Given's Rotation SVD example

Time bar (total: 12.7s)

analyze452.0ms (3.6%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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 28 to 20 computations (28.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 260.0ms
ival-mult: 99.0ms (38.1% of total)
ival-add: 46.0ms (17.7% of total)
ival-sqrt: 42.0ms (16.2% of total)
ival-<: 22.0ms (8.5% of total)
ival-div: 20.0ms (7.7% of total)
ival-fabs: 20.0ms (7.7% of total)
const: 6.0ms (2.3% of total)
ival-and: 3.0ms (1.2% of total)
backward-pass: 1.0ms (0.4% of total)

sample1.9s (14.8%)

Results
826.0ms6236×0valid
251.0ms1043×1valid
365.0ms977×2valid
Precisions
Click to see histograms. Total time spent on operations: 1.1s
ival-mult: 362.0ms (32.7% of total)
ival-sqrt: 223.0ms (20.1% of total)
ival-add: 172.0ms (15.5% of total)
ival-div: 92.0ms (8.3% of total)
backward-pass: 91.0ms (8.2% of total)
ival-<: 73.0ms (6.6% of total)
ival-fabs: 61.0ms (5.5% of total)
const: 25.0ms (2.3% of total)
ival-and: 10.0ms (0.9% of total)
Bogosity

preprocess63.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
248×distribute-lft-neg-in
218×unsub-neg
196×associate-*r*
196×associate-*l*
166×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042108
1102104
2202104
3407104
4666104
51003104
61335104
71547104
81699104
91935104
102002104
112030104
122032104
01417
12917
23617
33817
43917
03915
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
Outputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))))
Call 2
Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))
Outputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt (+ 1/2 (* 1/2 (/ x (sqrt (+ (* 4 (* p p)) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (+ 1/2 (* 1/2 (/ x (sqrt (+ (* 4 (* p p)) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(sqrt (+ 1/2 (* (/ x (sqrt (+ (* 4 (* p p)) (* x x)))) -1/2)))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (+ 1/2 (* 1/2 (/ x (sqrt (+ (* 4 (* p p)) (* x x))))))))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(neg (sqrt (+ 1/2 (* (/ x (sqrt (+ (* 4 (* p p)) (* x x)))) -1/2))))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))
(sqrt (+ 1/2 (/ (* 1/2 p) (sqrt (+ (* x (* x 4)) (* p p))))))
Symmetry

(abs p)

explain301.0ms (2.4%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
640-0-(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
230-0-(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
220-2(5.802980117444558e-34 -1.0662513461966296e+127)(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)))))))
00-0-x
00-0-#s(literal 1/2 binary64)
00-0-(*.f64 #s(literal 4 binary64) p)
00-0-(*.f64 (*.f64 #s(literal 4 binary64) p) p)
00-0-(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
00-0-p
00-0-(*.f64 x x)
00-0-#s(literal 4 binary64)
00-0-(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
00-0-#s(literal 1 binary64)
00-0-(*.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
134.0ms414×0valid
53.0ms52×2valid
33.0ms46×1valid
Compiler

Compiled 213 to 126 computations (40.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 167.0ms
ival-mult: 72.0ms (43.1% of total)
ival-sqrt: 31.0ms (18.5% of total)
ival-add: 29.0ms (17.3% of total)
ival-div: 19.0ms (11.4% of total)
backward-pass: 12.0ms (7.2% of total)
const: 5.0ms (3% of total)

eval0.0ms (0%)

Compiler

Compiled 19 to 14 computations (26.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶84.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))))
Compiler

Compiled 19 to 14 computations (26.3% saved)

localize149.0ms (1.2%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))))
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) x)
✓accuracy92.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))))
✓accuracy92.2%
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
✓accuracy76.7%
(sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))
Rules
32×*-lowering-*.f32
32×*-lowering-*.f64
18×accelerator-lowering-fma.f32
18×accelerator-lowering-fma.f64
12×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01384
12184
22784
33184
43584
53784
03777
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))
1/2
(/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))
(* 1/2 x)
x
(sqrt (+ (* p (* 4 p)) (* x x)))
(+ (* p (* 4 p)) (* x x))
(* p (* 4 p))
p
(* 4 p)
4
(* x x)
Outputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(sqrt (+ (* p (* 4 p)) (* x x)))
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(+ (* p (* 4 p)) (* x x))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
(* p (* 4 p))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
p
(* 4 p)
(*.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
(* x x)
(*.f64 x x)
Results
63.0ms207×0valid
23.0ms26×2valid
14.0ms23×1valid
Compiler

Compiled 87 to 51 computations (41.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 77.0ms
ival-mult: 34.0ms (44.1% of total)
ival-add: 16.0ms (20.8% of total)
ival-sqrt: 13.0ms (16.9% of total)
ival-div: 7.0ms (9.1% of total)
backward-pass: 6.0ms (7.8% of total)
const: 2.0ms (2.6% of total)

series21.0ms (0.2%)

Counts
5 → 108
Calls
Call 1
Inputs
#<alt (sqrt (+ (* p (* 4 p)) (* x x)))>
#<alt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))>
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))))>
#<alt (* 1/2 x)>
#<alt (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))>
Outputs
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* 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)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -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))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 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)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 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))>
#<alt (/ (+ (* 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))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 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)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 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)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 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)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1/2 (+ (* -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))))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)>
#<alt (- (+ (* 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))) (/ (pow p 2) (pow x 2)))) 1/2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -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)>
#<alt (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)>
#<alt (* -1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))>
#<alt (* -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))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))>
Calls

27 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))))
1.0ms
x
@-inf
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))
1.0ms
x
@inf
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))
1.0ms
p
@inf
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))
1.0ms
x
@0
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))

rewrite515.0ms (4.1%)

Algorithm
1×batch-egg-rewrite
Rules
4842×accelerator-lowering-fma.f32
4842×accelerator-lowering-fma.f64
3888×*-lowering-*.f32
3888×*-lowering-*.f64
2592×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01360
16060
246160
3649460
0814654
Stop Event
1×iter limit
1×node limit
Counts
5 → 200
Calls
Call 1
Inputs
(sqrt (+ (* p (* 4 p)) (* x x)))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x)))))
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))))
(* 1/2 x)
(/ (* 1/2 x) (sqrt (+ (* p (* 4 p)) (* x x))))
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x)))))) (sqrt.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x)))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x))))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x))))))) (neg.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(*.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (neg.f64 (/.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (/.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (neg.f64 (/.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/2 binary64) (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
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(/.f64 (sqrt.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal -1/4 binary64))) (sqrt.f64 (+.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(neg.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(neg.f64 (*.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) x))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64))))
(/.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64)))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64)))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64))
(*.f64 (*.f64 x #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))))
(*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 #s(literal -1/2 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(*.f64 #s(literal -1/2 binary64) (*.f64 x (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/2 binary64) (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(*.f64 (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) x)
(*.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) (*.f64 x x))))))) (sqrt.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))

simplify656.0ms (5.2%)

Algorithm
1×egg-herbie
Rules
12742×accelerator-lowering-fma.f32
12742×accelerator-lowering-fma.f64
6156×*-lowering-*.f32
6156×*-lowering-*.f64
5216×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03802102
111132051
236631988
080271840
Stop Event
1×iter limit
1×node limit
Counts
108 → 108
Calls
Call 1
Inputs
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 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)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -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))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 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)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 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))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 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))
(/ (+ (* 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))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 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)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 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)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 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)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/4 (/ x p))
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1/2 (+ (* -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))))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)
(- (+ (* 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))) (/ (pow p 2) (pow x 2)))) 1/2)
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -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)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(* -1/4 (/ x p))
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(* -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))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
Outputs
x
(+ x (* 2 (/ (pow p 2) x)))
(+.f64 x (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+.f64 x (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -2 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(+.f64 x (*.f64 p (*.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x x)))))))))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p) (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 p p) (*.f64 p p))))))
(* 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)))))))
(*.f64 p (+.f64 #s(literal 2 binary64) (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p) (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 p p) (*.f64 p p)))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64))))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p) (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 p p) (*.f64 p p))))) (-.f64 #s(literal 0 binary64) p))
(* -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))))))))
(*.f64 p (+.f64 #s(literal -2 binary64) (neg.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p) (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 p p) (*.f64 p p)))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))))))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(+ (* 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)))))
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x)))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x)) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x)) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p)))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 p p) (*.f64 x x))))
(+ 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))))))
(+.f64 #s(literal 1 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 p p) (*.f64 x x))) (/.f64 (+.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -16 binary64)) (*.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) #s(literal -1/2 binary64))) (pow.f64 x #s(literal 6 binary64)))))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (+.f64 (*.f64 p p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x x))) (*.f64 x x))
(/ (+ (* 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))
(/.f64 (+.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x x)) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 x x))
(/ (+ (* 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))
(/.f64 (+.f64 (+.f64 (*.f64 p p) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64))) (+.f64 (*.f64 #s(literal -256 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 p p))))) (pow.f64 x #s(literal 6 binary64)))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -10 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
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1
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1
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(* 1/2 x)
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1/2
#s(literal 1/2 binary64)
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1/2
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(/.f64 (+.f64 (*.f64 (/.f64 x p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) p)) (*.f64 x (+.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/2 binary64)) #s(literal 1/4 binary64)))) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(/.f64 (+.f64 (*.f64 (/.f64 x p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) p)) (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/256 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (pow.f64 p #s(literal 6 binary64))))))) p)
(* -1/4 (/ x p))
(/.f64 (*.f64 x #s(literal -1/4 binary64)) p)
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 (/.f64 x p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) p)) (*.f64 x #s(literal 1/4 binary64))) p))
(* -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))
(/.f64 (+.f64 (*.f64 (/.f64 x p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) p)) (*.f64 x (+.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/2 binary64)) #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(/.f64 (+.f64 (*.f64 (/.f64 x p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) p)) (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/256 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (pow.f64 p #s(literal 6 binary64))))))) (-.f64 #s(literal 0 binary64) p))

eval109.0ms (0.9%)

Compiler

Compiled 10373 to 5571 computations (46.3% saved)

prune49.0ms (0.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New29711308
Fresh000
Picked011
Done000
Total29712309
Accuracy
100.0%
Counts
309 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶83.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
▶18.0%
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x))
21.4%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
52.6%
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
81.4%
(sqrt.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
▶57.7%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
57.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
20.6%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)))))
✓84.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))))
▶52.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
57.2%
(sqrt.f64 #s(literal 1/2 binary64))
▶40.5%
#s(literal 1 binary64)
Compiler

Compiled 439 to 304 computations (30.8% saved)

localize790.0ms (6.2%)

Algorithm
1×egg-herbie
Localize:

Found 32 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
✓cost-diff128
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))
✓cost-diff128
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))))
✓cost-diff128
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
✓cost-diff384
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))
✓cost-diff384
(+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p))))
✓cost-diff384
(/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x)
✓cost-diff512
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
✓accuracy99.9%
(*.f64 p (*.f64 p p))
✓accuracy99.3%
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))
✓accuracy98.3%
(*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
✓accuracy93.4%
(/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p)))
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
✓accuracy100.0%
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
✓accuracy97.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
✓accuracy99.8%
(*.f64 (*.f64 p p) (*.f64 p p))
✓accuracy99.7%
(*.f64 x (*.f64 x p))
✓accuracy97.5%
(/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x)
✓accuracy75.6%
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
✓accuracy100.0%
(*.f64 #s(literal 4 binary64) (*.f64 p p))
✓accuracy99.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
✓accuracy76.7%
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
Rules
4896×*-lowering-*.f32
4896×*-lowering-*.f64
4488×accelerator-lowering-fma.f32
4488×accelerator-lowering-fma.f64
3204×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047402
1111388
2299388
31125379
43518379
54697379
65771379
08030352
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))))
1
(sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))
(+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))
1/2
(/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))
(* x 1/2)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(+ (* 4 (* p p)) (* x x))
(* 4 (* p p))
4
(* p p)
p
(* x x)
(- 0 (/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x))
0
(/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x)
(+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p))))
(/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))
(* (* (* (* p p) (* p p)) -12) 1/8)
(* (* (* p p) (* p p)) -12)
(* (* p p) (* p p))
-12
1/8
(* x (* x p))
(* x p)
(sqrt (+ 1/2 (* 1/4 (/ x p))))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
1/4
(/ x p)
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))))
(+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))))
(/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))
(* 1/2 x)
(+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))
(* 2 p)
2
(* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))
(+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))
(/ (* (* x x) -1/64) (* p (* p p)))
(* (* x x) -1/64)
-1/64
(* p (* p p))
(/ 1/4 p)
Outputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
1/2
#s(literal 1/2 binary64)
(/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(* x 1/2)
(*.f64 #s(literal 1/2 binary64) x)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(+ (* 4 (* p p)) (* x x))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
(* 4 (* p p))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
4
#s(literal 4 binary64)
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)
(- 0 (/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x))
(/.f64 (*.f64 p (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 p (*.f64 p (/.f64 #s(literal -3/2 binary64) x))) x))) x)
0
#s(literal 0 binary64)
(/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x)
(/.f64 (*.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p (/.f64 #s(literal -3/2 binary64) x))) x))) x)
(+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p))))
(*.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p (/.f64 #s(literal -3/2 binary64) x))) x)))
(/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))
(/.f64 (*.f64 (*.f64 p p) (*.f64 p #s(literal -3/2 binary64))) (*.f64 x x))
(* (* (* (* p p) (* p p)) -12) 1/8)
(*.f64 p (*.f64 (*.f64 p p) (*.f64 p #s(literal -3/2 binary64))))
(* (* (* p p) (* p p)) -12)
(*.f64 (*.f64 p p) (*.f64 p (*.f64 p #s(literal -12 binary64))))
(* (* p p) (* p p))
(*.f64 (*.f64 p p) (*.f64 p p))
-12
#s(literal -12 binary64)
1/8
#s(literal 1/8 binary64)
(* x (* x p))
(*.f64 x (*.f64 x p))
(* x p)
(*.f64 x p)
(sqrt (+ 1/2 (* 1/4 (/ x p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
1/4
#s(literal 1/4 binary64)
(/ x p)
(/.f64 x p)
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p p))))))))
(+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p p)))))))
(/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p p))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p p)))))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))
(*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p p))))
(+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))
(+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))
(/ (* (* x x) -1/64) (* p (* p p)))
(/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p)))
(* (* x x) -1/64)
(*.f64 x (*.f64 x #s(literal -1/64 binary64)))
-1/64
#s(literal -1/64 binary64)
(* p (* p p))
(*.f64 p (*.f64 p p))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
Results
230.0ms206×0valid
54.0ms50×0invalid
Compiler

Compiled 465 to 209 computations (55.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 214.0ms
ival-mult: 91.0ms (42.5% of total)
ival-div: 59.0ms (27.5% of total)
ival-add: 32.0ms (14.9% of total)
ival-sqrt: 17.0ms (7.9% of total)
const: 8.0ms (3.7% of total)
ival-sub: 6.0ms (2.8% of total)
backward-pass: 0.0ms (0% of total)

series82.0ms (0.6%)

Counts
23 → 516
Calls
Call 1
Inputs
#<alt (sqrt (+ (* 4 (* p p)) (* x x)))>
#<alt (/ 1 (sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))))>
#<alt (* 4 (* p p))>
#<alt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))>
#<alt (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))>
#<alt (/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x)>
#<alt (* x (* x p))>
#<alt (* (* p p) (* p p))>
#<alt (sqrt (+ 1/2 (* 1/4 (/ x p))))>
#<alt (* 1/4 (/ x p))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (/ x p)>
#<alt (/ (* (* x x) -1/64) (* p (* p p)))>
#<alt (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))>
#<alt (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))>
#<alt (* p (* p p))>
#<alt (sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))))>
#<alt (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))>
#<alt (- 0 (/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x))>
#<alt (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p))))>
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))))>
#<alt (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))>
Outputs
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* 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)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -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))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 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)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 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)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))>
#<alt (+ 2 (* x (- (* x (+ (* -1/8 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))>
#<alt (/ (pow x 2) (pow p 2))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (/ 1 (pow p 2))) (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2))))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 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 p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 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 p 4) (pow x 4))))))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))>
#<alt (- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))>
#<alt 2>
#<alt (+ 2 (/ x p))>
#<alt (+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))>
#<alt (+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (/ p x)>
#<alt (* p (+ (* -3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (+ (* -3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (+ (* -3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 3))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 3))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 3))>
#<alt (/ p x)>
#<alt (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ p x)>
#<alt (* -1 (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))>
#<alt (* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/1024 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))>
#<alt (/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))) (pow x 4)))) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 16 (* (pow p 2) (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))))) (* 65536 (pow p 9))) (pow x 6)))) (+ (* 512 (/ (pow p 5) (pow x 2))) (+ (* 4096 (/ (pow p 7) (pow x 4))) (* 8192 (/ (pow p 7) (pow x 4)))))) (pow x 3))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (/ (+ (* 32 (pow p 3)) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* -8192 (pow p 7)) (* -4096 (pow p 7))) (pow x 4))) (* 32 (pow p 3))) (* -512 (/ (pow p 5) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* -65536 (pow p 9)) (* 16 (* (pow p 2) (+ (* -8192 (pow p 7)) (* -4096 (pow p 7)))))) (pow x 6))) (* 32 (pow p 3))) (+ (* -8192 (/ (pow p 7) (pow x 4))) (+ (* -4096 (/ (pow p 7) (pow x 4))) (* -512 (/ (pow p 5) (pow x 2)))))) (pow x 3)))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* (pow p 2) (- (* (pow p 2) (- (* -262144 (/ (pow p 2) (pow x 9))) (* 12288 (/ 1 (pow x 7))))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))))) (* 1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)>
#<alt (* 1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))))) (* -1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (* 1/2 (/ (pow p 2) (pow x 2)))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (pow p 2) (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (pow x 6))) (* 1/2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (+ (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow p 2))) (* 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 p 4))))))) (pow x 6))) (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (+ (* -9/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 49/16 (/ (pow p 2) (pow x 6))) (* 9/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2))))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* (pow p 3) (sqrt 2)))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1/2 (/ x (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* p (sqrt 2))))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (sqrt 2))) (* 1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* p (sqrt 2))))) p)) (* -1/2 (/ x (sqrt 2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 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))>
#<alt (/ (+ (* 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))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 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)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 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)))>
#<alt (* -1 (/ p x))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (/ (- (* -1 (* p (pow x 2))) (* -3/2 (pow p 3))) (pow x 3))>
#<alt (/ (- (* -1 (* p (pow x 2))) (* -3/2 (pow p 3))) (pow x 3))>
#<alt (/ (- (* -1 (* p (pow x 2))) (* -3/2 (pow p 3))) (pow x 3))>
#<alt (* -1 (/ p x))>
#<alt (/ (- (* 3/2 (/ (pow p 3) (pow x 2))) p) x)>
#<alt (/ (- (* 3/2 (/ (pow p 3) (pow x 2))) p) x)>
#<alt (/ (- (* 3/2 (/ (pow p 3) (pow x 2))) p) x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (- (* -3/2 (/ (pow p 3) (pow x 2))) (* -1 p)) x))>
#<alt (* -1 (/ (- (* -3/2 (/ (pow p 3) (pow x 2))) (* -1 p)) x))>
#<alt (* -1 (/ (- (* -3/2 (/ (pow p 3) (pow x 2))) (* -1 p)) x))>
#<alt p>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt p>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt p>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/32 (pow x 3)) (* 1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))>
#<alt (+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))))>
#<alt (+ 1/2 (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p)))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* 2 p)>
#<alt (* -1 (* p (- (* -1/4 (/ (pow x 2) (pow p 2))) 2)))>
#<alt (* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))>
#<alt (* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
Calls

129 calls:

TimeVariablePointExpression
6.0ms
x
@-inf
(* 1/4 (/ x p))
5.0ms
x
@inf
(* 1/4 (/ x p))
5.0ms
p
@inf
(/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))
3.0ms
x
@0
(/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))
3.0ms
x
@-inf
(sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))))

rewrite495.0ms (3.9%)

Algorithm
1×batch-egg-rewrite
Rules
4466×/-lowering-/.f32
4466×/-lowering-/.f64
3874×*-lowering-*.f32
3874×*-lowering-*.f64
2798×pow-lowering-pow.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047315
1280300
22773300
08482255
Stop Event
1×iter limit
1×node limit
Counts
23 → 736
Calls
Call 1
Inputs
(sqrt (+ (* 4 (* p p)) (* x x)))
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))))
(* 4 (* p p))
(/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))
(/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))
(/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x)
(* x (* x p))
(* (* p p) (* p p))
(sqrt (+ 1/2 (* 1/4 (/ x p))))
(* 1/4 (/ x p))
(+ 1/2 (* 1/4 (/ x p)))
(/ x p)
(/ (* (* x x) -1/64) (* p (* p p)))
(* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))
(/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))
(* p (* p p))
(sqrt (/ 1 (+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(+ 1/2 (/ (* x 1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))
(- 0 (/ (+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p)))) x))
(+ p (/ (* (* (* (* p p) (* p p)) -12) 1/8) (* x (* x p))))
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p)))))))
(+ 1/2 (/ (* 1/2 x) (+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))))
(+ (* 2 p) (* (* x x) (+ (/ (* (* x x) -1/64) (* p (* p p))) (/ 1/4 p))))
Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))
(hypot.f64 x (*.f64 p #s(literal 2 binary64)))
(hypot.f64 (*.f64 p #s(literal 2 binary64)) x)
(hypot.f64 (*.f64 p #s(literal 2 binary64)) (neg.f64 x))
(hypot.f64 (*.f64 p #s(literal 2 binary64)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (*.f64 p #s(literal 2 binary64)))
(hypot.f64 (exp.f64 (log.f64 x)) (*.f64 p #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))) (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 (*.f64 p (*.f64 p p)) #s(literal 1/64 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (-.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(/.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
(/.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 p p) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 (*.f64 p (*.f64 p p)) #s(literal 1/64 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))))) (sqrt.f64 (neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)))) (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
(/.f64 (neg.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(pow.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))
(*.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (pow.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))) (/.f64 #s(literal 1/2 binary64) (/.f64 (hypot.f64 x (*.f64 p #s(literal 2 binary64))) (*.f64 x #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 3/2 binary64)))) (sqrt.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))) (/.f64 #s(literal 1/2 binary64) (/.f64 (hypot.f64 x (*.f64 p #s(literal 2 binary64))) (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 (hypot.f64 x (*.f64 p #s(literal 2 binary64))) (*.f64 x #s(literal 1/2 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 3/2 binary64)))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))) (/.f64 #s(literal 1/2 binary64) (/.f64 (hypot.f64 x (*.f64 p #s(literal 2 binary64))) (*.f64 x #s(literal 1/2 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) (sqrt.f64 #s(literal -1 binary64)))
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(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))))) (neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))) (neg.f64 (-.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 4 binary64) (*.f64 p p))) (-.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))) (neg.f64 (neg.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (-.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))))) (neg.f64 (neg.f64 (-.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) (neg.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64)))))
(pow.f64 (/.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (-.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64))))) (+.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))) #s(literal -1 binary64))
(*.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (-.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64)))))))
(*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))))

simplify644.0ms (5.1%)

Algorithm
1×egg-herbie
Rules
9774×accelerator-lowering-fma.f32
9774×accelerator-lowering-fma.f64
8164×*-lowering-*.f32
8164×*-lowering-*.f64
4980×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010327964
130407743
085497341
Stop Event
1×iter limit
1×node limit
Counts
516 → 516
Calls
Call 1
Inputs
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 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)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -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))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 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)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 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)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))
(+ 2 (* x (- (* x (+ (* -1/8 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))
1
(+ 1 (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))
(/ (pow x 2) (pow p 2))
(* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (/ 1 (pow p 2))) (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2))))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 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 p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 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 p 4) (pow x 4))))))))
1
(+ 1 (/ (pow p 2) (pow x 2)))
(+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
2
(+ 2 (* -1 (/ x p)))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
(- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
2
(+ 2 (/ x p))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))
(+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(/ p x)
(* p (+ (* -3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
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(/ p x)
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(/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)
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(/ p x)
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(* p (pow x 2))
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(sqrt 1/2)
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1/2
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1/2
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(/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 16 (* (pow p 2) (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))))) (* 65536 (pow p 9))) (pow x 6)))) (+ (* 512 (/ (pow p 5) (pow x 2))) (+ (* 4096 (/ (pow p 7) (pow x 4))) (* 8192 (/ (pow p 7) (pow x 4)))))) (pow x 3))
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(* (pow p 3) (- (* (pow p 2) (- (* (pow p 2) (- (* -262144 (/ (pow p 2) (pow x 9))) (* 12288 (/ 1 (pow x 7))))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))
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(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)
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(pow p 3)
(pow p 3)
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(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
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(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
1
(+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))
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(* -1 (/ x p))
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(* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p)))))
(* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (+ (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow p 2))) (* 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 p 4))))))) (pow x 6))) (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))))
1
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(sqrt 2)
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(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* (pow p 3) (sqrt 2)))))))
(sqrt 2)
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1/2
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1
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(/ (pow p 2) (pow x 2))
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(/ (+ (* 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))
(/ (+ (* 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))
1
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1/2
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1/2
(+ 1/2 (* -1/4 (/ x p)))
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(* -1 (/ p x))
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(* 3/2 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/ (- (* -1 (* p (pow x 2))) (* -3/2 (pow p 3))) (pow x 3))
(/ (- (* -1 (* p (pow x 2))) (* -3/2 (pow p 3))) (pow x 3))
(/ (- (* -1 (* p (pow x 2))) (* -3/2 (pow p 3))) (pow x 3))
(* -1 (/ p x))
(/ (- (* 3/2 (/ (pow p 3) (pow x 2))) p) x)
(/ (- (* 3/2 (/ (pow p 3) (pow x 2))) p) x)
(/ (- (* 3/2 (/ (pow p 3) (pow x 2))) p) x)
(* -1 (/ p x))
(* -1 (/ (- (* -3/2 (/ (pow p 3) (pow x 2))) (* -1 p)) x))
(* -1 (/ (- (* -3/2 (/ (pow p 3) (pow x 2))) (* -1 p)) x))
(* -1 (/ (- (* -3/2 (/ (pow p 3) (pow x 2))) (* -1 p)) x))
p
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/32 (pow x 3)) (* 1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))
(+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))))
(+ 1/2 (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p)))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 2 p)
(* -1 (* p (- (* -1/4 (/ (pow x 2) (pow p 2))) 2)))
(* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))
(* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
Outputs
x
(+ x (* 2 (/ (pow p 2) x)))
(+.f64 x (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+.f64 x (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 p p)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(+.f64 x (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p (*.f64 p (+.f64 (/.f64 (*.f64 p (*.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x x)))))))))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))) (/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 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)))))))
(*.f64 p (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))) (/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (neg.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p)))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))) (/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) p))
(* -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))))))))
(*.f64 (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))) (/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) p))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 x x)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(+ (* 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)))))
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x x)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 x x))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 x x)) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 x x)) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 x x)))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 x x)) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 x x)) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) x) (*.f64 (*.f64 p p) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 p (*.f64 (*.f64 p p) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/128 binary64) (*.f64 (*.f64 p p) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 p p)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 p p)) (*.f64 x x)) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (pow.f64 x #s(literal 4 binary64)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64)))))) (pow.f64 x #s(literal 6 binary64))))))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 p (*.f64 (/.f64 #s(literal 1/8 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 x x)))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (+.f64 p (*.f64 (/.f64 #s(literal 1/8 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 x x)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (*.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 #s(literal -1/64 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))))) x))
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2
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2
#s(literal 2 binary64)
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1
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(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal -16 binary64) (*.f64 p (*.f64 p p))) (*.f64 (*.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (*.f64 (*.f64 p p) (+.f64 (*.f64 (/.f64 #s(literal -256 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (*.f64 p p) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 1/2 binary64))))))))
(+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 p (*.f64 p p)) (+.f64 (*.f64 (*.f64 p p) (+.f64 (*.f64 (/.f64 #s(literal -128 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 p (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -256 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 1/2 binary64)))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/128 binary64) (*.f64 x x)) (*.f64 (*.f64 p p) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/128 binary64) (*.f64 x x)) (*.f64 (*.f64 p p) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/32 binary64)) (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (*.f64 (*.f64 p p) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/128 binary64) (*.f64 x x)) (*.f64 p (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/32 (pow x 3)) (* 1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (*.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/32 binary64)) (/.f64 (*.f64 #s(literal -1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x x)) (*.f64 p (*.f64 p p))))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 3/512 binary64) (*.f64 x x)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p (*.f64 (*.f64 p p) #s(literal -32 binary64))) (*.f64 x (*.f64 x x))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 p (*.f64 (*.f64 p p) #s(literal -32 binary64))) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 #s(literal -512 binary64) (pow.f64 p #s(literal 5 binary64))) (pow.f64 x #s(literal 5 binary64)))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))
(+.f64 (+.f64 (/.f64 (*.f64 p (*.f64 (*.f64 p p) #s(literal -32 binary64))) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 #s(literal -512 binary64) (pow.f64 p #s(literal 5 binary64))) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 p #s(literal 7 binary64)) #s(literal 24576 binary64))) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p (*.f64 (*.f64 p p) #s(literal -32 binary64))) (*.f64 x (*.f64 x x))))
(+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal 512 binary64) (pow.f64 p #s(literal 5 binary64))) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 32 binary64))) (*.f64 x (*.f64 x x))))
(+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 p #s(literal 7 binary64)) #s(literal 24576 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 512 binary64) (pow.f64 p #s(literal 5 binary64))) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 32 binary64)))) (*.f64 x (*.f64 x x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p (*.f64 (*.f64 p p) #s(literal -32 binary64))) (*.f64 x (*.f64 x x))))
(+ 1/2 (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p (*.f64 p p)) (+.f64 (/.f64 (*.f64 #s(literal -512 binary64) (*.f64 p p)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -32 binary64) (*.f64 x (*.f64 x x))))))
(+ 1/2 (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 p (*.f64 (*.f64 p p) (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 #s(literal -12288 binary64) (*.f64 p p)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal -512 binary64) (pow.f64 x #s(literal 5 binary64))))) (/.f64 #s(literal -32 binary64) (*.f64 x (*.f64 x x)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))))
(+ 1/2 (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (+.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -3/256 binary64))) (pow.f64 p #s(literal 5 binary64))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/32 binary64)) (*.f64 p p))) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/32 binary64)) (*.f64 p p))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 3/256 binary64))) (pow.f64 p #s(literal 4 binary64)))) p))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/.f64 (+.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 p p) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))
(/.f64 (+.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 2 binary64) (*.f64 p p))))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))
(/.f64 (+.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 2 binary64) (*.f64 p p))))) (*.f64 p (*.f64 p p)))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))) (/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p))) (/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64)))))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* -1 (* p (- (* -1/4 (/ (pow x 2) (pow p 2))) 2)))
(*.f64 p (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 p p)) #s(literal -2 binary64))))
(* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 p (+.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 p p)) #s(literal -2 binary64)))))
(* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 p (+.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (*.f64 p p)) #s(literal -2 binary64)))))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 x x)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 x x)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 p (*.f64 p p)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (*.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 p (*.f64 p p)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))

eval362.0ms (2.9%)

Compiler

Compiled 40811 to 22134 computations (45.8% saved)

prune434.0ms (3.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New124661252
Fresh246
Picked235
Done101
Total1251131264
Accuracy
100.0%
Counts
1264 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
21.1%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64)) p) x)
▶7.1%
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (-.f64 #s(literal 0 binary64) x)))
▶53.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
56.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
▶21.4%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
81.4%
(sqrt.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
▶84.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
57.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)))))
✓57.7%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
20.6%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)))))
✓52.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
▶57.2%
(sqrt.f64 #s(literal 1/2 binary64))
✓40.5%
#s(literal 1 binary64)
Compiler

Compiled 405 to 282 computations (30.4% saved)

localize825.0ms (6.5%)

Algorithm
1×egg-herbie
Localize:

Found 30 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))
✓cost-diff128
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))
✓cost-diff256
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (-.f64 #s(literal 0 binary64) x))
✓cost-diff256
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (-.f64 #s(literal 0 binary64) x)))
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 p x)
✓cost-diff0
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓cost-diff0
(*.f64 x #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
✓accuracy99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (-.f64 #s(literal 0 binary64) x)))
✓accuracy95.5%
(*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))
✓accuracy94.5%
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (-.f64 #s(literal 0 binary64) x))
✓accuracy68.2%
(/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
✓accuracy99.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 p #s(literal 2 binary64))
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
Rules
6304×*-lowering-*.f32
6304×*-lowering-*.f64
6224×accelerator-lowering-fma.f32
6224×accelerator-lowering-fma.f64
1852×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037219
180209
2241208
31000208
45352207
08405182
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))
(+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))
1/2
(/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))
(* x 1/2)
x
(sqrt (+ (* x x) (* (* p 2) (* p 2))))
(* p 2)
p
2
(- 0 (/ p x))
0
(/ p x)
(sqrt 1/2)
(/ 1 (sqrt (- 2 (/ x p))))
1
(sqrt (- 2 (/ x p)))
(- 2 (/ x p))
(/ x p)
(/ 1 (* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x)))
(* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x))
(+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p)))))
(/ 1 p)
(/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))
(* -1/8 (* (pow p 4) -12))
-1/8
(* (pow p 4) -12)
(pow p 4)
4
-12
(* (* x x) (* p (* p p)))
(* x x)
(* p (* p p))
(* p p)
(- 0 x)
Outputs
(sqrt (+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))
1/2
#s(literal 1/2 binary64)
(/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))
(* x 1/2)
(*.f64 #s(literal 1/2 binary64) x)
x
(sqrt (+ (* x x) (* (* p 2) (* p 2))))
(hypot.f64 x (*.f64 p #s(literal 2 binary64)))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(- 0 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
0
#s(literal 0 binary64)
(/ p x)
(/.f64 p x)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(/ 1 (sqrt (- 2 (/ x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
1
#s(literal 1 binary64)
(sqrt (- 2 (/ x p)))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
(- 2 (/ x p))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ x p)
(/.f64 x p)
(/ 1 (* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x)))
(/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3/2 binary64)) (*.f64 (*.f64 x p) (*.f64 p (*.f64 x p))))))
(* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x))
(*.f64 x (-.f64 (/.f64 #s(literal -1 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3/2 binary64)) (*.f64 (*.f64 x p) (*.f64 p (*.f64 x p))))))
(+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p)))))
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3/2 binary64)) (*.f64 (*.f64 x p) (*.f64 p (*.f64 x p)))))
(/ 1 p)
(/.f64 #s(literal 1 binary64) p)
(/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))
(/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3/2 binary64)) (*.f64 (*.f64 x p) (*.f64 p (*.f64 x p))))
(* -1/8 (* (pow p 4) -12))
(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3/2 binary64))
-1/8
#s(literal -1/8 binary64)
(* (pow p 4) -12)
(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))
(pow p 4)
(pow.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
-12
#s(literal -12 binary64)
(* (* x x) (* p (* p p)))
(*.f64 (*.f64 x p) (*.f64 p (*.f64 x p)))
(* x x)
(*.f64 x x)
(* p (* p p))
(*.f64 p (*.f64 p p))
(* p p)
(*.f64 p p)
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
Results
101.0ms132×0valid
54.0ms75×0invalid
167.0ms49×5exit
Compiler

Compiled 228 to 125 computations (45.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 267.0ms
ival-mult: 69.0ms (25.8% of total)
backward-pass: 46.0ms (17.2% of total)
<compiled-spec>: 37.0ms (13.8% of total)
ival-pow: 33.0ms (12.3% of total)
ival-div: 32.0ms (12% of total)
ival-sqrt: 18.0ms (6.7% of total)
ival-add: 15.0ms (5.6% of total)
ival-sub: 11.0ms (4.1% of total)
const: 8.0ms (3% of total)

series37.0ms (0.3%)

Counts
17 → 360
Calls
Call 1
Inputs
#<alt (sqrt (+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))>
#<alt (+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))>
#<alt (* p 2)>
#<alt (* x 1/2)>
#<alt (- 0 (/ p x))>
#<alt (/ p x)>
#<alt (sqrt 1/2)>
#<alt (/ 1 (sqrt (- 2 (/ x p))))>
#<alt (sqrt (- 2 (/ x p)))>
#<alt (- 2 (/ x p))>
#<alt (/ x p)>
#<alt (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))>
#<alt (* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x))>
#<alt (* (* x x) (* p (* p p)))>
#<alt (/ 1 (* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x)))>
#<alt (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))>
#<alt (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p)))))>
Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 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)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 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))>
#<alt (/ (+ (* 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))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 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)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 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)))>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (- (* -1/8 (/ x (* (pow p 2) (pow (sqrt 2) 3)))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (+ (sqrt 2) (* x (- (* x (- (* -1/16 (/ x (* (pow p 3) (pow (sqrt 2) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt 2) 3)))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (* (sqrt (/ x p)) (sqrt -1))>
#<alt (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1))))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))))>
#<alt (* -1 (* (sqrt (/ x p)) (sqrt -1)))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))))>
#<alt (* (sqrt (/ x p)) (sqrt -1))>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (sqrt (/ (pow p 3) x)) (/ 1 (sqrt -1)))) p)>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1)))))) p)>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1))) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ 1 (* (pow p 3) (pow x 3)))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (pow (sqrt -1) 5))))))))) p)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3))))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3)))) (* -1/16 (/ (pow x 3) (* (pow p 3) (pow (sqrt 2) 5)))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (* -1 (/ x p))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (/ x p))>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* -1 (/ x p))>
#<alt (/ (+ (* -3/2 (/ (pow p 2) x)) (* -1 x)) p)>
#<alt (/ (+ (* -3/2 (/ (pow p 2) x)) (* -1 x)) p)>
#<alt (/ (+ (* -3/2 (/ (pow p 2) x)) (* -1 x)) p)>
#<alt (* -3/2 (/ p x))>
#<alt (* p (- (* -1 (/ x (pow p 2))) (* 3/2 (/ 1 x))))>
#<alt (* p (- (* -1 (/ x (pow p 2))) (* 3/2 (/ 1 x))))>
#<alt (* p (- (* -1 (/ x (pow p 2))) (* 3/2 (/ 1 x))))>
#<alt (* -3/2 (/ p x))>
#<alt (* -1 (* p (+ (* 3/2 (/ 1 x)) (/ x (pow p 2)))))>
#<alt (* -1 (* p (+ (* 3/2 (/ 1 x)) (/ x (pow p 2)))))>
#<alt (* -1 (* p (+ (* 3/2 (/ 1 x)) (/ x (pow p 2)))))>
#<alt (* -3/2 (/ p x))>
#<alt (/ (+ (* -3/2 p) (* -1 (/ (pow x 2) p))) x)>
#<alt (/ (+ (* -3/2 p) (* -1 (/ (pow x 2) p))) x)>
#<alt (/ (+ (* -3/2 p) (* -1 (/ (pow x 2) p))) x)>
#<alt (* -1 (/ x p))>
#<alt (* x (- (* -3/2 (/ p (pow x 2))) (/ 1 p)))>
#<alt (* x (- (* -3/2 (/ p (pow x 2))) (/ 1 p)))>
#<alt (* x (- (* -3/2 (/ p (pow x 2))) (/ 1 p)))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))))>
#<alt (* -1 (* x (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))))>
#<alt (* -1 (* x (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* (pow p 3) (pow x 2))>
#<alt (* -1 (/ p x))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))>
#<alt (* p (- (* (pow p 2) (+ (* (pow p 2) (- (* 27/8 (/ (pow p 2) (pow x 7))) (* 9/4 (/ 1 (pow x 5))))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))>
#<alt (* -2/3 (/ x p))>
#<alt (/ (+ (* -2/3 x) (* 4/9 (/ (pow x 3) (pow p 2)))) p)>
#<alt (/ (- (+ (* -2/3 x) (* -8/27 (/ (pow x 5) (pow p 4)))) (* -4/9 (/ (pow x 3) (pow p 2)))) p)>
#<alt (/ (- (+ (* -2/3 x) (* 16/81 (/ (pow x 7) (pow p 6)))) (+ (* -4/9 (/ (pow x 3) (pow p 2))) (* 8/27 (/ (pow x 5) (pow p 4))))) p)>
#<alt (* -2/3 (/ x p))>
#<alt (* -1 (/ (+ (* -4/9 (/ (pow x 3) (pow p 2))) (* 2/3 x)) p))>
#<alt (* -1 (/ (- (+ (* 8/27 (/ (pow x 5) (pow p 4))) (* 2/3 x)) (* 4/9 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (- (+ (* -16/81 (/ (pow x 7) (pow p 6))) (* 2/3 x)) (+ (* -8/27 (/ (pow x 5) (pow p 4))) (* 4/9 (/ (pow x 3) (pow p 2))))) p))>
#<alt (* -2/3 (/ x p))>
#<alt (* x (- (* 4/9 (/ (pow x 2) (pow p 3))) (* 2/3 (/ 1 p))))>
#<alt (* x (- (* (pow x 2) (+ (* -8/27 (/ (pow x 2) (pow p 5))) (* 4/9 (/ 1 (pow p 3))))) (* 2/3 (/ 1 p))))>
#<alt (* x (- (* (pow x 2) (+ (* (pow x 2) (- (* 16/81 (/ (pow x 2) (pow p 7))) (* 8/27 (/ 1 (pow p 5))))) (* 4/9 (/ 1 (pow p 3))))) (* 2/3 (/ 1 p))))>
#<alt (* -1 (/ p x))>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2))))) x)>
#<alt (/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (+ (* 3/2 (/ (pow p 3) (pow x 2))) (* 27/8 (/ (pow p 7) (pow x 6)))))) x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ p (* 9/4 (/ (pow p 5) (pow x 4)))) (* 3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ p (* -27/8 (/ (pow p 7) (pow x 6)))) (+ (* -9/4 (/ (pow p 5) (pow x 4))) (* 3/2 (/ (pow p 3) (pow x 2))))) x))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1/2 (+ (* -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))))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)>
#<alt (- (+ (* 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))) (/ (pow p 2) (pow x 2)))) 1/2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -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)>
#<alt (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)>
#<alt (* -1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))>
#<alt (* -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))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))>
#<alt (/ 1 p)>
#<alt (/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)>
#<alt (/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)>
#<alt (/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* 3/2 (/ p (pow x 2)))>
#<alt (/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))>
#<alt (/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))>
#<alt (/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))>
#<alt (/ 1 p)>
#<alt (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))>
#<alt (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))>
#<alt (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))>
#<alt (/ 1 p)>
#<alt (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))>
#<alt (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))>
#<alt (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))>
Calls

90 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/ 1 (sqrt (- 2 (/ x p))))
1.0ms
p
@0
(/ 1 (sqrt (- 2 (/ x p))))
1.0ms
x
@inf
(sqrt (- 2 (/ x p)))
1.0ms
x
@-inf
(/ 1 (sqrt (- 2 (/ x p))))
1.0ms
p
@inf
(/ 1 (sqrt (- 2 (/ x p))))

rewrite546.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
6494×*-lowering-*.f32
6494×*-lowering-*.f64
4900×/-lowering-/.f32
4900×/-lowering-/.f64
3128×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037171
1210162
22095146
010062126
Stop Event
1×iter limit
1×node limit
Counts
17 → 568
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))
(+ 1/2 (/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))
(* p 2)
(* x 1/2)
(- 0 (/ p x))
(/ p x)
(sqrt 1/2)
(/ 1 (sqrt (- 2 (/ x p))))
(sqrt (- 2 (/ x p)))
(- 2 (/ x p))
(/ x p)
(/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))
(* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x))
(* (* x x) (* p (* p p)))
(/ 1 (* (+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p))))) (- 0 x)))
(/ (* x 1/2) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))
(+ (/ 1 p) (/ (* -1/8 (* (pow p 4) -12)) (* (* x x) (* p (* p p)))))
Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 p (*.f64 p #s(literal 4 binary64))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 p (*.f64 p #s(literal 4 binary64))))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))
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(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 p (*.f64 p p)))) (*.f64 p (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) x))) (*.f64 p (*.f64 x (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 p (*.f64 p p))))) (*.f64 x (*.f64 x p)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 p (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x p))))) (*.f64 p (*.f64 p p)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 p (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)) p))) (*.f64 p (*.f64 p p)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) p) (*.f64 p (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)) (*.f64 p p)))) (*.f64 p p))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))) #s(literal 1 binary64))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (*.f64 p (*.f64 p p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) #s(literal -1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 p (*.f64 p p))))
(/.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) #s(literal 1 binary64)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (*.f64 p (*.f64 p p)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 p (*.f64 p p))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 x x)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 p (*.f64 p p)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) x))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 x (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 p (*.f64 p p))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 x x)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x p))))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 p p)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)) p))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (*.f64 p p)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) p) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)) (*.f64 p p)))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) p))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))) #s(literal 1 binary64))))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 p (*.f64 p p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)))) (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (*.f64 p (*.f64 p p)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))))) (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal -1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) p) (neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))))))
(/.f64 (+.f64 (neg.f64 (*.f64 p (*.f64 p p))) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 p (*.f64 p p))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) #s(literal 1 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))) (*.f64 (-.f64 #s(literal 0 binary64) p) (neg.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) p) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))))))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (*.f64 p (*.f64 p p)))) (*.f64 (-.f64 #s(literal 0 binary64) p) (neg.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))))) (*.f64 (-.f64 #s(literal 0 binary64) p) (neg.f64 (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (neg.f64 (*.f64 p (*.f64 p p))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 p (*.f64 p p))))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 x x)))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 p (*.f64 p p)))) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) x))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 x (*.f64 p (*.f64 p p)))))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 p (*.f64 p p))))) (*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 x x)))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 p p)) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x p))))) (neg.f64 (*.f64 p (*.f64 p p))))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 p p)) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)) p))) (neg.f64 (*.f64 p (*.f64 p p))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x)) (*.f64 p p)))) (*.f64 (-.f64 #s(literal 0 binary64) p) p))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) (+.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x))))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)))) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)))))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x))))))
(pow.f64 (/.f64 (*.f64 p (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))) (+.f64 (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p))) (*.f64 (/.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal -1728 binary64) (*.f64 p (*.f64 p p)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)))) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)))))) #s(literal -1 binary64))
(*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 p (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p))) (*.f64 (/.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal -1728 binary64) (*.f64 p (*.f64 p p))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p))))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x)) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal -12 binary64) p) (*.f64 x x))))))

simplify614.0ms (4.8%)

Algorithm
1×egg-herbie
Rules
9680×accelerator-lowering-fma.f32
9680×accelerator-lowering-fma.f64
7372×*-lowering-*.f32
7372×*-lowering-*.f64
2728×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07504802
121604605
269674545
080244324
Stop Event
1×iter limit
1×node limit
Counts
360 → 360
Calls
Call 1
Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 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)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 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))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 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))
(/ (+ (* 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))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 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)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 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)))
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* x (- (* -1/8 (/ x (* (pow p 2) (pow (sqrt 2) 3)))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+ (sqrt 2) (* x (- (* x (- (* -1/16 (/ x (* (pow p 3) (pow (sqrt 2) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt 2) 3)))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(* (sqrt (/ x p)) (sqrt -1))
(* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))
(* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1))))))
(* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))))
(* -1 (* (sqrt (/ x p)) (sqrt -1)))
(* -1 (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))))
(* (sqrt (/ x p)) (sqrt -1))
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (sqrt (/ (pow p 3) x)) (/ 1 (sqrt -1)))) p)
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1)))))) p)
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1))) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ 1 (* (pow p 3) (pow x 3)))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (pow (sqrt -1) 5))))))))) p)
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3))))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3)))) (* -1/16 (/ (pow x 3) (* (pow p 3) (pow (sqrt 2) 5)))))))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(* -1 (/ x p))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* -1 (/ x p))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (/ x p))
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* 3/2 (/ p (pow x 2)))
(* -1 (/ x p))
(/ (+ (* -3/2 (/ (pow p 2) x)) (* -1 x)) p)
(/ (+ (* -3/2 (/ (pow p 2) x)) (* -1 x)) p)
(/ (+ (* -3/2 (/ (pow p 2) x)) (* -1 x)) p)
(* -3/2 (/ p x))
(* p (- (* -1 (/ x (pow p 2))) (* 3/2 (/ 1 x))))
(* p (- (* -1 (/ x (pow p 2))) (* 3/2 (/ 1 x))))
(* p (- (* -1 (/ x (pow p 2))) (* 3/2 (/ 1 x))))
(* -3/2 (/ p x))
(* -1 (* p (+ (* 3/2 (/ 1 x)) (/ x (pow p 2)))))
(* -1 (* p (+ (* 3/2 (/ 1 x)) (/ x (pow p 2)))))
(* -1 (* p (+ (* 3/2 (/ 1 x)) (/ x (pow p 2)))))
(* -3/2 (/ p x))
(/ (+ (* -3/2 p) (* -1 (/ (pow x 2) p))) x)
(/ (+ (* -3/2 p) (* -1 (/ (pow x 2) p))) x)
(/ (+ (* -3/2 p) (* -1 (/ (pow x 2) p))) x)
(* -1 (/ x p))
(* x (- (* -3/2 (/ p (pow x 2))) (/ 1 p)))
(* x (- (* -3/2 (/ p (pow x 2))) (/ 1 p)))
(* x (- (* -3/2 (/ p (pow x 2))) (/ 1 p)))
(* -1 (/ x p))
(* -1 (* x (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))))
(* -1 (* x (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))))
(* -1 (* x (+ (* 3/2 (/ p (pow x 2))) (/ 1 p))))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* (pow p 3) (pow x 2))
(* -1 (/ p x))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(* p (- (* (pow p 2) (+ (* (pow p 2) (- (* 27/8 (/ (pow p 2) (pow x 7))) (* 9/4 (/ 1 (pow x 5))))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(* -2/3 (/ x p))
(/ (+ (* -2/3 x) (* 4/9 (/ (pow x 3) (pow p 2)))) p)
(/ (- (+ (* -2/3 x) (* -8/27 (/ (pow x 5) (pow p 4)))) (* -4/9 (/ (pow x 3) (pow p 2)))) p)
(/ (- (+ (* -2/3 x) (* 16/81 (/ (pow x 7) (pow p 6)))) (+ (* -4/9 (/ (pow x 3) (pow p 2))) (* 8/27 (/ (pow x 5) (pow p 4))))) p)
(* -2/3 (/ x p))
(* -1 (/ (+ (* -4/9 (/ (pow x 3) (pow p 2))) (* 2/3 x)) p))
(* -1 (/ (- (+ (* 8/27 (/ (pow x 5) (pow p 4))) (* 2/3 x)) (* 4/9 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (- (+ (* -16/81 (/ (pow x 7) (pow p 6))) (* 2/3 x)) (+ (* -8/27 (/ (pow x 5) (pow p 4))) (* 4/9 (/ (pow x 3) (pow p 2))))) p))
(* -2/3 (/ x p))
(* x (- (* 4/9 (/ (pow x 2) (pow p 3))) (* 2/3 (/ 1 p))))
(* x (- (* (pow x 2) (+ (* -8/27 (/ (pow x 2) (pow p 5))) (* 4/9 (/ 1 (pow p 3))))) (* 2/3 (/ 1 p))))
(* x (- (* (pow x 2) (+ (* (pow x 2) (- (* 16/81 (/ (pow x 2) (pow p 7))) (* 8/27 (/ 1 (pow p 5))))) (* 4/9 (/ 1 (pow p 3))))) (* 2/3 (/ 1 p))))
(* -1 (/ p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2))))) x)
(/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (+ (* 3/2 (/ (pow p 3) (pow x 2))) (* 27/8 (/ (pow p 7) (pow x 6)))))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (- (+ p (* 9/4 (/ (pow p 5) (pow x 4)))) (* 3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (- (+ p (* -27/8 (/ (pow p 7) (pow x 6)))) (+ (* -9/4 (/ (pow p 5) (pow x 4))) (* 3/2 (/ (pow p 3) (pow x 2))))) x))
(* 1/4 (/ x p))
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1/2 (+ (* -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))))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)
(- (+ (* 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))) (/ (pow p 2) (pow x 2)))) 1/2)
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -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)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(* -1/4 (/ x p))
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(* -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))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(/ 1 p)
(/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)
(/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)
(/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)
(* 3/2 (/ p (pow x 2)))
(* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* 3/2 (/ p (pow x 2)))
(* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* 3/2 (/ p (pow x 2)))
(/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))
(/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))
(/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))
(/ 1 p)
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(/ 1 p)
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) p))
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(*.f64 x (+.f64 (/.f64 #s(literal -2/3 binary64) p) (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4/9 binary64)) p) (*.f64 p p))))
(* x (- (* (pow x 2) (+ (* -8/27 (/ (pow x 2) (pow p 5))) (* 4/9 (/ 1 (pow p 3))))) (* 2/3 (/ 1 p))))
(*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -8/27 binary64)) (pow.f64 p #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 4/9 binary64) p) (*.f64 p p)))) (/.f64 #s(literal -2/3 binary64) p)))
(* x (- (* (pow x 2) (+ (* (pow x 2) (- (* 16/81 (/ (pow x 2) (pow p 7))) (* 8/27 (/ 1 (pow p 5))))) (* 4/9 (/ 1 (pow p 3))))) (* 2/3 (/ 1 p))))
(*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (/.f64 (/.f64 #s(literal 4/9 binary64) p) (*.f64 p p)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 16/81 binary64)) (pow.f64 p #s(literal 7 binary64))) (/.f64 #s(literal -8/27 binary64) (pow.f64 p #s(literal 5 binary64)))))))) (/.f64 #s(literal -2/3 binary64) p)))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p (/.f64 p x))) (/.f64 #s(literal 3/2 binary64) x)) p) x)
(/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2))))) x)
(/.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p (/.f64 p x))) (/.f64 #s(literal 3/2 binary64) x)) (-.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 4 binary64))) p)) x)
(/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (+ (* 3/2 (/ (pow p 3) (pow x 2))) (* 27/8 (/ (pow p 7) (pow x 6)))))) x)
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p (/.f64 p x))) (/.f64 #s(literal 3/2 binary64) x)) p) (+.f64 (/.f64 (*.f64 #s(literal 27/8 binary64) (pow.f64 p #s(literal 7 binary64))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 4 binary64))))) x)
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (+.f64 p (*.f64 (*.f64 p (*.f64 p (/.f64 p x))) (/.f64 #s(literal -3/2 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (+ p (* 9/4 (/ (pow p 5) (pow x 4)))) (* 3/2 (/ (pow p 3) (pow x 2)))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 (*.f64 p (*.f64 p (/.f64 p x))) (/.f64 #s(literal -3/2 binary64) x)) (+.f64 p (*.f64 #s(literal 9/4 binary64) (/.f64 (pow.f64 p #s(literal 5 binary64)) (pow.f64 x #s(literal 4 binary64)))))) x))
(* -1 (/ (- (+ p (* -27/8 (/ (pow p 7) (pow x 6)))) (+ (* -9/4 (/ (pow p 5) (pow x 4))) (* 3/2 (/ (pow p 3) (pow x 2))))) x))
(/.f64 (+.f64 p (-.f64 (-.f64 (*.f64 (/.f64 (pow.f64 p #s(literal 7 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -27/8 binary64)) (*.f64 (*.f64 p (*.f64 p (/.f64 p x))) (/.f64 #s(literal 3/2 binary64) x))) (/.f64 (*.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(*.f64 x (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 x x) p) p) (/.f64 #s(literal -1/32 binary64) p)) (/.f64 #s(literal 1/4 binary64) p)))
(* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p)))))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -5/4096 binary64)) (pow.f64 p #s(literal 7 binary64))) (/.f64 #s(literal 3/512 binary64) (pow.f64 p #s(literal 5 binary64))))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 p p) (*.f64 x x))))
(+ 1/2 (+ (* -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))))))
(+.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 p p) (*.f64 x x)))) (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))))
-1/2
#s(literal -1/2 binary64)
(- (/ (pow p 2) (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(- (+ (* 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))) (/ (pow p 2) (pow x 2)))) 1/2)
(+.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -10 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x x)) p) (/.f64 #s(literal -1/32 binary64) p)) (*.f64 x #s(literal 1/4 binary64))) p)
(/ (+ (* -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)
(/.f64 (+.f64 (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x x)) p) (/.f64 #s(literal -1/32 binary64) p)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -3/256 binary64) x))) (pow.f64 p #s(literal 4 binary64)))) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(/.f64 (+.f64 (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x x)) p) (/.f64 #s(literal -1/32 binary64) p)) (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -3/256 binary64) x)) (pow.f64 p #s(literal 4 binary64))) (/.f64 (+.f64 (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (*.f64 (*.f64 x (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -3/256 binary64) x))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) p)
(* -1/4 (/ x p))
(/.f64 (*.f64 x #s(literal -1/4 binary64)) p)
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(/.f64 (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x x)) p) (/.f64 #s(literal -1/32 binary64) p)) (*.f64 x #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) p))
(* -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))
(/.f64 (+.f64 (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x x)) p) (/.f64 #s(literal -1/32 binary64) p)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -3/256 binary64) x))) (pow.f64 p #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(/.f64 (+.f64 (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x x)) p) (/.f64 #s(literal -1/32 binary64) p)) (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -3/256 binary64) x)) (pow.f64 p #s(literal 4 binary64))) (/.f64 (+.f64 (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (*.f64 (*.f64 x (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -3/256 binary64) x))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) p))
(/ 1 p)
(/.f64 #s(literal 1 binary64) p)
(/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) p)
(/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) p)
(/ (+ 1 (* 3/2 (/ (pow p 2) (pow x 2)))) p)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) p)
(* 3/2 (/ p (pow x 2)))
(/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x))
(* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(*.f64 p (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) p) p) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))))
(* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(*.f64 p (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) p) p) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))))
(* p (+ (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(*.f64 p (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) p) p) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))))
(* 3/2 (/ p (pow x 2)))
(/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x))
(* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(*.f64 p (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) p) p) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))))
(* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(*.f64 p (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) p) p) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))))
(* p (+ (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(*.f64 p (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) p) p) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))))
(* 3/2 (/ p (pow x 2)))
(/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x))
(/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))
(/.f64 (+.f64 (/.f64 (*.f64 x x) p) (*.f64 p #s(literal 3/2 binary64))) (*.f64 x x))
(/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))
(/.f64 (+.f64 (/.f64 (*.f64 x x) p) (*.f64 p #s(literal 3/2 binary64))) (*.f64 x x))
(/ (+ (* 3/2 p) (/ (pow x 2) p)) (pow x 2))
(/.f64 (+.f64 (/.f64 (*.f64 x x) p) (*.f64 p #s(literal 3/2 binary64))) (*.f64 x x))
(/ 1 p)
(/.f64 #s(literal 1 binary64) p)
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)))
(/ 1 p)
(/.f64 #s(literal 1 binary64) p)
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)))
(+ (* 3/2 (/ p (pow x 2))) (/ 1 p))
(+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)))

eval214.0ms (1.7%)

Compiler

Compiled 21874 to 12439 computations (43.1% saved)

prune120.0ms (0.9%)

Pruning

14 alts after pruning (9 fresh and 5 done)

PrunedKeptTotal
New9235928
Fresh145
Picked325
Done033
Total92714941
Accuracy
100.0%
Counts
941 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶54.7%
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
▶21.7%
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
18.4%
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 p #s(literal -3/2 binary64)) (/.f64 (*.f64 x x) p)) x))
56.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
▶18.4%
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1 binary64) x)))
▶81.4%
(sqrt.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
✓84.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
57.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)))))
✓57.7%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
20.6%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)))))
✓52.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
✓57.2%
(sqrt.f64 #s(literal 1/2 binary64))
▶21.4%
(neg.f64 (/.f64 p x))
✓40.5%
#s(literal 1 binary64)
Compiler

Compiled 421 to 289 computations (31.4% saved)

localize998.0ms (7.9%)

Algorithm
1×egg-herbie
Localize:

Found 34 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 p p)
✓cost-diff0
(*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x)))))
✓cost-diff0
(+.f64 (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1 binary64) x))
✓cost-diff0
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1 binary64) x)))
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓cost-diff0
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
✓cost-diff128
(/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))
✓cost-diff128
(+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
✓cost-diff512
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
✓cost-diff-64
(neg.f64 (/.f64 p x))
✓cost-diff0
(/.f64 p x)
✓cost-diff0
(pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))
✓cost-diff0
(/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
✓cost-diff13440
(fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
✓cost-diff13440
(sqrt.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
✓accuracy99.6%
(/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x)))
✓accuracy97.4%
(*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x)))))
✓accuracy86.6%
(+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))))
✓accuracy84.9%
(/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))
✓accuracy100.0%
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓accuracy100.0%
(*.f64 #s(literal -12 binary64) p)
✓accuracy100.0%
(+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p))
✓accuracy99.8%
(/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x))
✓accuracy94.1%
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(neg.f64 (/.f64 p x))
✓accuracy100.0%
(sqrt.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
✓accuracy99.8%
(/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
✓accuracy99.7%
(/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
✓accuracy76.0%
(pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))
Rules
7362×accelerator-lowering-fma.f32
7362×accelerator-lowering-fma.f64
4830×*-lowering-*.f32
4830×*-lowering-*.f64
1352×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048315
1111315
2261310
3605286
41309284
52713284
65806278
08100264
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt (+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2))
(+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2)
(/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4))
x
(pow (+ (* 4 (* p p)) (* x x)) 1/4)
(+ (* 4 (* p p)) (* x x))
(* 4 (* p p))
4
(* p p)
p
(* x x)
1/4
(/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))
1/2
(neg (/ p x))
(/ p x)
(/ (/ 1 (- 0 x)) (+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p)))
(/ 1 (- 0 x))
1
(- 0 x)
0
(+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p))
(/ (* -1/8 (* -12 p)) (* x x))
(* -1/8 (* -12 p))
-1/8
(* -12 p)
-12
(/ 1 p)
(pow (- 2 (/ x p)) -1/2)
(- 2 (/ x p))
2
(/ x p)
-1/2
(* p (+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x)))
(+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x))
(* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x)))))
(+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))
(* -9/4 (/ (* p p) (pow x 5)))
-9/4
(/ (* p p) (pow x 5))
(pow x 5)
5
(/ 3/2 (* x (* x x)))
3/2
(* x (* x x))
(/ -1 x)
-1
Outputs
(sqrt (+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2)
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4))
(/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
x
(pow (+ (* 4 (* p p)) (* x x)) 1/4)
(pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))
(+ (* 4 (* p p)) (* x x))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
(* 4 (* p p))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
4
#s(literal 4 binary64)
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)
1/4
#s(literal 1/4 binary64)
(/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))
(/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
1/2
#s(literal 1/2 binary64)
(neg (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/ p x)
(/.f64 p x)
(/ (/ 1 (- 0 x)) (+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p)))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 p #s(literal -3/2 binary64)) x) (/.f64 x p)))
(/ 1 (- 0 x))
(/.f64 #s(literal -1 binary64) x)
1
#s(literal 1 binary64)
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
(+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p))
(+.f64 (/.f64 (*.f64 (/.f64 p x) #s(literal 3/2 binary64)) x) (/.f64 #s(literal 1 binary64) p))
(/ (* -1/8 (* -12 p)) (* x x))
(/.f64 (*.f64 (/.f64 p x) #s(literal 3/2 binary64)) x)
(* -1/8 (* -12 p))
(*.f64 p #s(literal 3/2 binary64))
-1/8
#s(literal -1/8 binary64)
(* -12 p)
(*.f64 p #s(literal -12 binary64))
-12
#s(literal -12 binary64)
(/ 1 p)
(/.f64 #s(literal 1 binary64) p)
(pow (- 2 (/ x p)) -1/2)
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(- 2 (/ x p))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(/ x p)
(/.f64 x p)
-1/2
#s(literal -1/2 binary64)
(* p (+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x)))
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (/.f64 #s(literal -1 binary64) x)))
(+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x))
(+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (/.f64 #s(literal -1 binary64) x))
(* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x)))))
(*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) x)))
(+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))
(+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))
(* -9/4 (/ (* p p) (pow x 5)))
(/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (pow.f64 x #s(literal 5 binary64)))
-9/4
#s(literal -9/4 binary64)
(/ (* p p) (pow x 5))
(/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))
(pow x 5)
(pow.f64 x #s(literal 5 binary64))
5
#s(literal 5 binary64)
(/ 3/2 (* x (* x x)))
(/.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) x)
3/2
#s(literal 3/2 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
-1
#s(literal -1 binary64)
Results
159.0ms132×0valid
130.0ms75×0invalid
198.0ms49×5exit
Compiler

Compiled 355 to 178 computations (49.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 397.0ms
ival-mult: 107.0ms (27% of total)
ival-pow: 107.0ms (27% of total)
ival-div: 67.0ms (16.9% of total)
backward-pass: 60.0ms (15.1% of total)
ival-add: 26.0ms (6.6% of total)
<compiled-spec>: 9.0ms (2.3% of total)
const: 9.0ms (2.3% of total)
ival-sub: 7.0ms (1.8% of total)
ival-sqrt: 2.0ms (0.5% of total)
ival-neg: 1.0ms (0.3% of total)

series74.0ms (0.6%)

Counts
22 → 480
Calls
Call 1
Inputs
#<alt (pow (+ (* 4 (* p p)) (* x x)) 1/4)>
#<alt (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))>
#<alt (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4))>
#<alt (sqrt (+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2))>
#<alt (neg (/ p x))>
#<alt (/ p x)>
#<alt (/ (/ 1 (- 0 x)) (+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p)))>
#<alt (/ (* -1/8 (* -12 p)) (* x x))>
#<alt (+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p))>
#<alt (* -12 p)>
#<alt (- 2 (/ x p))>
#<alt (/ x p)>
#<alt (pow (- 2 (/ x p)) -1/2)>
#<alt (/ (* p p) (pow x 5))>
#<alt (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))>
#<alt (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x)))))>
#<alt (/ 3/2 (* x (* x x)))>
#<alt (+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2)>
#<alt (/ 1 (- 0 x))>
#<alt (* p (+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x)))>
#<alt (+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x))>
#<alt (* p p)>
Outputs
#<alt (* (pow 1 1/4) (sqrt x))>
#<alt (+ (* (pow 1 1/4) (sqrt x)) (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 3))))))>
#<alt (+ (* (pow 1 1/4) (sqrt x)) (* (pow p 2) (+ (* -3/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 7)))))) (* (pow 1 1/4) (sqrt (/ 1 (pow x 3)))))))>
#<alt (+ (* (pow 1 1/4) (sqrt x)) (* (pow p 2) (+ (* (pow 1 1/4) (sqrt (/ 1 (pow x 3)))) (* (pow p 2) (+ (* -3/2 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* 7/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 11)))))))))))>
#<alt (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))>
#<alt (+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))))>
#<alt (+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4))))>
#<alt (+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))) (+ (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4)) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/2048 (pow x 6)) (+ (* 1/24576 (pow x 6)) (* 1/768 (pow x 6))))) (pow p 6)))))>
#<alt (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))>
#<alt (+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))))>
#<alt (+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4))))>
#<alt (+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))) (+ (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4)) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/2048 (pow x 6)) (+ (* 1/24576 (pow x 6)) (* 1/768 (pow x 6))))) (pow p 6)))))>
#<alt (* (pow 4 1/4) (sqrt p))>
#<alt (+ (* 1/16 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 3))) (pow x 2)))) (* (pow 4 1/4) (sqrt p)))>
#<alt (+ (* (pow 4 1/4) (sqrt p)) (* (pow x 2) (+ (* -3/512 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 7))) (pow x 2)))) (* 1/16 (* (pow 4 1/4) (sqrt (/ 1 (pow p 3))))))))>
#<alt (+ (* (pow 4 1/4) (sqrt p)) (* (pow x 2) (+ (* 1/16 (* (pow 4 1/4) (sqrt (/ 1 (pow p 3))))) (* (pow x 2) (+ (* -3/512 (* (pow 4 1/4) (sqrt (/ 1 (pow p 7))))) (* 7/8192 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 11))) (pow x 2)))))))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* (pow p 2) (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt x) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4)))) (* (pow p 2) (sqrt (/ 1 (pow x 3))))))>
#<alt (+ (sqrt x) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4)))) (+ (* (sqrt (/ 1 (pow x 11))) (+ (* -2 (pow p 6)) (+ (* 1/6 (pow p 6)) (* 16/3 (pow p 6))))) (* (pow p 2) (sqrt (/ 1 (pow x 3)))))))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (+ (* (sqrt x) (sqrt -1)) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4))))) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 3))))))>
#<alt (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4))))) (+ (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -2 (pow p 6)) (+ (* 1/6 (pow p 6)) (* 16/3 (pow p 6)))))) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 3)))))))>
#<alt (* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x))))>
#<alt (+ (* -1/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 5)))))) (* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x)))))>
#<alt (+ (* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x)))) (* (pow p 2) (+ (* -1/2 (* (pow 1 1/4) (sqrt (/ 1 (pow x 5))))) (* 5/4 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 9)))))))))>
#<alt (+ (* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x)))) (* (pow p 2) (+ (* -1/2 (* (pow 1 1/4) (sqrt (/ 1 (pow x 5))))) (* (pow p 2) (+ (* -15/4 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 13)))))) (* 5/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 9))))))))))>
#<alt (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))))>
#<alt (+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (pow p 2))) (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))))>
#<alt (+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4)))))>
#<alt (+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (+ (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))) (+ (* -1/1536 (* (pow x 2) (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4))))) (+ (* -1/24576 (pow x 6)) (* 1/2880 (+ (* -45/4 (pow x 6)) (+ (* -15/4 (pow x 6)) (* 45/4 (pow x 6)))))))) (pow p 6))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4))))))>
#<alt (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))))>
#<alt (+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (pow p 2))) (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))))>
#<alt (+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4)))))>
#<alt (+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (+ (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))) (+ (* -1/1536 (* (pow x 2) (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4))))) (+ (* -1/24576 (pow x 6)) (* 1/2880 (+ (* -45/4 (pow x 6)) (+ (* -15/4 (pow x 6)) (* 45/4 (pow x 6)))))))) (pow p 6))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4))))))>
#<alt (* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p))))>
#<alt (+ (* -1/32 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 5))) (pow x 2)))) (* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p)))))>
#<alt (+ (* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p)))) (* (pow x 2) (+ (* -1/32 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 5))))) (* 5/1024 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 9))) (pow x 2)))))))>
#<alt (+ (* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p)))) (* (pow x 2) (+ (* -1/32 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 5))))) (* (pow x 2) (+ (* -15/16384 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 13))) (pow x 2)))) (* 5/1024 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 9))))))))))>
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#<alt (sqrt x)>
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#<alt (sqrt 1/2)>
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#<alt 1>
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#<alt 1>
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#<alt (sqrt 1/2)>
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#<alt (sqrt 1/2)>
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#<alt (+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
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#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ (pow p 2) (pow x 5))>
#<alt (/ 3/2 (pow x 3))>
#<alt (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))>
#<alt (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))>
#<alt (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))>
#<alt (* -9/4 (/ (pow p 2) (pow x 5)))>
#<alt (* (pow p 2) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 2) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 2) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* -9/4 (/ (pow p 2) (pow x 5)))>
#<alt (* (pow p 2) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 2) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 2) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* -9/4 (/ (pow p 2) (pow x 5)))>
#<alt (/ (+ (* -9/4 (pow p 2)) (* 3/2 (pow x 2))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 2)) (* 3/2 (pow x 2))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 2)) (* 3/2 (pow x 2))) (pow x 5))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ (+ 3/2 (* -9/4 (/ (pow p 2) (pow x 2)))) (pow x 3))>
#<alt (/ (+ 3/2 (* -9/4 (/ (pow p 2) (pow x 2)))) (pow x 3))>
#<alt (/ (+ 3/2 (* -9/4 (/ (pow p 2) (pow x 2)))) (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (* -1 (/ (- (* 9/4 (/ (pow p 2) (pow x 2))) 3/2) (pow x 3)))>
#<alt (* -1 (/ (- (* 9/4 (/ (pow p 2) (pow x 2))) 3/2) (pow x 3)))>
#<alt (* -1 (/ (- (* 9/4 (/ (pow p 2) (pow x 2))) 3/2) (pow x 3)))>
#<alt (* 3/2 (/ (pow p 2) (pow x 3)))>
#<alt (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3)))))>
#<alt (* -9/4 (/ (pow p 4) (pow x 5)))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* -9/4 (/ (pow p 4) (pow x 5)))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* -9/4 (/ (pow p 4) (pow x 5)))>
#<alt (/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))>
#<alt (* 3/2 (/ (pow p 2) (pow x 3)))>
#<alt (/ (+ (* -9/4 (/ (pow p 4) (pow x 2))) (* 3/2 (pow p 2))) (pow x 3))>
#<alt (/ (+ (* -9/4 (/ (pow p 4) (pow x 2))) (* 3/2 (pow p 2))) (pow x 3))>
#<alt (/ (+ (* -9/4 (/ (pow p 4) (pow x 2))) (* 3/2 (pow p 2))) (pow x 3))>
#<alt (* 3/2 (/ (pow p 2) (pow x 3)))>
#<alt (* -1 (/ (+ (* -3/2 (pow p 2)) (* 9/4 (/ (pow p 4) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (+ (* -3/2 (pow p 2)) (* 9/4 (/ (pow p 4) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (+ (* -3/2 (pow p 2)) (* 9/4 (/ (pow p 4) (pow x 2)))) (pow x 3)))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt (/ 3/2 (pow x 3))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 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))>
#<alt (/ (+ (* 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))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 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)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 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)))>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ p x))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))>
#<alt (* p (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))>
#<alt (* -9/4 (/ (pow p 5) (pow x 5)))>
#<alt (* (pow p 5) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 5) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5))))))>
#<alt (* (pow p 5) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5))))))>
#<alt (* -9/4 (/ (pow p 5) (pow x 5)))>
#<alt (* -1 (* (pow p 5) (- (* 9/4 (/ 1 (pow x 5))) (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))))))>
#<alt (* -1 (* (pow p 5) (- (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5)))) (/ 3/2 (* (pow p 2) (pow x 3))))))>
#<alt (* -1 (* (pow p 5) (- (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5)))) (/ 3/2 (* (pow p 2) (pow x 3))))))>
#<alt (* -9/4 (/ (pow p 5) (pow x 5)))>
#<alt (/ (+ (* -9/4 (pow p 5)) (* 3/2 (* (pow p 3) (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 5)) (* (pow x 2) (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 5)) (* (pow x 2) (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))))) (pow x 5))>
#<alt (* -1 (/ p x))>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2))))) x)>
#<alt (/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2))))) x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* 9/4 (/ (pow p 5) (pow x 4))))) x))>
#<alt (* -1 (/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* 9/4 (/ (pow p 5) (pow x 4))))) x))>
#<alt (/ -1 x)>
#<alt (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x))>
#<alt (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x))>
#<alt (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x))>
#<alt (* -9/4 (/ (pow p 4) (pow x 5)))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))>
#<alt (* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))>
#<alt (* -9/4 (/ (pow p 4) (pow x 5)))>
#<alt (* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))>
#<alt (* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))>
#<alt (* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))>
#<alt (* -9/4 (/ (pow p 4) (pow x 5)))>
#<alt (/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 4)) (* (pow x 2) (+ (* -1 (pow x 2)) (* 3/2 (pow p 2))))) (pow x 5))>
#<alt (/ (+ (* -9/4 (pow p 4)) (* (pow x 2) (+ (* -1 (pow x 2)) (* 3/2 (pow p 2))))) (pow x 5))>
#<alt (/ -1 x)>
#<alt (/ (- (* 3/2 (/ (pow p 2) (pow x 2))) 1) x)>
#<alt (/ (- (+ (* -9/4 (/ (pow p 4) (pow x 4))) (* 3/2 (/ (pow p 2) (pow x 2)))) 1) x)>
#<alt (/ (- (+ (* -9/4 (/ (pow p 4) (pow x 4))) (* 3/2 (/ (pow p 2) (pow x 2)))) 1) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1 (+ (* -3/2 (/ (pow p 2) (pow x 2))) (* 9/4 (/ (pow p 4) (pow x 4))))) x))>
#<alt (* -1 (/ (+ 1 (+ (* -3/2 (/ (pow p 2) (pow x 2))) (* 9/4 (/ (pow p 4) (pow x 4))))) x))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
Calls

120 calls:

TimeVariablePointExpression
11.0ms
x
@0
(/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))
10.0ms
x
@inf
(/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))
2.0ms
p
@inf
(/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))
1.0ms
p
@0
(/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))
1.0ms
p
@inf
(pow (+ (* 4 (* p p)) (* x x)) 1/4)

rewrite576.0ms (4.5%)

Algorithm
1×batch-egg-rewrite
Rules
4178×/-lowering-/.f32
4178×/-lowering-/.f64
4034×accelerator-lowering-fma.f32
4034×accelerator-lowering-fma.f64
4010×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048254
1297230
22788227
09094212
Stop Event
1×iter limit
1×node limit
Counts
22 → 659
Calls
Call 1
Inputs
(pow (+ (* 4 (* p p)) (* x x)) 1/4)
(/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))
(/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4))
(sqrt (+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2))
(neg (/ p x))
(/ p x)
(/ (/ 1 (- 0 x)) (+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p)))
(/ (* -1/8 (* -12 p)) (* x x))
(+ (/ (* -1/8 (* -12 p)) (* x x)) (/ 1 p))
(* -12 p)
(- 2 (/ x p))
(/ x p)
(pow (- 2 (/ x p)) -1/2)
(/ (* p p) (pow x 5))
(+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))
(* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x)))))
(/ 3/2 (* x (* x x)))
(+ (* (/ x (pow (+ (* 4 (* p p)) (* x x)) 1/4)) (/ 1/2 (pow (+ (* 4 (* p p)) (* x x)) 1/4))) 1/2)
(/ 1 (- 0 x))
(* p (+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x)))
(+ (* (* p p) (+ (* -9/4 (/ (* p p) (pow x 5))) (/ 3/2 (* x (* x x))))) (/ -1 x))
(* p p)
Outputs
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/8 binary64)) (*.f64 (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/8 binary64))))
(pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/8 binary64)))
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(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal -9/4 binary64))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))) #s(literal 3 binary64)) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p))) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 27/8 binary64)))) (+.f64 (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal -9/4 binary64))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))) (+.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal -9/4 binary64))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))) (-.f64 (*.f64 (/.f64 (*.f64 p p) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 3/2 binary64))) (/.f64 (*.f64 p p) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 3/2 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal -9/4 binary64))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 p p) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 3/2 binary64)))))))
(pow.f64 (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x))))) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))) (+.f64 (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))))) (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (-.f64 (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(*.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))))) (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x))))) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)))))
(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 p p))) (/.f64 (/.f64 #s(literal 3/2 binary64) x) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 p) #s(literal 2 binary64)))
(pow.f64 p #s(literal 2 binary64))
(pow.f64 (*.f64 p p) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 2 binary64))
(*.f64 p p)
(*.f64 (*.f64 p p) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) p))

simplify773.0ms (6.1%)

Algorithm
1×egg-herbie
Rules
13050×accelerator-lowering-fma.f32
13050×accelerator-lowering-fma.f64
9280×*-lowering-*.f32
9280×*-lowering-*.f64
5068×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010818004
131877628
091937241
Stop Event
1×iter limit
1×node limit
Counts
480 → 480
Calls
Call 1
Inputs
(* (pow 1 1/4) (sqrt x))
(+ (* (pow 1 1/4) (sqrt x)) (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 3))))))
(+ (* (pow 1 1/4) (sqrt x)) (* (pow p 2) (+ (* -3/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 7)))))) (* (pow 1 1/4) (sqrt (/ 1 (pow x 3)))))))
(+ (* (pow 1 1/4) (sqrt x)) (* (pow p 2) (+ (* (pow 1 1/4) (sqrt (/ 1 (pow x 3)))) (* (pow p 2) (+ (* -3/2 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* 7/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 11)))))))))))
(exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))) (+ (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4)) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/2048 (pow x 6)) (+ (* 1/24576 (pow x 6)) (* 1/768 (pow x 6))))) (pow p 6)))))
(exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))) (+ (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4)) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/2048 (pow x 6)) (+ (* 1/24576 (pow x 6)) (* 1/768 (pow x 6))))) (pow p 6)))))
(* (pow 4 1/4) (sqrt p))
(+ (* 1/16 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 3))) (pow x 2)))) (* (pow 4 1/4) (sqrt p)))
(+ (* (pow 4 1/4) (sqrt p)) (* (pow x 2) (+ (* -3/512 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 7))) (pow x 2)))) (* 1/16 (* (pow 4 1/4) (sqrt (/ 1 (pow p 3))))))))
(+ (* (pow 4 1/4) (sqrt p)) (* (pow x 2) (+ (* 1/16 (* (pow 4 1/4) (sqrt (/ 1 (pow p 3))))) (* (pow x 2) (+ (* -3/512 (* (pow 4 1/4) (sqrt (/ 1 (pow p 7))))) (* 7/8192 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 11))) (pow x 2)))))))))
(sqrt x)
(+ (sqrt x) (* (pow p 2) (sqrt (/ 1 (pow x 3)))))
(+ (sqrt x) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4)))) (* (pow p 2) (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4)))) (+ (* (sqrt (/ 1 (pow x 11))) (+ (* -2 (pow p 6)) (+ (* 1/6 (pow p 6)) (* 16/3 (pow p 6))))) (* (pow p 2) (sqrt (/ 1 (pow x 3)))))))
(* (sqrt x) (sqrt -1))
(+ (* (sqrt x) (sqrt -1)) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 3)))))
(+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4))))) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 3))))))
(+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4))))) (+ (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -2 (pow p 6)) (+ (* 1/6 (pow p 6)) (* 16/3 (pow p 6)))))) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 3)))))))
(* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x))))
(+ (* -1/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 5)))))) (* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x)))))
(+ (* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x)))) (* (pow p 2) (+ (* -1/2 (* (pow 1 1/4) (sqrt (/ 1 (pow x 5))))) (* 5/4 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 9)))))))))
(+ (* 1/2 (* (pow 1 1/4) (sqrt (/ 1 x)))) (* (pow p 2) (+ (* -1/2 (* (pow 1 1/4) (sqrt (/ 1 (pow x 5))))) (* (pow p 2) (+ (* -15/4 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 13)))))) (* 5/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 9))))))))))
(* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))))
(+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (pow p 2))) (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))))
(+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4)))))
(+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p))))))) (+ (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))) (+ (* -1/1536 (* (pow x 2) (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4))))) (+ (* -1/24576 (pow x 6)) (* 1/2880 (+ (* -45/4 (pow x 6)) (+ (* -15/4 (pow x 6)) (* 45/4 (pow x 6)))))))) (pow p 6))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ 1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4))))))
(* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))))
(+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (pow p 2))) (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))))
(+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4)))))
(+ (* -1/32 (/ (* (pow x 2) (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (pow p 2))) (+ (* 1/2 (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p))))))) (+ (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))) (+ (* -1/1536 (* (pow x 2) (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4))))) (+ (* -1/24576 (pow x 6)) (* 1/2880 (+ (* -45/4 (pow x 6)) (+ (* -15/4 (pow x 6)) (* 45/4 (pow x 6)))))))) (pow p 6))) (* 1/2 (/ (* (exp (* 1/4 (+ (log 1/4) (* 2 (log (/ -1 p)))))) (+ (* 1/512 (pow x 4)) (* 1/96 (+ (* -3/4 (pow x 4)) (* 3/2 (pow x 4)))))) (pow p 4))))))
(* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p))))
(+ (* -1/32 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 5))) (pow x 2)))) (* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p)))))
(+ (* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p)))) (* (pow x 2) (+ (* -1/32 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 5))))) (* 5/1024 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 9))) (pow x 2)))))))
(+ (* 1/2 (* (pow 1/4 1/4) (sqrt (/ 1 p)))) (* (pow x 2) (+ (* -1/32 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 5))))) (* (pow x 2) (+ (* -15/16384 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 13))) (pow x 2)))) (* 5/1024 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 9))))))))))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/2 (* (pow p 2) (sqrt (/ 1 (pow x 5))))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/2 (* (pow p 2) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (* (sqrt (/ 1 (pow x 9))) (+ (* 1/96 (+ (* -192 (pow p 4)) (* 384 (pow p 4)))) (* 1/2 (pow p 4)))))))
(+ (* -1/2 (* (pow p 2) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 9))) (+ (* 1/96 (+ (* -192 (pow p 4)) (* 384 (pow p 4)))) (* 1/2 (pow p 4))))) (* 1/2 (* (sqrt (/ 1 (pow x 13))) (+ (* -1/6 (pow p 6)) (+ (* -1/96 (* (pow p 2) (+ (* -192 (pow p 4)) (* 384 (pow p 4))))) (* 1/2880 (+ (* -46080 (pow p 6)) (+ (* -15360 (pow p 6)) (* 46080 (pow p 6))))))))))))
(* 1/2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -1/2 (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -1/2 (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 9))) (* (sqrt -1) (+ (* 1/96 (+ (* -192 (pow p 4)) (* 384 (pow p 4)))) (* 1/2 (pow p 4))))))))
(+ (* -1/2 (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 9))) (* (sqrt -1) (+ (* 1/96 (+ (* -192 (pow p 4)) (* 384 (pow p 4)))) (* 1/2 (pow p 4)))))) (* 1/2 (* (sqrt (/ 1 (pow x 13))) (* (sqrt -1) (+ (* -1/6 (pow p 6)) (+ (* -1/96 (* (pow p 2) (+ (* -192 (pow p 4)) (* 384 (pow p 4))))) (* 1/2880 (+ (* -46080 (pow p 6)) (+ (* -15360 (pow p 6)) (* 46080 (pow p 6)))))))))))))
(* (pow 1/4 1/4) (* (sqrt (/ 1 p)) x))
(* x (+ (* -1/16 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 5))) (pow x 2)))) (* (pow 1/4 1/4) (sqrt (/ 1 p)))))
(* x (+ (* (pow 1/4 1/4) (sqrt (/ 1 p))) (* (pow x 2) (+ (* -1/16 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 5))))) (* 5/512 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 9))) (pow x 2))))))))
(* x (+ (* (pow 1/4 1/4) (sqrt (/ 1 p))) (* (pow x 2) (+ (* -1/16 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 5))))) (* (pow x 2) (+ (* -15/8192 (* (pow 1/4 1/4) (* (sqrt (/ 1 (pow p 13))) (pow x 2)))) (* 5/512 (* (pow 1/4 1/4) (sqrt (/ 1 (pow p 9)))))))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1 (* (pow p 2) (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (pow p 2) (sqrt (/ 1 (pow x 5))))) (* (sqrt (/ 1 (pow x 9))) (+ (* 1/96 (+ (* -192 (pow p 4)) (* 384 (pow p 4)))) (* 1/2 (pow p 4)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1 (* (pow p 2) (sqrt (/ 1 (pow x 5))))) (+ (* (sqrt (/ 1 (pow x 9))) (+ (* 1/96 (+ (* -192 (pow p 4)) (* 384 (pow p 4)))) (* 1/2 (pow p 4)))) (* (sqrt (/ 1 (pow x 13))) (+ (* -1/6 (pow p 6)) (+ (* -1/96 (* (pow p 2) (+ (* -192 (pow p 4)) (* 384 (pow p 4))))) (* 1/2880 (+ (* -46080 (pow p 6)) (+ (* -15360 (pow p 6)) (* 46080 (pow p 6))))))))))))
(* (sqrt x) (sqrt -1))
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1
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1
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(sqrt 1/2)
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(sqrt 1/2)
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2
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2
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2
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(sqrt 1/2)
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(sqrt 1/2)
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(sqrt 1/2)
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(* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3)))))
(* -9/4 (/ (pow p 4) (pow x 5)))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* -9/4 (/ (pow p 4) (pow x 5)))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* -9/4 (/ (pow p 4) (pow x 5)))
(/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))
(/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))
(/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))
(* 3/2 (/ (pow p 2) (pow x 3)))
(/ (+ (* -9/4 (/ (pow p 4) (pow x 2))) (* 3/2 (pow p 2))) (pow x 3))
(/ (+ (* -9/4 (/ (pow p 4) (pow x 2))) (* 3/2 (pow p 2))) (pow x 3))
(/ (+ (* -9/4 (/ (pow p 4) (pow x 2))) (* 3/2 (pow p 2))) (pow x 3))
(* 3/2 (/ (pow p 2) (pow x 3)))
(* -1 (/ (+ (* -3/2 (pow p 2)) (* 9/4 (/ (pow p 4) (pow x 2)))) (pow x 3)))
(* -1 (/ (+ (* -3/2 (pow p 2)) (* 9/4 (/ (pow p 4) (pow x 2)))) (pow x 3)))
(* -1 (/ (+ (* -3/2 (pow p 2)) (* 9/4 (/ (pow p 4) (pow x 2)))) (pow x 3)))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
(/ 3/2 (pow x 3))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 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))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 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))
(/ (+ (* 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))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 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)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 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)))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* -1 (/ p x))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(* p (- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(* -9/4 (/ (pow p 5) (pow x 5)))
(* (pow p 5) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* (pow p 5) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5))))))
(* (pow p 5) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5))))))
(* -9/4 (/ (pow p 5) (pow x 5)))
(* -1 (* (pow p 5) (- (* 9/4 (/ 1 (pow x 5))) (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))))))
(* -1 (* (pow p 5) (- (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5)))) (/ 3/2 (* (pow p 2) (pow x 3))))))
(* -1 (* (pow p 5) (- (+ (/ 1 (* (pow p 4) x)) (* 9/4 (/ 1 (pow x 5)))) (/ 3/2 (* (pow p 2) (pow x 3))))))
(* -9/4 (/ (pow p 5) (pow x 5)))
(/ (+ (* -9/4 (pow p 5)) (* 3/2 (* (pow p 3) (pow x 2)))) (pow x 5))
(/ (+ (* -9/4 (pow p 5)) (* (pow x 2) (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))))) (pow x 5))
(/ (+ (* -9/4 (pow p 5)) (* (pow x 2) (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))))) (pow x 5))
(* -1 (/ p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2))))) x)
(/ (+ (* -9/4 (/ (pow p 5) (pow x 4))) (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2))))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* 9/4 (/ (pow p 5) (pow x 4))))) x))
(* -1 (/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* 9/4 (/ (pow p 5) (pow x 4))))) x))
(/ -1 x)
(- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x))
(- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x))
(- (* (pow p 2) (+ (* -9/4 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x))
(* -9/4 (/ (pow p 4) (pow x 5)))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))
(* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))
(* -9/4 (/ (pow p 4) (pow x 5)))
(* (pow p 4) (- (* 3/2 (/ 1 (* (pow p 2) (pow x 3)))) (* 9/4 (/ 1 (pow x 5)))))
(* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))
(* (pow p 4) (- (/ 3/2 (* (pow p 2) (pow x 3))) (+ (* 9/4 (/ 1 (pow x 5))) (/ 1 (* (pow p 4) x)))))
(* -9/4 (/ (pow p 4) (pow x 5)))
(/ (+ (* -9/4 (pow p 4)) (* 3/2 (* (pow p 2) (pow x 2)))) (pow x 5))
(/ (+ (* -9/4 (pow p 4)) (* (pow x 2) (+ (* -1 (pow x 2)) (* 3/2 (pow p 2))))) (pow x 5))
(/ (+ (* -9/4 (pow p 4)) (* (pow x 2) (+ (* -1 (pow x 2)) (* 3/2 (pow p 2))))) (pow x 5))
(/ -1 x)
(/ (- (* 3/2 (/ (pow p 2) (pow x 2))) 1) x)
(/ (- (+ (* -9/4 (/ (pow p 4) (pow x 4))) (* 3/2 (/ (pow p 2) (pow x 2)))) 1) x)
(/ (- (+ (* -9/4 (/ (pow p 4) (pow x 4))) (* 3/2 (/ (pow p 2) (pow x 2)))) 1) x)
(/ -1 x)
(* -1 (/ (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -3/2 (/ (pow p 2) (pow x 2))) (* 9/4 (/ (pow p 4) (pow x 4))))) x))
(* -1 (/ (+ 1 (+ (* -3/2 (/ (pow p 2) (pow x 2))) (* 9/4 (/ (pow p 4) (pow x 4))))) x))
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
Outputs
(* (pow 1 1/4) (sqrt x))
(sqrt.f64 x)
(+ (* (pow 1 1/4) (sqrt x)) (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 3))))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 p p) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(+ (* (pow 1 1/4) (sqrt x)) (* (pow p 2) (+ (* -3/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 7)))))) (* (pow 1 1/4) (sqrt (/ 1 (pow x 3)))))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 p p) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal -3/2 binary64) (*.f64 (*.f64 p p) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(+ (* (pow 1 1/4) (sqrt x)) (* (pow p 2) (+ (* (pow 1 1/4) (sqrt (/ 1 (pow x 3)))) (* (pow p 2) (+ (* -3/2 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* 7/2 (* (pow 1 1/4) (* (pow p 2) (sqrt (/ 1 (pow x 11)))))))))))
(+.f64 (sqrt.f64 x) (*.f64 p (*.f64 p (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (*.f64 #s(literal 7/2 binary64) (*.f64 (*.f64 p p) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64))))))))))))
(exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))
(exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))))
(+.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (*.f64 x x))) (*.f64 p p)))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4))))
(+.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (*.f64 x x))) (*.f64 p p)) (+.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (*.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/512 binary64)) (pow.f64 p #s(literal 4 binary64))))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p))))))) (pow p 2))) (+ (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4)) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ 1 p)))))) (+ (* -1/2048 (pow x 6)) (+ (* 1/24576 (pow x 6)) (* 1/768 (pow x 6))))) (pow p 6)))))
(+.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (*.f64 x x))) (*.f64 p p)) (*.f64 (exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) p)) #s(literal -1/2 binary64)))) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/512 binary64)) (pow.f64 p #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/8192 binary64)) (pow.f64 p #s(literal 6 binary64)))))))
(exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))
(exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p)))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))))
(+.f64 (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p))))) (/.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p)))))) (*.f64 p p)))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4))))
(+.f64 (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p))))) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p)))))) (*.f64 p p)) (*.f64 (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p))))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/512 binary64)) (pow.f64 p #s(literal 4 binary64))))))
(+ (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* 1/16 (/ (* (pow x 2) (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p))))))) (pow p 2))) (+ (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/128 (pow x 4)) (* 1/512 (pow x 4)))) (pow p 4)) (/ (* (exp (* 1/4 (+ (log 4) (* -2 (log (/ -1 p)))))) (+ (* -1/2048 (pow x 6)) (+ (* 1/24576 (pow x 6)) (* 1/768 (pow x 6))))) (pow p 6)))))
(+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p)))))) (*.f64 p p)) (+.f64 (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p))))) (*.f64 (exp.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) p))))) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/512 binary64)) (pow.f64 p #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/8192 binary64)) (pow.f64 p #s(literal 6 binary64)))))))
(* (pow 4 1/4) (sqrt p))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 p))
(+ (* 1/16 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 3))) (pow x 2)))) (* (pow 4 1/4) (sqrt p)))
(+.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 p)) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p))))) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))))
(+ (* (pow 4 1/4) (sqrt p)) (* (pow x 2) (+ (* -3/512 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 7))) (pow x 2)))) (* 1/16 (* (pow 4 1/4) (sqrt (/ 1 (pow p 3))))))))
(+.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 p)) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p)))) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))) (*.f64 (*.f64 (*.f64 #s(literal -3/512 binary64) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 p #s(literal 7 binary64))))))))
(+ (* (pow 4 1/4) (sqrt p)) (* (pow x 2) (+ (* 1/16 (* (pow 4 1/4) (sqrt (/ 1 (pow p 3))))) (* (pow x 2) (+ (* -3/512 (* (pow 4 1/4) (sqrt (/ 1 (pow p 7))))) (* 7/8192 (* (pow 4 1/4) (* (sqrt (/ 1 (pow p 11))) (pow x 2)))))))))
(+.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 p)) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p)))) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 p #s(literal 7 binary64)))) #s(literal -3/512 binary64))) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 p #s(literal 11 binary64))))) #s(literal 7/8192 binary64))))))))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* (pow p 2) (sqrt (/ 1 (pow x 3)))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 p p) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(+ (sqrt x) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4)))) (* (pow p 2) (sqrt (/ 1 (pow x 3))))))
(+.f64 (sqrt.f64 x) (+.f64 (*.f64 (*.f64 p p) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3/2 binary64)))))
(+ (sqrt x) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -2 (pow p 4)) (* 1/2 (pow p 4)))) (+ (* (sqrt (/ 1 (pow x 11))) (+ (* -2 (pow p 6)) (+ (* 1/6 (pow p 6)) (* 16/3 (pow p 6))))) (* (pow p 2) (sqrt (/ 1 (pow x 3)))))))
(+.f64 (sqrt.f64 x) (+.f64 (*.f64 (*.f64 p p) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 7/2 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3/2 binary64))))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* (sqrt x) (sqrt -1)) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 3)))))
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(* (pow 1/4 1/4) (* (sqrt (/ 1 p)) x))
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(* (sqrt x) (sqrt -1))
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(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (* (pow p 2) (sqrt -1)) (sqrt (/ 1 (pow x 5)))))))
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(* (pow 1 1/4) (sqrt x))
(sqrt.f64 x)
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(sqrt 1/2)
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(* -1 (/ (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -3/2 binary64)) (*.f64 x x))) x))
(* -1 (/ (+ 1 (+ (* -3/2 (/ (pow p 2) (pow x 2))) (* 9/4 (/ (pow p 4) (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -3/2 binary64)) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 9/4 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ 1 (+ (* -3/2 (/ (pow p 2) (pow x 2))) (* 9/4 (/ (pow p 4) (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -3/2 binary64)) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 9/4 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)

eval360.0ms (2.8%)

Compiler

Compiled 40646 to 20045 computations (50.7% saved)

prune204.0ms (1.6%)

Pruning

14 alts after pruning (6 fresh and 8 done)

PrunedKeptTotal
New123021232
Fresh044
Picked235
Done055
Total1232141246
Accuracy
100.0%
Counts
1246 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓54.7%
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
21.7%
(/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
18.4%
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 p #s(literal -3/2 binary64)) (/.f64 (*.f64 x x) p)) x))
56.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
20.3%
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
✓81.4%
(sqrt.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
✓84.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
57.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)))))
✓57.7%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
20.6%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)))))
✓52.8%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
✓57.2%
(sqrt.f64 #s(literal 1/2 binary64))
✓21.4%
(neg.f64 (/.f64 p x))
✓40.5%
#s(literal 1 binary64)
Compiler

Compiled 658 to 410 computations (37.7% saved)

regimes72.0ms (0.6%)

Counts
26 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 p #s(literal -3/2 binary64)) (/.f64 (*.f64 x x) p)) x))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64)) p) x)
(/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x))
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)))))
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (-.f64 #s(literal 0 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 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) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(sqrt.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
Outputs
(neg.f64 (/.f64 p x))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
Calls

7 calls:

22.0ms
x
21.0ms
p
13.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
5.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms
(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
AccuracySegmentsBranch
86.7%3p
88.3%4x
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)))))))
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(+.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 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
86.7%3(*.f64 (*.f64 #s(literal 4 binary64) p) p)
Compiler

Compiled 80 to 56 computations (30% saved)

regimes30.0ms (0.2%)

Counts
21 → 4
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 p #s(literal -3/2 binary64)) (/.f64 (*.f64 x x) p)) x))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64)) p) x)
(/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x))
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)))))
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -9/4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 (*.f64 x x) (*.f64 p (*.f64 p p))))) (-.f64 #s(literal 0 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x)) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
Outputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 #s(literal 2 binary64) p) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
Calls

2 calls:

18.0ms
x
10.0ms
p
Results
AccuracySegmentsBranch
79.4%4p
72.4%5x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts
14 → 4
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 p #s(literal -3/2 binary64)) (/.f64 (*.f64 x x) p)) x))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64)) p) x)
(/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x))
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
Outputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
Calls

1 calls:

7.0ms
p
Results
AccuracySegmentsBranch
78.8%4p
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts
9 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 p #s(literal -3/2 binary64)) (/.f64 (*.f64 x x) p)) x))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64)) p) x)
(/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 (*.f64 p #s(literal 3/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -12 binary64) p)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x p)))) x))
(*.f64 p (+.f64 (*.f64 (*.f64 p p) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -9/4 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
Outputs
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
Calls

2 calls:

6.0ms
x
5.0ms
p
Results
AccuracySegmentsBranch
55.9%2x
42.7%3p
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 1 binary64)
Outputs
#s(literal 1 binary64)
Calls

1 calls:

0.0ms
x
Results
AccuracySegmentsBranch
40.5%1x
Compiler

Compiled 3 to 2 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-0.9999999999999999
-0.8444400555539764
Compiler

Compiled 24 to 18 computations (25% saved)

bsearch76.0ms (0.6%)

Algorithm
3×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
20.0ms
1.6920451177764686e-51
1.699730937259005e-48
23.0ms
2.675525478933201e-109
1.1934948640760139e-104
24.0ms
2.997940026497908e-119
1.1854726718380523e-114
Results
21.0ms236×0valid
19.0ms97×1valid
15.0ms51×2valid
Compiler

Compiled 400 to 322 computations (19.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-mult: 15.0ms (38.3% of total)
ival-sqrt: 9.0ms (23% of total)
ival-add: 6.0ms (15.3% of total)
ival-div: 5.0ms (12.8% of total)
backward-pass: 4.0ms (10.2% of total)
const: 2.0ms (5.1% of total)

bsearch73.0ms (0.6%)

Algorithm
3×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
19.0ms
1.6920451177764686e-51
1.699730937259005e-48
23.0ms
2.675525478933201e-109
1.1934948640760139e-104
23.0ms
2.997940026497908e-119
1.1854726718380523e-114
Results
24.0ms250×0valid
18.0ms96×1valid
11.0ms38×2valid
Compiler

Compiled 272 to 234 computations (14% saved)

Precisions
Click to see histograms. Total time spent on operations: 38.0ms
ival-mult: 16.0ms (41.9% of total)
ival-sqrt: 8.0ms (20.9% of total)
ival-add: 5.0ms (13.1% of total)
ival-div: 4.0ms (10.5% of total)
backward-pass: 3.0ms (7.9% of total)
const: 1.0ms (2.6% of total)

bsearch21.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
17.0ms
-1.2293738729983326e-101
-1.7508569279804595e-103
Results
7.0ms77×0valid
6.0ms33×1valid
1.0ms2×2valid
Compiler

Compiled 101 to 81 computations (19.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-mult: 4.0ms (42.2% of total)
ival-sqrt: 2.0ms (21.1% of total)
ival-add: 1.0ms (10.5% of total)
ival-div: 1.0ms (10.5% of total)
backward-pass: 1.0ms (10.5% of total)
const: 0.0ms (0% of total)

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 99 to 65 computations (34.3% saved)

preprocess50.0ms (0.4%)

Compiler

Compiled 400 to 276 computations (31% saved)

end0.0ms (0%)

Profiling

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