 x x) (.f64 (neg.f64 (*.f64 p #s(literal 4 binary64))) p))
(-.f64 (.f64 x x) (.f64 (neg.f64 p) (*.f64 p #s(literal 4 binary64))))
(-.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 p p)))
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(-.f64 (.f64 (.f64 p #s(literal 4 binary64)) p) (neg.f64 (*.f64 x x)))
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(.f64 (.f64 p p) #s(literal 4 binary64))
(.f64 (.f64 p #s(literal 4 binary64)) p)
(.f64 p (.f64 p #s(literal 4 binary64)))
(.f64 #s(literal 4 binary64) (.f64 p p))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
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#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) (pow.f64 p #s(literal -5 binary64))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) p))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x) (+.f64 p p)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 (fma.f64 (.f64 (/.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (.f64 p p)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 (-.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -1/4 binary64)) (/.f64 (.f64 p p) (*.f64 x x))) #s(literal -1 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64)) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -6 binary64)))))))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (-.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -4 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -2 binary64)))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64)) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -6 binary64)))) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -2 binary64)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (-.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -4 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -1 binary64)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64)) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -6 binary64)))) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -1 binary64)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (.f64 (fma.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)) x))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (.f64 (-.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) #s(literal -1 binary64)) x))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (.f64 (-.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -2 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal -6 binary64))) #s(literal 4 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (.f64 x x)))) #s(literal -1 binary64)) x))
#s(approx (+ (* (* 4 p) p) (* x x)) (.f64 (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 4 binary64) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (fma.f64 (.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (*.f64 p #s(literal 1 binary64))) (neg.f64 x)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (fma.f64 (.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (*.f64 p #s(literal 1 binary64)))) (neg.f64 x)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (fma.f64 (.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (-.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 p #s(literal 1 binary64))))) (neg.f64 x)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (.f64 p p)) (.f64 x x)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 p p))) (*.f64 x x)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal -6 binary64))) #s(literal 1/4 binary64) (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 p p)))) (.f64 x x)))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (*.f64 x x)))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (.f64 (.f64 p p) #s(literal 2 binary64))) (*.f64 x x)))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 (.f64 p p) #s(literal 2 binary64)))) (.f64 x x)))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal -6 binary64))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 (.f64 p p) #s(literal 2 binary64))))) (*.f64 x x)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (pow.f64 x #s(literal -4 binary64)) (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal -6 binary64)) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (.f64 x x)))) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (.f64 (neg.f64 x) (fma.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (.f64 (neg.f64 x) (-.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) #s(literal -1 binary64))))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (.f64 (neg.f64 x) (-.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -2 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal -6 binary64))) #s(literal 4 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (.f64 x x)))) #s(literal -1 binary64))))

eval26.0ms (0.8%)

Memory: 43.3MiB live, 43.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 190 to 1 267 computations (60.3% saved)

prune13.0ms (0.4%)

Memory

-26.3MiB live, 18.9MiB allocated; 4ms collecting garbage

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	192	15	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	15	208

Accuracy

95.1%

Counts

208 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.1%	(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
	78.5%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 1 binary64))))
	79.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
	77.7%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))))))
	6.3%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))))))
▶	5.4%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
	51.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
	50.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
▶	14.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
	28.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
	56.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	51.6%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
▶	28.8%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
	24.1%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
▶	38.3%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Compiler

Compiled 536 to 534 computations (0.4% saved)

series19.0ms (0.6%)

Memory

28.1MiB live, 28.1MiB allocated; 0ms collecting garbage

Counts

27 → 111

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))
x
(sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))
(fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))
(.f64 (.f64 p #s(literal 4 binary64)) p)
(*.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x)))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
(*.f64 x x)
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))

Outputs
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 2))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* 2 (/ (pow p 2) x)))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (+ (* 4 (pow p 2)) (pow x 2))))
#s(approx (* (* p 4) p) #s(hole binary64 (* 4 (pow p 2))))
#s(approx (* p 4) #s(hole binary64 (* 4 p)))
#s(approx p #s(hole binary64 p))
#s(approx (/ (* p p) (* x x)) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (* p p) #s(hole binary64 (pow p 2)))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))))
#s(approx (* (/ (* p p) (* x x)) 1/2) #s(hole binary64 (* 1/2 (/ (pow p 2) (pow x 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1/2))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* 2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (* -1/2 (/ (pow p 2) (pow x 2)))))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (/ (- (pow x 2) (* 1/2 (pow p 2))) (pow x 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 -1))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))))

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* x x) (* (* p 4) p)) (* (* p 4) p) (* p 4) p 4 -1 1/2 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) 1 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (- 1 (* (/ (* p p) (* x x)) 1/2)) (* (/ (* p p) (* x x)) 1/2))
3.0ms	p	@	inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* x x) (* (* p 4) p)) (* (* p 4) p) (* p 4) p 4 -1 1/2 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) 1 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (- 1 (* (/ (* p p) (* x x)) 1/2)) (* (/ (* p p) (* x x)) 1/2))
2.0ms	x	@	-inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* x x) (* (* p 4) p)) (* (* p 4) p) (* p 4) p 4 -1 1/2 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) 1 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (- 1 (* (/ (* p p) (* x x)) 1/2)) (* (/ (* p p) (* x x)) 1/2))
2.0ms	p	@	0	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* x x) (* (* p 4) p)) (* (* p 4) p) (* p 4) p 4 -1 1/2 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) 1 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (- 1 (* (/ (* p p) (* x x)) 1/2)) (* (/ (* p p) (* x x)) 1/2))
2.0ms	p	@	-inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* x x) (* (* p 4) p)) (* (* p 4) p) (* p 4) p 4 -1 1/2 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) 1 (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (- 1 (* (/ (* p p) (* x x)) 1/2)) (* (/ (* p p) (* x x)) 1/2))

rewrite233.0ms (6.8%)

Memory

-34.5MiB live, 249.2MiB allocated; 117ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	635	4907
0	659	4366
1	2551	4201
0	8452	4035

Stop Event

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

Counts

138 → 409

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))
x
(sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))
(fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))
(.f64 (.f64 p #s(literal 4 binary64)) p)
(*.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64)))
#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x)))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
(*.f64 x x)
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 2))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* 2 (/ (pow p 2) x)))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (+ (* 4 (pow p 2)) (pow x 2))))
#s(approx (* (* p 4) p) #s(hole binary64 (* 4 (pow p 2))))
#s(approx (* p 4) #s(hole binary64 (* 4 p)))
#s(approx p #s(hole binary64 p))
#s(approx (/ (* p p) (* x x)) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (* p p) #s(hole binary64 (pow p 2)))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))))
#s(approx (* (/ (* p p) (* x x)) 1/2) #s(hole binary64 (* 1/2 (/ (pow p 2) (pow x 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1/2))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* 2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (* -1/2 (/ (pow p 2) (pow x 2)))))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) #s(hole binary64 (/ (- (pow x 2) (* 1/2 (pow p 2))) (pow x 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))))
#s(approx (+ (* x x) (* (* p 4) p)) #s(hole binary64 (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 -1))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))))

Outputs
(pow.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))))
(fabs.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))))
(.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(/.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))) #s(literal -1 binary64)) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x))))))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x))))) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))))))
(-.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x))))))
(+.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1/2 binary64)))
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(neg.f64 (-.f64 (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))))) #s(literal 1 binary64)))
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(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))) #s(literal 1 binary64))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))) #s(literal -1 binary64))
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(-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))))))
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(.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))))))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))))
x
(pow.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))) (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x)))))
(sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))
(fabs.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))))
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(neg.f64 (-.f64 (.f64 (neg.f64 (.f64 #s(literal 4 binary64) p)) p) (*.f64 x x)))
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(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (.f64 (neg.f64 (neg.f64 (.f64 #s(literal 4 binary64) p))) p))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (neg.f64 (.f64 (neg.f64 (.f64 #s(literal 4 binary64) p)) p)))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (neg.f64 (neg.f64 (.f64 (.f64 p p) #s(literal 4 binary64)))))
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(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (.f64 (neg.f64 (neg.f64 (.f64 #s(literal 4 binary64) p))) p))
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(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (.f64 (.f64 p p) #s(literal 4 binary64)))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 (neg.f64 (neg.f64 (.f64 #s(literal 4 binary64) p))) p))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (neg.f64 (.f64 (neg.f64 (.f64 #s(literal 4 binary64) p)) p)))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (neg.f64 (neg.f64 (.f64 (.f64 p p) #s(literal 4 binary64)))))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 (.f64 p p) #s(literal 4 binary64)))
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(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 (.f64 (neg.f64 (.f64 #s(literal 4 binary64) p)) p)))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 (neg.f64 (.f64 (.f64 p p) #s(literal 4 binary64)))))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (.f64 p p) #s(literal 4 binary64)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 4 binary64) p))) p))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (neg.f64 (.f64 (neg.f64 (*.f64 #s(literal 4 binary64) p)) p)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (*.f64 p p) #s(literal 4 binary64)))))
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#s(approx (sqrt (+ (* x x) (* (* p 4) p))) (neg.f64 x))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) (.f64 (neg.f64 x) (fma.f64 (.f64 p (/.f64 p (*.f64 x x))) #s(literal 2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) (.f64 (neg.f64 x) (-.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) #s(literal -1 binary64))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) (.f64 (neg.f64 x) (-.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -2 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal -6 binary64))) #s(literal 4 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (.f64 x x)))) #s(literal -1 binary64))))

eval66.0ms (1.9%)

Memory: 1.9MiB live, 90.3MiB allocated; 17ms collecting garbage
Compiler: Compiled 5 342 to 2 072 computations (61.2% saved)

prune14.0ms (0.4%)

Memory

33.4MiB live, 33.4MiB allocated; 0ms collecting garbage

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	436	13	449
Fresh	10	0	10
Picked	2	3	5
Done	0	0	0
Total	448	16	464

Accuracy

96.7%

Counts

464 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
✓	81.1%	(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
▶	77.7%	(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
	6.4%	(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
	51.8%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
▶	50.2%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
	28.4%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (.f64 p (/.f64 p (.f64 x x))))))
	18.3%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
▶	56.0%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
✓	14.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
▶	18.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
▶	51.6%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	28.8%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
	24.1%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
	12.3%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 p p))))
✓	38.3%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Compiler

Compiled 557 to 549 computations (1.4% saved)

series30.0ms (0.9%)

Memory

-13.0MiB live, 44.7MiB allocated; 10ms collecting garbage

Counts

30 → 117

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 x #s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64))
(/.f64 x #s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)))
x
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)
(/.f64 (*.f64 p p) x)
(*.f64 p p)
p
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
#s(literal -1/4 binary64)
(/.f64 x p)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x)))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 p x)
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/4 binary64)

Outputs
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 2))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* 2 (/ (pow p 2) x)))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))))
#s(approx (/ (* p p) x) #s(hole binary64 (/ (pow p 2) x)))
#s(approx (* p p) #s(hole binary64 (pow p 2)))
#s(approx p #s(hole binary64 p))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* -1/4 (/ x p))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (/ (+ (* -1/4 x) (* 1/2 p)) p)))
#s(approx (/ x p) #s(hole binary64 (/ x p)))
#s(approx (* (/ p x) (/ p x)) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (/ p x) #s(hole binary64 (/ p x)))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (* 1/4 (/ (* x (sqrt 1/2)) p))))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)))
#s(approx (/ (* (sqrt 1/2) x) p) #s(hole binary64 (/ (* x (sqrt 1/2)) p)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1/2))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* 2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (* 2 (/ (pow p 2) x))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (/ (+ (* 2 (pow p 2)) (pow x 2)) x)))
#s(approx (* (sqrt 1/2) x) #s(hole binary64 (* x (sqrt 1/2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* x (- (* 1/2 (/ 1 x)) (* 1/4 (/ 1 p))))))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 -1))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* -1 (* x (- (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	p	@	inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* (/ (* p p) x) 2) x) (/ (* p p) x) (* p p) p 2 -1 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) -1/4 (/ x p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* (/ p x) (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) (/ (* (sqrt 1/2) x) p) (* (sqrt 1/2) x) (sqrt 1/2) 1/4)
5.0ms	x	@	-inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* (/ (* p p) x) 2) x) (/ (* p p) x) (* p p) p 2 -1 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) -1/4 (/ x p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* (/ p x) (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) (/ (* (sqrt 1/2) x) p) (* (sqrt 1/2) x) (sqrt 1/2) 1/4)
4.0ms	p	@	-inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* (/ (* p p) x) 2) x) (/ (* p p) x) (* p p) p 2 -1 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) -1/4 (/ x p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* (/ p x) (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) (/ (* (sqrt 1/2) x) p) (* (sqrt 1/2) x) (sqrt 1/2) 1/4)
3.0ms	p	@	0	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* (/ (* p p) x) 2) x) (/ (* p p) x) (* p p) p 2 -1 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) -1/4 (/ x p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* (/ p x) (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) (/ (* (sqrt 1/2) x) p) (* (sqrt 1/2) x) (sqrt 1/2) 1/4)
3.0ms	x	@	inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) x (sqrt (+ (* x x) (* (* p 4) p))) (+ (* (/ (* p p) x) 2) x) (/ (* p p) x) (* p p) p 2 -1 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) -1/4 (/ x p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* (/ p x) (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) (/ (* (sqrt 1/2) x) p) (* (sqrt 1/2) x) (sqrt 1/2) 1/4)

rewrite200.0ms (5.8%)

Memory

18.0MiB live, 200.4MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	660	5135
0	686	4539
1	2626	4448
0	8640	4182

Stop Event

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

Counts

147 → 339

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 x #s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64))
(/.f64 x #s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)))
x
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)
(/.f64 (*.f64 p p) x)
(*.f64 p p)
p
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
#s(literal -1/4 binary64)
(/.f64 x p)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x)))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 p x)
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/4 binary64)
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 2))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* 2 (/ (pow p 2) x)))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))))
#s(approx (/ (* p p) x) #s(hole binary64 (/ (pow p 2) x)))
#s(approx (* p p) #s(hole binary64 (pow p 2)))
#s(approx p #s(hole binary64 p))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* -1/4 (/ x p))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (/ (+ (* -1/4 x) (* 1/2 p)) p)))
#s(approx (/ x p) #s(hole binary64 (/ x p)))
#s(approx (* (/ p x) (/ p x)) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (/ p x) #s(hole binary64 (/ p x)))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (* 1/4 (/ (* x (sqrt 1/2)) p))))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)))
#s(approx (/ (* (sqrt 1/2) x) p) #s(hole binary64 (/ (* x (sqrt 1/2)) p)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1/2))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* 2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (* 2 (/ (pow p 2) x))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -2 p)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (/ (+ (* 2 (pow p 2)) (pow x 2)) x)))
#s(approx (* (sqrt 1/2) x) #s(hole binary64 (* x (sqrt 1/2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* x (- (* 1/2 (/ 1 x)) (* 1/4 (/ 1 p))))))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 -1))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* (* p 4) p))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))))
#s(approx (+ (* (/ (* p p) x) 2) x) #s(hole binary64 (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* -1 (* x (- (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))))

Outputs
(pow.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (*.f64 p (/.f64 p x)) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (.f64 p (/.f64 p x)) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (*.f64 p (/.f64 p x)) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))))
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#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (-.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -1/2 binary64) (.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (*.f64 x x)))) #s(literal -2 binary64)))
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#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) (*.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) x))
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#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 p p))) (*.f64 x x)))
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#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 2 binary64)))
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#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 (.f64 p p) #s(literal 2 binary64)))) (.f64 x x)))
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#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(literal -1 binary64))
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#s(approx (sqrt (+ (* x x) (* (* p 4) p))) (neg.f64 x))
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#s(approx (+ (* (/ (* p p) x) 2) x) (.f64 (neg.f64 x) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -1 binary64))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (+ (* (/ (* (sqrt 1/2) x) p) 1/4) (sqrt 1/2)) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal -1/4 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))))

eval42.0ms (1.2%)

Memory: -10.5MiB live, 80.7MiB allocated; 7ms collecting garbage
Compiler: Compiled 4 225 to 1 648 computations (61% saved)

prune13.0ms (0.4%)

Memory

-18.2MiB live, 28.3MiB allocated; 3ms collecting garbage

Pruning

16 alts after pruning (8 fresh and 8 done)

	Pruned	Kept	Total
New	313	3	316
Fresh	3	5	8
Picked	0	5	5
Done	0	3	3
Total	316	16	332

Accuracy

96.7%

Counts

332 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
✓	81.1%	(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
✓	77.7%	(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
▶	6.3%	(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
▶	51.8%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
✓	50.2%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
▶	28.4%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
	18.3%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
▶	2.5%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
✓	56.0%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
✓	14.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
✓	18.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
✓	51.6%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	28.8%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	24.1%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
✓	38.3%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Compiler

Compiled 449 to 447 computations (0.4% saved)

series19.0ms (0.5%)

Memory

37.3MiB live, 37.3MiB allocated; 0ms collecting garbage

Counts

30 → 95

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(/.f64 x p)
x
p
#s(literal 1/4 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
(neg.f64 (/.f64 p x))
(/.f64 p x)
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))
(*.f64 (/.f64 x p) #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
#s(literal 1 binary64)
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
(*.f64 x x)
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(-.f64 #s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))
#s(literal 2 binary64)
#s(literal -1 binary64)

Outputs
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (+ (* (/ x p) 1/4) 1/2) #s(hole binary64 (* 1/4 (/ x p))))
#s(approx (+ (* (/ x p) 1/4) 1/2) #s(hole binary64 (/ (+ (* 1/4 x) (* 1/2 p)) p)))
#s(approx (/ x p) #s(hole binary64 (/ x p)))
#s(approx p #s(hole binary64 p))
#s(approx (neg (/ p x)) #s(hole binary64 (* -1 (/ p x))))
#s(approx (/ p x) #s(hole binary64 (/ p x)))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* -1/4 (/ x p))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (/ (+ (* -1/4 x) (* 1/2 p)) p)))
#s(approx (/ (* p p) (* x x)) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (* p p) #s(hole binary64 (pow p 2)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 2))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 -1))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1/2))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (- 1 (/ (* p p) (* x x))) #s(hole binary64 (* -1 (/ (pow p 2) (pow x 2)))))
#s(approx (- 1 (/ (* p p) (* x x))) #s(hole binary64 (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx x #s(hole binary64 x))
#s(approx (- 1 (/ (* p p) (* x x))) #s(hole binary64 (/ (- (pow x 2) (pow p 2)) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (+ (* (/ x p) 1/4) 1/2) #s(hole binary64 (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* x (- (* 1/2 (/ 1 x)) (* 1/4 (/ 1 p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* -1 (* x (- (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) x p 1/4 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) (* (/ x p) -1/4) -1/4 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- 1 (/ (* p p) (* x x))) 1 (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (+ (* (/ (* p p) (* x x)) 2) -1) 2 -1)
3.0ms	x	@	inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) x p 1/4 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) (* (/ x p) -1/4) -1/4 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- 1 (/ (* p p) (* x x))) 1 (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (+ (* (/ (* p p) (* x x)) 2) -1) 2 -1)
3.0ms	p	@	-inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) x p 1/4 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) (* (/ x p) -1/4) -1/4 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- 1 (/ (* p p) (* x x))) 1 (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (+ (* (/ (* p p) (* x x)) 2) -1) 2 -1)
3.0ms	p	@	inf	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) x p 1/4 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) (* (/ x p) -1/4) -1/4 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- 1 (/ (* p p) (* x x))) 1 (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (+ (* (/ (* p p) (* x x)) 2) -1) 2 -1)
2.0ms	p	@	0	((sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) x p 1/4 1/2 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg (/ p x)) (/ p x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (+ (* -1/4 (/ x p)) 1/2) (* (/ x p) -1/4) -1/4 (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- 1 (/ (* p p) (* x x))) 1 (/ (* p p) (* x x)) (* p p) (* x x) (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (+ (* (/ (* p p) (* x x)) 2) -1) 2 -1)

rewrite212.0ms (6.2%)

Memory

-16.7MiB live, 174.5MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	554	4456
0	574	3918
1	2221	3748
0	8186	3527

Stop Event

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

Counts

125 → 358

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(/.f64 x p)
x
p
#s(literal 1/4 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
(neg.f64 (/.f64 p x))
(/.f64 p x)
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))
(*.f64 (/.f64 x p) #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
#s(literal 1 binary64)
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
(*.f64 x x)
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(-.f64 #s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* (sqrt 1/2) (sqrt 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* -1 (/ (pow p 2) (pow x 2))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))))
#s(approx (+ (* (/ x p) 1/4) 1/2) #s(hole binary64 (* 1/4 (/ x p))))
#s(approx (+ (* (/ x p) 1/4) 1/2) #s(hole binary64 (/ (+ (* 1/4 x) (* 1/2 p)) p)))
#s(approx (/ x p) #s(hole binary64 (/ x p)))
#s(approx p #s(hole binary64 p))
#s(approx (neg (/ p x)) #s(hole binary64 (* -1 (/ p x))))
#s(approx (/ p x) #s(hole binary64 (/ p x)))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* -1/4 (/ x p))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (/ (+ (* -1/4 x) (* 1/2 p)) p)))
#s(approx (/ (* p p) (* x x)) #s(hole binary64 (/ (pow p 2) (pow x 2))))
#s(approx (* p p) #s(hole binary64 (pow p 2)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 2))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* -2 (/ (pow p 2) (pow x 2))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 -1))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (- (* 2 (/ (pow p 2) (pow x 2))) 1)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (sqrt 1/2)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 1/2))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* 1/4 (/ x p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (+ 1/2 (* -1/4 (/ x p)))))
#s(approx (- 1 (/ (* p p) (* x x))) #s(hole binary64 (* -1 (/ (pow p 2) (pow x 2)))))
#s(approx (- 1 (/ (* p p) (* x x))) #s(hole binary64 (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* 1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* 1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (* 2 (/ (pow p 2) (pow x 2)))))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1/2 (/ x p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1/2 (/ x p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))))
#s(approx x #s(hole binary64 x))
#s(approx (- 1 (/ (* p p) (* x x))) #s(hole binary64 (/ (- (pow x 2) (pow p 2)) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))))
#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) #s(hole binary64 (/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (+ (* (/ x p) 1/4) 1/2) #s(hole binary64 (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))))
#s(approx (+ (* -1/4 (/ x p)) 1/2) #s(hole binary64 (* x (- (* 1/2 (/ 1 x)) (* 1/4 (/ 1 p))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) #s(hole binary64 (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(hole binary64 (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))))
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#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) #s(hole binary64 (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) #s(hole binary64 (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)))
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Outputs
(pow.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
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#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
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(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 p)))
(/.f64 (neg.f64 x) (neg.f64 p))
(/.f64 x p)
(neg.f64 (/.f64 x (neg.f64 p)))
(neg.f64 (/.f64 (neg.f64 x) p))
x
p
#s(literal 1/4 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (/.f64 (neg.f64 p) x))
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(*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x))
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(/.f64 (neg.f64 p) (neg.f64 (neg.f64 x)))
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(neg.f64 (/.f64 (neg.f64 p) x))
(pow.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))) #s(literal 1/2 binary64))
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#s(literal -1/4 binary64)
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#s(literal -1 binary64)
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#s(approx x x)
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#s(approx (* x x) (*.f64 x x))
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#s(approx (+ (* (/ (* p p) (* x x)) 2) -1) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal 2 binary64) #s(literal -1 binary64)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (-.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 p (/.f64 p (*.f64 x x))) #s(literal 1/2 binary64))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (-.f64 (fma.f64 (.f64 (/.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (.f64 p p)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal 1/2 binary64))))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 (-.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal -1/4 binary64)) (.f64 p (/.f64 p (*.f64 x x)))) #s(literal -1 binary64)))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 p (/.f64 p (.f64 x x)))) (.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64)) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -6 binary64)))))))
#s(approx (+ (* (/ x p) 1/4) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/4 binary64) p)) x))
#s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) p) (/.f64 #s(literal -1/2 binary64) x)) x))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (-.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -4 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -2 binary64)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (-.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64)) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -6 binary64)))) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -2 binary64)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (-.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -4 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -1 binary64)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64)) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -6 binary64)))) (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -1 binary64)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (/.f64 (neg.f64 p) x))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 (fma.f64 (.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64) p) x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (/.f64 (fma.f64 (.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) p))) (neg.f64 x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (/.f64 (fma.f64 (.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (-.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 #s(literal 1 binary64) p)))) (neg.f64 x)))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (.f64 p p)) (.f64 x x)))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 p p))) (*.f64 x x)))
#s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal -6 binary64))) #s(literal 1/4 binary64) (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 p p)))) (.f64 x x)))
#s(approx (+ (* -1/4 (/ x p)) 1/2) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1/4 binary64) p)) x)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (.f64 (.f64 p p) #s(literal 2 binary64))) (*.f64 x x)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 (.f64 p p) #s(literal 2 binary64)))) (.f64 x x)))
#s(approx (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) (/.f64 (fma.f64 (.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal -6 binary64))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal -4 binary64))) (.f64 (.f64 p p) #s(literal 2 binary64))))) (*.f64 x x)))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal -4 binary64))) #s(literal 1/2 binary64) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal 2 binary64) #s(literal -1 binary64))))
#s(approx (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (pow.f64 x #s(literal -4 binary64)) (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal -6 binary64)) (/.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (.f64 x x)))) #s(literal 1 binary64)))

eval50.0ms (1.5%)

Memory: -3.7MiB live, 94.7MiB allocated; 15ms collecting garbage
Compiler: Compiled 4 842 to 2 019 computations (58.3% saved)

prune20.0ms (0.6%)

Memory

-0.4MiB live, 45.2MiB allocated; 4ms collecting garbage

Pruning

17 alts after pruning (4 fresh and 13 done)

	Pruned	Kept	Total
New	412	1	413
Fresh	0	3	3
Picked	0	5	5
Done	0	8	8
Total	412	17	429

Accuracy

96.7%

Counts

429 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
✓	81.1%	(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
✓	77.7%	(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
✓	6.3%	(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
✓	51.8%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
✓	50.2%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
✓	28.4%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
	18.3%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
✓	2.5%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
✓	56.0%	(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
✓	14.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
✓	18.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
✓	51.6%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	28.8%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
	24.0%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x)))
✓	24.1%	#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
✓	38.3%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Compiler

Compiled 718 to 477 computations (33.6% saved)

regimes68.0ms (2%)

Memory

-2.1MiB live, 96.4MiB allocated; 9ms collecting garbage

Counts

33 → 2

Calls

Call 1

Inputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (.f64 p (/.f64 p (.f64 x x))))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 p p))))
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))))))
(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))))))
(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 1 binary64))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))

Outputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
(sqrt.f64 (.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))

Outputs

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))

(sqrt.f64 (*.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))

Calls

7 calls:

20.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
11.0ms	p
9.0ms	x
7.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
6.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
81.1%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
100.0%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
100.0%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
100.0%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
81.1%	1	`p`
84.2%	2	`x`

Compiler

Compiled 53 to 56 computations (-5.7% saved)

regimes27.0ms (0.8%)

Memory

-1.2MiB live, 45.0MiB allocated; 3ms collecting garbage

Counts

29 → 2

Calls

Call 1

Inputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (.f64 p (/.f64 p (.f64 x x))))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 p p))))
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))))))
(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))))))

Outputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
(sqrt.f64 (.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ ( x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))

Outputs

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))

(sqrt.f64 (*.f64 (-.f64 (/.f64 x #s(approx (sqrt (+ (* x x) (* (* p 4) p))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))

Calls

4 calls:

7.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
6.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
6.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
98.5%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
98.5%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.5%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.5%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`

Compiler

Compiled 47 to 47 computations (0% saved)

regimes25.0ms (0.7%)

Memory

7.9MiB live, 54.0MiB allocated; 2ms collecting garbage

Counts

27 → 3

Calls

Call 1

Inputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (.f64 p (/.f64 p (.f64 x x))))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (- 1 (* (/ (* p p) (* x x)) 1/2)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 p p))))
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 (-.f64 #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))))))

Outputs

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))

(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))

#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (fma.f64 (*.f64 p (/.f64 p (*.f64 x x))) #s(literal -1/2 binary64) #s(literal 1 binary64)))

Calls

4 calls:

6.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
6.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
5.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
5.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
99.2%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
99.2%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.2%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.2%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`

Compiler

Compiled 47 to 47 computations (0% saved)

regimes20.0ms (0.6%)

Memory

-3.1MiB live, 42.3MiB allocated; 4ms collecting garbage

Counts

19 → 3

Calls

Call 1

Inputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (.f64 p (/.f64 p (.f64 x x))))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))))

Outputs

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))

(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))

(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))

Calls

4 calls:

6.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
4.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
99.2%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
99.2%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.2%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.2%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`

Compiler

Compiled 47 to 47 computations (0% saved)

regimes19.0ms (0.5%)

Memory

-13.4MiB live, 36.0MiB allocated; 6ms collecting garbage

Counts

16 → 3

Calls

Call 1

Inputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))

Outputs

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))

(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Calls

4 calls:

7.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
3.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
99.1%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
99.1%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.1%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.1%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`

Compiler

Compiled 47 to 47 computations (0% saved)

regimes11.0ms (0.3%)

Memory

19.3MiB live, 19.3MiB allocated; 0ms collecting garbage

Counts

10 → 3

Calls

Call 1

Inputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (neg.f64 (/.f64 p x)))
#s(approx (sqrt (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2)) (*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) #s(approx (/ x (sqrt (+ ( x x) (* (* p 4) p)))) #s(literal -1 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(approx (+ (* -1/4 (/ x p)) 1/2) (*.f64 (/.f64 x p) #s(literal -1/4 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))

Outputs

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (neg.f64 (/.f64 p x)))

(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Calls

4 calls:

3.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
2.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
2.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
98.5%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
98.5%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.5%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.5%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`

Compiler

Compiled 47 to 47 computations (0% saved)

regimes10.0ms (0.3%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))

(sqrt.f64 #s(approx (* (- (/ x (sqrt (+ (* x x) (* (* p 4) p)))) -1) 1/2) #s(literal 1/2 binary64)))

Outputs
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Calls

7 calls:

1.0ms	x
1.0ms	p
1.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
1.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
1.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
73.2%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
73.2%	2	`p`
61.8%	2	`x`
77.7%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
77.7%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
77.7%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
77.7%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`

Compiler

Compiled 53 to 56 computations (-5.7% saved)

regimes29.0ms (0.8%)

Memory

-32.9MiB live, 14.2MiB allocated; 1ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Outputs
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(literal 1 binary64))

Calls

7 calls:

23.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
1.0ms	x
1.0ms	p
1.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
1.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)

Results

Accuracy	Segments	Branch
38.3%	1	`x`
38.3%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
38.3%	1	`p`
38.3%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
38.3%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
38.3%	1	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
38.3%	1	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`

Compiler

Compiled 53 to 56 computations (-5.7% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	0.10448456218903679

Compiler

Compiled 17 to 19 computations (-11.8% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.10448456218903679	0.7071012464016306

Compiler

Compiled 17 to 19 computations (-11.8% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.7071067813937039	0.9698054731577692
0.0ms	0.10448456218903679	0.7071012464016306

Compiler

Compiled 17 to 19 computations (-11.8% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.7071067813937039	0.9698054731577692
0.0ms	0.10448456218903679	0.7071012464016306

Compiler

Compiled 17 to 19 computations (-11.8% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.7071067813937039	0.9698054731577692
0.0ms	0.10448456218903679	0.7071012464016306

Compiler

Compiled 17 to 19 computations (-11.8% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.7071067813937039	0.9698054731577692
0.0ms	0.10448456218903679	0.7071012464016306

Compiler

Compiled 17 to 19 computations (-11.8% saved)

bsearch4.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.7071067813937039	0.9698054731577692

Samples

1.0ms

64×

valid

Compiler

Compiled 145 to 155 computations (-6.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0% of total)

derivations261.0ms (7.6%)

Memory

-10.7MiB live, 218.1MiB allocated; 74ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 148 to 92 computations (37.8% saved)

preprocess70.0ms (2%)

Memory: -30.6MiB live, 157.4MiB allocated; 22ms collecting garbage
Remove: (abs p)
Compiler: Compiled 941 to 744 computations (20.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze542.0ms (15.7%)

sample1.2s (33.5%)

preprocess48.0ms (1.4%)

series29.0ms (0.8%)

rewrite170.0ms (4.9%)

eval26.0ms (0.8%)

prune13.0ms (0.4%)

series19.0ms (0.6%)

rewrite233.0ms (6.8%)

eval66.0ms (1.9%)

prune14.0ms (0.4%)

series30.0ms (0.9%)

rewrite200.0ms (5.8%)

eval42.0ms (1.2%)

prune13.0ms (0.4%)

series19.0ms (0.5%)

rewrite212.0ms (6.2%)

eval50.0ms (1.5%)

prune20.0ms (0.6%)

regimes68.0ms (2%)

regimes27.0ms (0.8%)

regimes25.0ms (0.7%)

regimes20.0ms (0.6%)

regimes19.0ms (0.5%)

regimes11.0ms (0.3%)

regimes10.0ms (0.3%)

regimes29.0ms (0.8%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch4.0ms (0.1%)

derivations261.0ms (7.6%)

preprocess70.0ms (2%)

end0.0ms (0%)

Profiling