Given's Rotation SVD example

Time bar (total: 9.5s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze713.0ms (7.5%)

Memory
-107.7MiB live, 902.6MiB allocated
Algorithm
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 27 to 21 computations (22.2% saved)

sample2.2s (22.8%)

Memory
8.0MiB live, 1 726.5MiB allocated
Samples
1.0s6 251×0valid
303.0ms995×2valid
160.0ms609×1valid
134.0ms401×3valid
Precisions
Click to see histograms. Total time spent on operations: 1.2s
const: 355.0ms (28.8% of total)
ival-mult: 283.0ms (22.9% of total)
ival-sqrt: 185.0ms (15% of total)
ival-add: 120.0ms (9.7% of total)
ival-div: 93.0ms (7.5% of total)
ival-fabs: 69.0ms (5.6% of total)
adjust: 68.0ms (5.5% of total)
ival-<: 38.0ms (3.1% of total)
ival-and: 11.0ms (0.9% of total)
exact: 9.0ms (0.7% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

explain413.0ms (4.4%)

Memory
-24.6MiB live, 268.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
630-0-(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
340-0-(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
240-0-(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-(*.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-#s(literal 1 binary64)
00-0-(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
00-0-#s(literal 4 binary64)
00-0-(*.f64 x x)
00-0-p
00-0-(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
00-0-(*.f64 (*.f64 #s(literal 4 binary64) p) p)
00-0-#s(literal 1/2 binary64)
00-0-(*.f64 #s(literal 4 binary64) p)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))oflow-rescue630
(*.f64 #s(literal 4 binary64) p)overflow1
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))overflow63
(*.f64 (*.f64 #s(literal 4 binary64) p) p)overflow63
+.f64(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))cancellation340
sqrt.f64(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)))))))uflow-rescue240
(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)))))))underflow3
(*.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))))))underflow27
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))underflow27
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))underflow9
(*.f64 (*.f64 #s(literal 4 binary64) p) p)underflow59
Confusion
Predicted +Predicted -
+580
-63135
Precision
0.4793388429752066
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+5800
-630135
Precision?
0.4793388429752066
Recall?
1.0
Freqs
test
numberfreq
0135
1121
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
57.0ms56×2valid
53.0ms396×0valid
7.0ms42×1valid
6.0ms18×3valid
Compiler

Compiled 211 to 46 computations (78.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 82.0ms
ival-div: 49.0ms (59.6% of total)
ival-mult: 12.0ms (14.6% of total)
ival-sqrt: 10.0ms (12.2% of total)
ival-add: 7.0ms (8.5% of total)
adjust: 3.0ms (3.6% of total)
exact: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess65.0ms (0.7%)

Memory
-2.9MiB live, 36.0MiB allocated
Algorithm
egg-herbie
Rules
252×distribute-lft-neg-in
218×unsub-neg
198×associate-*r*
196×associate-*l*
162×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03693
19087
219487
340187
466187
599987
6133487
7154487
8169887
9193287
10199987
11202787
12202987
01417
02317
13817
24517
34717
44817
04815
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
Outputs
(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 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
Symmetry

(abs p)

Compiler

Compiled 19 to 14 computations (26.3% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
79.7%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0%)

Memory
6.4MiB live, 6.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
cost-diff0
(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)))))))
cost-diff128
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
cost-diff128
(*.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))))))
Rules
32×lower-*.f32
24×lower-*.f64
18×lower-fma.f64
18×lower-fma.f32
12×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01494
02394
13894
24594
34794
44894
04886
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
#s(literal 1 binary64)
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
x
(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)
Outputs
(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 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(*.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))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
x
(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
(*.f64 (*.f64 p #s(literal 4 binary64)) p)
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
p
(*.f64 x x)

localize54.0ms (0.6%)

Memory
-6.7MiB live, 74.2MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.015625
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
accuracy5.36585188626102
(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)))))))
accuracy7.523476986281956
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy14.63530602503128
(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
Samples
25.0ms198×0valid
10.0ms21×1valid
7.0ms28×2valid
3.0ms3valid
Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-sqrt: 12.0ms (36.5% of total)
ival-mult: 12.0ms (36.5% of total)
ival-add: 4.0ms (12.2% of total)
ival-div: 2.0ms (6.1% of total)
adjust: 2.0ms (6.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series32.0ms (0.3%)

Memory
-1.1MiB live, 38.1MiB allocated
Counts
5 → 120
Calls
Call 1
Inputs
#s(alt (*.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)))))) (patch (*.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)))))) #<representation binary64>) () ())
#s(alt (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) (patch (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) (patch (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 p) (#s(alt (*.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)))))) (patch (*.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (*.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)))))) (patch (*.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (*.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)))))) (patch (*.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (*.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)))))) (patch (*.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)))))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 p) (#s(alt (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) (patch (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) (patch (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) (patch (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) (patch (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 p) (#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 p) (#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x)) (taylor -inf x) (#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x)) (taylor -inf x) (#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x)) (taylor -inf x) (#s(alt (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))))))) (patch (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))))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow p 2) (pow x 2))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) (patch (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) (patch (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) (patch (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) (patch (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
15.0ms
x
@-inf
((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
3.0ms
x
@inf
((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
3.0ms
p
@0
((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
2.0ms
p
@inf
((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
2.0ms
x
@0
((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))

simplify200.0ms (2.1%)

Memory
24.9MiB live, 218.5MiB allocated
Algorithm
egg-herbie
Rules
9 590×lower-fma.f64
9 590×lower-fma.f32
6 900×lower-*.f64
6 900×lower-*.f32
4 472×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04342486
113252377
246112304
080842141
Stop Event
iter limit
node limit
Counts
120 → 118
Calls
Call 1
Inputs
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)))))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
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)))))
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)))))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
(* 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)))))))
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)))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1
(+ 1 (* -1/2 (/ x p)))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
(* -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))))))))
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)))))
(* 4 (pow p 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
(* 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)))))
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 x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
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)))))))
(/ (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))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
(* -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))))))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 3 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 p (/.f64 p (pow.f64 x #s(literal 6 binary64)))) #s(literal -10 binary64) (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (*.f64 (neg.f64 p) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(fma.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 1/2 binary64)) (/.f64 (*.f64 (-.f64 (/.f64 #s(literal 6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x))) (*.f64 p p) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 x x)) (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 p p) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (*.f64 p p) (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x))) (*.f64 p p) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -2 binary64) (*.f64 p (/.f64 p (*.f64 x x))) #s(literal 2 binary64))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 2 binary64))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -20 binary64) (*.f64 p (/.f64 p (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 2 binary64))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 p (/.f64 p (*.f64 (*.f64 x x) x))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) x)) #s(literal 4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) x))) (*.f64 p p) (/.f64 #s(literal 2 binary64) x)) (*.f64 p p) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 (fma.f64 (*.f64 x (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -1/32 binary64) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(fma.f64 x (fma.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 5 binary64)))) #s(literal -1/2 binary64) (fma.f64 (*.f64 x (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -1/32 binary64) (/.f64 #s(literal 1/4 binary64) p))) #s(literal 1/2 binary64))
(* 4 (pow p 2))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)) (*.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)) (*.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)) (*.f64 p p))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/32 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/32 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal -3/64 binary64) (*.f64 (*.f64 p p) p))) (sqrt.f64 #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(fma.f64 (fma.f64 (*.f64 x (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)) x #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
(fma.f64 x (fma.f64 (neg.f64 (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 5 binary64))) (fma.f64 (*.f64 x (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p))) #s(literal 1 binary64))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 (fma.f64 (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 1/4 binary64) #s(literal 2 binary64)) p)
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/64 binary64) (fma.f64 (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 1/4 binary64) #s(literal 2 binary64))) 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 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal 1/512 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/64 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) x) (*.f64 p p)))) #s(literal 2 binary64)) p)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (/.f64 x (*.f64 p p))) #s(literal -1/32 binary64) (*.f64 #s(literal 1/4 binary64) 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)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x (fma.f64 (/.f64 (*.f64 #s(literal -3/256 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) (/.f64 (*.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x x)) x) (*.f64 p p))) p))
(* 4 (pow p 2))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)) (*.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)) (*.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)) (*.f64 p p))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (*.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p)) #s(literal 1/32 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/4 binary64))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (*.f64 #s(literal -1/32 binary64) x) x (*.f64 (/.f64 (*.f64 #s(literal -3/64 binary64) (*.f64 (*.f64 x x) x)) p) #s(literal -1/2 binary64)))) (neg.f64 p))) p))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (/.f64 x (*.f64 p p))) #s(literal -1/16 binary64) (*.f64 #s(literal 1/2 binary64) x)) p))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (fma.f64 (neg.f64 (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal -3/256 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 1/2 binary64)) (*.f64 (*.f64 (*.f64 x x) x) (/.f64 #s(literal -1/16 binary64) (*.f64 p p)))) p))
(* -2 p)
(*.f64 #s(literal -2 binary64) p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 (neg.f64 p) (fma.f64 (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 1/4 binary64) #s(literal 2 binary64)))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (neg.f64 p) (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/64 binary64) (fma.f64 (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 1/4 binary64) #s(literal 2 binary64))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (neg.f64 p) (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal 1/512 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/64 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) x) (*.f64 p p)))) #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (fma.f64 (*.f64 x (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -1/32 binary64) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal 3/512 binary64) (/.f64 #s(literal -1/32 binary64) (*.f64 (*.f64 p p) p))) (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
(* 4 (pow p 2))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/32 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -3/128 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)) #s(literal -1/32 binary64))) x (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(fma.f64 (fma.f64 (*.f64 x (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 3/256 binary64) (*.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (*.f64 (*.f64 p p) p))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) p)) x #s(literal 1 binary64))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 (*.f64 x (/.f64 x p)) #s(literal 1/4 binary64) (*.f64 #s(literal 2 binary64) p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (fma.f64 (*.f64 x (/.f64 x (*.f64 (*.f64 p p) p))) #s(literal -1/64 binary64) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x) (*.f64 #s(literal 2 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)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) p))) (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x) (*.f64 #s(literal 2 binary64) p))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(fma.f64 (/.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/4 binary64) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) (fma.f64 (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (*.f64 (neg.f64 p) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(fma.f64 (*.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)) p) p (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 6 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(fma.f64 (*.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)) p) p (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 6 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 6 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64))) #s(literal 2 binary64)) (*.f64 p p) (fma.f64 #s(literal -32 binary64) (pow.f64 p #s(literal 6 binary64)) (neg.f64 (*.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 p p))))) (pow.f64 x #s(literal 6 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -2 binary64) (*.f64 p (/.f64 p (*.f64 x x))) #s(literal 2 binary64))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 (fma.f64 #s(literal -2 binary64) (*.f64 p (/.f64 p (*.f64 x x))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 6 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) #s(literal 2 binary64))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 (+.f64 (fma.f64 #s(literal -2 binary64) (*.f64 p (/.f64 p (*.f64 x x))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 6 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal -32 binary64) (pow.f64 p #s(literal 6 binary64)) (neg.f64 (*.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 p p)))) (pow.f64 x #s(literal 6 binary64))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -2 binary64) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 4 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -2 binary64) (*.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x))))) x x)
(/ (pow p 2) (pow x 2))
(*.f64 p (/.f64 p (*.f64 x x)))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.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 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p)) (*.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 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -256 binary64) (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 #s(literal 144 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 p p)) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(/.f64 (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))) (neg.f64 x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (*.f64 #s(literal 144 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 p p)))) (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)))) (neg.f64 x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (*.f64 #s(literal 144 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 p p)))) (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (*.f64 #s(literal 144 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 p p)))) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -256 binary64) (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 #s(literal 144 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))) (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 6 binary64))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)))) (neg.f64 x))
(* 2 (/ (pow p 2) (pow x 2)))
(*.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) p) p)) (*.f64 x x))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/2 binary64) (fma.f64 (*.f64 #s(literal 2 binary64) p) p (/.f64 (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 x x))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -256 binary64) (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 #s(literal 144 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 #s(literal 2 binary64) p) p (/.f64 (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 p p))) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 x x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (fma.f64 (*.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -2 binary64) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 4 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -2 binary64) (*.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x))))) x x))

rewrite242.0ms (2.6%)

Memory
-41.6MiB live, 263.3MiB allocated
Rules
4 862×lower-fma.f64
4 862×lower-fma.f32
3 532×lower-*.f32
3 524×lower-*.f64
2 388×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01466
02366
17766
250166
3696766
0849259
Stop Event
iter limit
node limit
iter limit
Counts
5 → 276
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
Outputs
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x) (*.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) (-.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (-.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (-.f64 (-.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (fma.f64 x (+.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)))
(*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(*.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(*.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x)) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 (*.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64))) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(/.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/8 binary64)) (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))))
(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p)))) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (*.f64 p #s(literal 4 binary64)) p))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p))))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
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(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(*.f64 (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (*.f64 p #s(literal 4 binary64)) p)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -4 binary64) (*.f64 p p) (*.f64 x x)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x))))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x))))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x)))) #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p)))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (*.f64 p #s(literal 4 binary64)) p)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p))))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (*.f64 #s(literal -16 binary64) (*.f64 (*.f64 (*.f64 p p) p) p)))) (sqrt.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) (fma.f64 #s(literal -4 binary64) (*.f64 p p) (*.f64 x x)))) (sqrt.f64 (fma.f64 #s(literal -4 binary64) (*.f64 p p) (*.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (*.f64 p #s(literal 4 binary64)) p)))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p))) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (*.f64 p #s(literal 4 binary64)) p))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p)))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 (*.f64 p #s(literal 4 binary64)) p))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x (*.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 p p)) p) p (*.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 p p))) (*.f64 x x)))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (*.f64 p p) p) #s(literal 64 binary64)) (*.f64 (*.f64 p p) p))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(exp.f64 (*.f64 (log.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/2 binary64)))

eval187.0ms (2%)

Memory
-2.6MiB live, 114.7MiB allocated
Compiler

Compiled 15 630 to 1 953 computations (87.5% saved)

prune106.0ms (1.1%)

Memory
13.3MiB live, 174.8MiB allocated
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New37717394
Fresh000
Picked101
Done000
Total37817395
Accuracy
99.8%
Counts
395 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.7%
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
79.7%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
77.6%
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
50.8%
(sqrt.f64 (/.f64 (*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) (*.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
16.0%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (*.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
49.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
28.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
12.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
11.4%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p)) (*.f64 x x))))
18.8%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
38.4%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
53.6%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
49.6%
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
25.4%
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x)))
Compiler

Compiled 1 042 to 424 computations (59.3% saved)

simplify165.0ms (1.7%)

Memory
-20.1MiB live, 177.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
cost-diff0
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
cost-diff320
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
cost-diff2688
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
cost-diff0
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
cost-diff0
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
cost-diff0
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
cost-diff0
(neg.f64 p)
cost-diff0
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
cost-diff0
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
cost-diff0
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
cost-diff0
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
Rules
8 040×lower-fma.f32
8 032×lower-fma.f64
3 234×lower-*.f32
3 226×lower-*.f64
1 282×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039507
066499
1125499
2232499
3584499
41710499
54291466
66233459
77167459
87720459
97833459
107853459
08024456
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(neg.f64 p)
p
(/.f64 p (*.f64 x x))
(*.f64 x x)
x
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
#s(literal 1/2 binary64)
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
(*.f64 x x)
x
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
#s(literal 1/2 binary64)
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
#s(literal -1 binary64)
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
(*.f64 x x)
(/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
#s(literal 1 binary64)
Outputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)
p
#s(literal 4 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 p (*.f64 x x)) (neg.f64 p) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 p (*.f64 x x)) (neg.f64 p) #s(literal 1 binary64)))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(fma.f64 (/.f64 p (*.f64 x x)) (neg.f64 p) #s(literal 1 binary64))
(neg.f64 p)
p
(/.f64 p (*.f64 x x))
(*.f64 x x)
x
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
#s(literal 1/2 binary64)
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)
p
#s(literal 4 binary64)
(*.f64 x x)
x
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(sqrt.f64 (*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
#s(literal 1/2 binary64)
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 #s(literal -1 binary64) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64)))
#s(literal -1 binary64)
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)
p
#s(literal 4 binary64)
(*.f64 x x)
(/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
#s(literal 1 binary64)

localize183.0ms (1.9%)

Memory
20.6MiB live, 453.1MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy8.254723807951137
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
accuracy8.254723807951137
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
accuracy24.498133012507097
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
accuracy0.0078125
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
accuracy5.36585188626102
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
accuracy14.205459821490946
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
accuracy0.07421875
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
accuracy0.1953125
(/.f64 p (*.f64 x x))
accuracy5.36585188626102
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
accuracy45.431940470665594
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
accuracy5.36585188626102
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy30.104816230271524
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy0.015625
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
accuracy5.36585188626102
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy7.522607369904728
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
Samples
55.0ms63×2valid
39.0ms128×0valid
36.0ms49×1valid
16.0ms16×3valid
Compiler

Compiled 519 to 41 computations (92.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 102.0ms
ival-mult: 26.0ms (25.5% of total)
ival-sqrt: 19.0ms (18.6% of total)
ival-div: 18.0ms (17.7% of total)
adjust: 17.0ms (16.7% of total)
ival-add: 16.0ms (15.7% of total)
ival-sub: 4.0ms (3.9% of total)
ival-neg: 1.0ms (1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series104.0ms (1.1%)

Memory
6.1MiB live, 203.3MiB allocated
Counts
21 → 492
Calls
Call 1
Inputs
#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (patch (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) (patch (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (patch (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) #<representation binary64>) () ())
#s(alt (/.f64 p (*.f64 x x)) (patch (/.f64 p (*.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) (patch (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 2 (/ (pow p 2) x))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
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Calls

6 calls:

TimeVariablePointExpression
25.0ms
x
@inf
((sqrt (+ (* (/ 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)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x)))))) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))))) (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ p (* x x)) (+ (* (* p 4) p) (* x x)) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
22.0ms
x
@-inf
((sqrt (+ (* (/ 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)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x)))))) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))))) (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ p (* x x)) (+ (* (* p 4) p) (* x x)) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
9.0ms
p
@inf
((sqrt (+ (* (/ 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)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x)))))) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))))) (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ p (* x x)) (+ (* (* p 4) p) (* x x)) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
6.0ms
p
@0
((sqrt (+ (* (/ 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)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x)))))) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))))) (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ p (* x x)) (+ (* (* p 4) p) (* x x)) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
5.0ms
x
@0
((sqrt (+ (* (/ 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)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x)))))) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (+ (* (* p 4) p) (* x x))))))) (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ p (* x x)) (+ (* (* p 4) p) (* x x)) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))

simplify231.0ms (2.4%)

Memory
6.3MiB live, 402.1MiB allocated
Algorithm
egg-herbie
Rules
6 992×lower-fma.f64
6 992×lower-fma.f32
6 964×lower-*.f64
6 964×lower-*.f32
4 820×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0146020510
1478820185
0819618822
Stop Event
iter limit
node limit
Counts
492 → 490
Calls
Call 1
Inputs
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))))))
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
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
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)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
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(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
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(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
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))))))
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 x)
(+ (* -1 (/ (pow p 2) (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 5))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))
(+ (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 7))) (* 3 (/ 1 (pow x 5))))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))
(* -1 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow p 2)))
(/ (- (* 2 (pow p 2)) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(/ (- (* (pow p 2) (+ 2 (* -2 (/ (pow p 2) (pow x 2))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(/ (- (* (pow p 2) (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow p 2)))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2)) (pow p 2))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (* (pow p 2) (+ 1 (* -1 (/ (pow p 2) (pow x 2)))))) (pow p 2))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (* (pow p 2) (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))))) (pow p 2))
(* (/ (sqrt -1/2) p) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))
(/ (+ (* -1 (* (* (pow p 2) (sqrt -1/2)) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))) p)
(/ (+ (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* (pow p 2) (+ (* -1 (* (sqrt -1/2) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* 1/2 (* (* (pow p 2) (* (sqrt -1/2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))))))) p)
(/ (+ (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* (pow p 2) (+ (* -1 (* (sqrt -1/2) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* (pow p 2) (+ (* -1/2 (* (* (pow p 2) (* (sqrt -1/2) (+ (* -1 (/ (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 6 (/ 1 (pow x 4)))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* 1/2 (* (* (sqrt -1/2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))))))))) p)
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* 1/2 (pow x 2)) (* 3/2 (pow p 2))) (pow p 2))
(/ (+ (* 1/2 (pow x 2)) (* (pow p 2) (+ 3/2 (* -1/2 (/ (pow p 2) (pow x 2)))))) (pow p 2))
(/ (+ (* 1/2 (pow x 2)) (* (pow p 2) (+ 3/2 (* (pow p 2) (- (/ (pow p 2) (pow x 4)) (* 1/2 (/ 1 (pow x 2)))))))) (pow p 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(* -2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* 2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* -6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* 20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(sqrt 1/2)
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(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
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1/2
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(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* 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)))))))
(sqrt 1/2)
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(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
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(+ 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)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
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(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
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 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(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)))))))
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)))))
(/ 1/4 p)
(/ (+ 1/4 (* -1/32 (/ (pow x 2) (pow p 2)))) p)
(/ (+ 1/4 (+ (* -1/2 (/ (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))) (pow p 4))) (* -1/32 (/ (pow x 2) (pow p 2))))) p)
(/ (+ 1/4 (+ (* -1/2 (/ (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))) (pow p 4))) (+ (* -1/2 (/ (+ (* 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 2) (pow p 2)))))) p)
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/8 (/ (pow x 3) (pow p 3))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (+ (* 1/8 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))))
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1/2
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(* (sqrt -1) (sqrt -1/2))
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1
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(/ p (pow x 2))
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(/ p (pow x 2))
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1
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1/2
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(* -2 p)
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(sqrt 1/2)
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1/2
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(sqrt 1/2)
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1/2
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(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
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1/2
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(/ -1/4 p)
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(* -1 (/ (+ 1/4 (+ (* -1/2 (/ (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))) (pow p 4))) (+ (* -1/2 (/ (+ (* 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 2) (pow p 2)))))) p))
1
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(+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (pow x 4)) (+ (* -1/32 (pow x 4)) (+ (* 1/16 (pow x 4)) (* 1/2 (* x (+ (* -1/16 (pow x 3)) (* 1/8 (pow x 3)))))))) (pow p 3))) (+ (* -1/8 (/ (pow x 3) (pow p 2))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (+ (* 1/8 (/ (pow x 3) (pow p 2))) (* 1/2 x))))) p)))
1/2
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(* (sqrt -1) (sqrt -1/2))
(+ (* 1/4 (/ (* x (sqrt -1/2)) (* p (sqrt -1)))) (* (sqrt -1) (sqrt -1/2)))
(+ (* -1 (/ (+ (* -1/4 (/ (* x (sqrt -1/2)) (sqrt -1))) (* 1/32 (/ (* (pow x 2) (sqrt -1/2)) (* p (pow (sqrt -1) 3))))) p)) (* (sqrt -1) (sqrt -1/2)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/32 (/ (* (pow x 2) (sqrt -1/2)) (pow (sqrt -1) 3))) (* 1/2 (/ (* (sqrt -1/2) (+ (* -1/8 (pow x 3)) (+ (* -1/16 (pow x 3)) (+ (* 1/64 (/ (pow x 3) (pow (sqrt -1) 4))) (* 1/8 (pow x 3)))))) (* p (sqrt -1))))) p)) (* -1/4 (/ (* x (sqrt -1/2)) (sqrt -1)))) p)) (* (sqrt -1) (sqrt -1/2)))
1
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(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
-1
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(- (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)) 1)
(- (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)) 1)
1
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(+ 1 (* -1 (/ (- (* 1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (- (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4)) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
(sqrt 1/2)
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(+ (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)))))))
1/2
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(+ 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 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* 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)))))
(sqrt 1/2)
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(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
1/2
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(sqrt 1/2)
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(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
1/2
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(+ 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 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
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(+ (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)))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
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(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(/ 1/4 p)
(+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))
(+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))
(+ (* (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
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(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 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)))))
(* (sqrt -1) (sqrt -1/2))
(+ (* -1/4 (/ (* x (sqrt -1/2)) (* p (sqrt -1)))) (* (sqrt -1) (sqrt -1/2)))
(+ (* x (+ (* -1/4 (/ (sqrt -1/2) (* p (sqrt -1)))) (* -1/32 (/ (* x (sqrt -1/2)) (* (pow p 2) (pow (sqrt -1) 3)))))) (* (sqrt -1) (sqrt -1/2)))
(+ (* x (+ (* -1/4 (/ (sqrt -1/2) (* p (sqrt -1)))) (* x (+ (* -1/32 (/ (sqrt -1/2) (* (pow p 2) (pow (sqrt -1) 3)))) (* 1/2 (/ (* x (* (sqrt -1/2) (- (* 1/16 (/ 1 (pow p 3))) (* 1/64 (/ 1 (* (pow p 3) (pow (sqrt -1) 4))))))) (sqrt -1))))))) (* (sqrt -1) (sqrt -1/2)))
1
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(+ 1 (* x (+ (* x (+ (* 1/16 (/ x (pow p 3))) (* 1/4 (/ 1 (pow p 2))))) (* 1/2 (/ 1 p)))))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(* 4 (pow p 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
-1
(- (* 1/2 (/ x p)) 1)
(- (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))) 1)
(- (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) 1)
1
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(+ 1 (* x (- (* 1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (- (* (pow x 2) (+ (* -3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
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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))))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
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)))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
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))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
1
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(* 1/2 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/8 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (* 1/2 (/ 1 (pow p 2)))) (* 1/8 (/ (+ (* -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))) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/8 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/32 (/ (* (+ (* -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 (/ (+ (* -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 (/ 1 (pow p 2)))) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/8 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (* (pow p 4) (pow x 4))))))))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (- (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -2 (pow p 2))) (pow x 2))
(/ (- (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))))) (pow x 2))
(/ (- (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
(* -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))
(/ (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
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
(* -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 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(/ (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 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(/ (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 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(* -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))
(/ (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))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))) x))
(* -1 (/ (+ 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)))))) x))
(/ (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))) (pow x 2))
(/ (+ (* -1/8 (/ (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2) (pow x 2))) (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (+ (* 1/4 (/ (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2))) (+ (* 1/2 (/ (pow p 4) (pow x 2))) (* 1/2 (pow p 2))))))) (pow x 2))
(/ (+ (* -1/2 (/ (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 4))) (+ (* -1/8 (/ (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (pow x 4))) (+ (* -1/8 (/ (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2) (pow x 2))) (+ (* 1/8 (/ (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (pow x 4))) (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/8 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (+ (* 1/4 (/ (+ (* -8 (pow p 4)) (* -1/2 (+ (* -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))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (pow x 4))) (+ (* 1/2 (/ (pow p 4) (pow x 2))) (+ (* 1/2 (pow p 2)) (/ (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))) (pow x 4))))))))))))) (pow x 2))
(/ (+ (* -1/2 (/ (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6))) (+ (* -1/2 (/ (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))))) (pow x 6))) (+ (* -1/2 (/ (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 4))) (+ (* -1/8 (/ (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (pow x 4))) (+ (* -1/8 (/ (* (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (pow x 6))) (+ (* -1/8 (/ (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2) (pow x 2))) (+ (* 1/8 (/ (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (pow x 4))) (+ (* 1/8 (/ (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow x 6))) (+ (* 1/8 (/ (+ (* -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))) (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/8 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))) (pow x 6))) (+ (* 1/4 (/ (+ (* -8 (pow p 4)) (* -1/2 (+ (* -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))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (pow x 4))) (+ (* 1/4 (/ (+ (* -2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))))) (pow x 6))) (+ (* 1/2 (/ (pow p 4) (pow x 2))) (+ (* 1/2 (pow p 2)) (+ (/ (* (pow p 2) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))) (pow x 6)) (/ (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))) (pow x 4))))))))))))))))))))) (pow x 2))
(* 1/2 (/ (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))) (pow x 2)))
(/ (+ (* 1/2 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))) (* 1/2 (/ (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) (pow x 2)))) (pow x 2))
(/ (+ (* 1/2 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))) (+ (* 1/2 (/ (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))))) (pow x 4))) (* 1/2 (/ (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) (pow x 2))))) (pow x 2))
(/ (+ (* 1/2 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))) (+ (* 1/2 (/ (+ (* -1/2 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (+ (* -1/8 (* (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* 1/8 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (+ (* 1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (* (pow p 2) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))))))))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))))) (pow x 4))) (* 1/2 (/ (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) (pow x 2)))))) (pow x 2))
(* -1 (* (/ (* (sqrt -1) (sqrt -1/2)) x) (sqrt (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))
(* -1 (/ (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4)))))) (* (pow x 2) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (* (* (sqrt -1) (sqrt -1/2)) (sqrt (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))) x))
(* -1 (/ (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (+ (* 1/4 (/ (pow (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) 2) (* (pow (sqrt -1) 2) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))))))) (* (pow x 4) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4)))))) (* (pow x 2) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (* (* (sqrt -1) (sqrt -1/2)) (sqrt (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) x))
(* -1 (/ (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/2 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (+ (* -1/8 (* (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* 1/8 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (+ (* 1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (+ (* 1/2 (/ (* (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (+ (* 1/4 (/ (pow (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) 2) (* (pow (sqrt -1) 2) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))))))))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4)))))) (* (pow (sqrt -1) 2) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))) (* (pow p 2) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))))))))))))))) (* (pow x 6) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (+ (* 1/4 (/ (pow (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) 2) (* (pow (sqrt -1) 2) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))))))) (* (pow x 4) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4)))))) (* (pow x 2) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (* (* (sqrt -1) (sqrt -1/2)) (sqrt (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))))) x))
1/2
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1/2 (/ (pow p 2) (pow x 2))))
(- (+ 1/2 (* -1 (/ (+ (* -1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (pow p 4) (pow x 4))) (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
-2
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 11/8 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
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)))))
(fma.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -10 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 6 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -20 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 (*.f64 x x) x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64))) #s(literal 4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 (*.f64 x x) x))) (*.f64 p p) (/.f64 #s(literal 2 binary64) x)) (*.f64 p p) x)
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (*.f64 (neg.f64 p) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
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1
#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
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#s(literal 1/2 binary64)
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x
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#s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64)))))) (fma.f64 (*.f64 (*.f64 p p) #s(literal 6 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 p p))))))))))))) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 p p) #s(literal 6 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 p p))))) (fma.f64 (*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 p p) #s(literal 6 binary64))) (fma.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 p #s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 36 binary64)) #s(literal -1/8 binary64))) (fma.f64 (*.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal -8 binary64) (pow.f64 p #s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64)))) (*.f64 (*.f64 p p) #s(literal 6 binary64)) (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (fma.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) #s(literal 1/8 binary64) (fma.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (fma.f64 (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64))) (*.f64 p p) (*.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 36 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/8 binary64) (fma.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 p #s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (fma.f64 (*.f64 (*.f64 p p) #s(literal 6 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 p p))))))))))) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 p p) #s(literal 6 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 p p)))))) #s(literal -1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 p p) #s(literal 6 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 p p))))) (/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 36 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/8 binary64) (fma.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 p #s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64))))) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 6 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 p p)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64))))))) (neg.f64 x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))
(- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1/2 (/ (pow p 2) (pow x 2))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 p p)) (*.f64 x x)))
(- (+ 1/2 (* -1 (/ (+ (* -1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (pow p 4) (pow x 4))) (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (fma.f64 (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/2 binary64))) (*.f64 p p) (*.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) #s(literal -1/8 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (/.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/ p (pow x 2))
(/.f64 p (*.f64 x x))
(/ p (pow x 2))
(/.f64 p (*.f64 x x))
(/ p (pow x 2))
(/.f64 p (*.f64 x x))
(/ p (pow x 2))
(/.f64 p (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
-2
#s(literal -2 binary64)
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -2 binary64))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -2 binary64)))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
(fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (-.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(-.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x)))
(- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
(-.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)) (*.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/2 binary64) #s(literal 2 binary64)) (fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))))

rewrite233.0ms (2.5%)

Memory
-17.8MiB live, 461.6MiB allocated
Rules
4 740×lower-/.f32
4 730×lower-/.f64
4 628×lower-fma.f32
4 620×lower-fma.f64
4 038×lower-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
039375
066307
1288307
22178278
08239278
Stop Event
iter limit
node limit
iter limit
Counts
21 → 780
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(neg.f64 p)
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 p (*.f64 x x))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
Outputs
(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x #s(literal -1/2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/4 binary64)))))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/4 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(pow.f64 (exp.f64 (log.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
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(pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
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(fma.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))
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(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
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(pow.f64 (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) #s(literal -1 binary64))
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(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))) (neg.f64 (neg.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (neg.f64 (-.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))) (neg.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (neg.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (neg.f64 (neg.f64 (-.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (-.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (neg.f64 (-.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64)))
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1 binary64))
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(fma.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))
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(fma.f64 x (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (/.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
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(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (/.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64))) (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal 1 binary64))))
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(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
(+.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))
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eval273.0ms (2.9%)

Memory
43.7MiB live, 624.6MiB allocated
Compiler

Compiled 87 622 to 5 870 computations (93.3% saved)

prune246.0ms (2.6%)

Memory
-24.6MiB live, 576.3MiB allocated
Pruning

18 alts after pruning (14 fresh and 4 done)

PrunedKeptTotal
New1 74381 751
Fresh6612
Picked145
Done000
Total1 750181 768
Accuracy
99.9%
Counts
1 768 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
79.7%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
77.6%
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
6.6%
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
50.8%
(sqrt.f64 (/.f64 (*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))))
52.4%
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
50.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) (*.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
16.0%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (*.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
49.9%
(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
28.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
12.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
11.4%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p)) (*.f64 x x))))
18.8%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
53.6%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
49.6%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
25.6%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
38.4%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Compiler

Compiled 958 to 404 computations (57.8% saved)

simplify128.0ms (1.4%)

Memory
14.9MiB live, 167.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
cost-diff0
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
cost-diff0
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
cost-diff128
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64))
cost-diff0
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))
cost-diff0
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
cost-diff0
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
cost-diff0
(/.f64 p (*.f64 x x))
cost-diff0
(*.f64 p (/.f64 p (*.f64 x x)))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x))))
cost-diff0
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
cost-diff0
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
cost-diff0
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
cost-diff0
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
cost-diff704
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))
cost-diff3008
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
Rules
6 540×lower-fma.f32
6 534×lower-fma.f64
3 158×lower-*.f32
3 142×lower-*.f64
1 572×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059655
098687
1172687
2315669
3708669
42122599
55177599
67644599
08046590
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
#s(literal 1/2 binary64)
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
#s(literal -1 binary64)
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
(*.f64 x x)
(/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x)))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x)
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x))))
(*.f64 p (/.f64 p (*.f64 x x)))
p
(/.f64 p (*.f64 x x))
(*.f64 x x)
x
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
#s(literal 1 binary64)
(/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
Outputs
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(sqrt.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x #s(literal -1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1 binary64))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 (fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x #s(literal -1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1 binary64)))
#s(literal 1/2 binary64)
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x #s(literal -1 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))))))
#s(literal -1 binary64)
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)
p
#s(literal 4 binary64)
(*.f64 x x)
(/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))))) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))))) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x)))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x)
(/.f64 (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x)
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p (*.f64 x x)) p)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p (*.f64 x x)) p))
(*.f64 p (/.f64 p (*.f64 x x)))
(*.f64 (/.f64 p (*.f64 x x)) p)
p
(/.f64 p (*.f64 x x))
(*.f64 x x)
x
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 #s(literal 2 binary64) (*.f64 (/.f64 p (*.f64 x x)) p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 #s(literal 2 binary64) (*.f64 (/.f64 p (*.f64 x x)) p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 #s(literal 2 binary64) (*.f64 (/.f64 p (*.f64 x x)) p) #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 (/.f64 p (*.f64 x x)) p) #s(literal -1 binary64))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 (/.f64 p (*.f64 x x)) p)
(*.f64 p p)
p
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(sqrt.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x #s(literal -1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(/.f64 (fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x #s(literal -1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(fma.f64 (/.f64 (neg.f64 x) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))) x #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(/.f64 (*.f64 x x) (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x))))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 p p) #s(literal 4 binary64) (*.f64 x x)))

localize220.0ms (2.3%)

Memory
31.7MiB live, 381.4MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy8.254723807951137
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
accuracy8.500096286778886
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
accuracy15.76837851663261
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
accuracy5.36585188626102
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy6.2409763046854065
(/.f64 (*.f64 p p) (*.f64 x x))
accuracy7.522607369904728
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy47.88070936590358
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
accuracy0.12109375
(*.f64 p (/.f64 p (*.f64 x x)))
accuracy0.1953125
(/.f64 p (*.f64 x x))
accuracy5.36585188626102
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
accuracy46.96840349816959
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x))))
accuracy39.3985358230606
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
accuracy8.254723807951137
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
accuracy24.498133012507097
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
Samples
69.0ms62×2valid
41.0ms128×0valid
26.0ms44×1valid
26.0ms22×3valid
Compiler

Compiled 649 to 48 computations (92.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 122.0ms
ival-mult: 30.0ms (24.5% of total)
ival-div: 27.0ms (22.1% of total)
ival-add: 23.0ms (18.8% of total)
ival-sqrt: 19.0ms (15.5% of total)
adjust: 14.0ms (11.4% of total)
ival-sub: 8.0ms (6.5% of total)
exact: 1.0ms (0.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series91.0ms (1%)

Memory
-16.7MiB live, 147.2MiB allocated
Counts
22 → 528
Calls
Call 1
Inputs
#s(alt (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) (patch (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x))))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x))))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))) #<representation binary64>) () ())
#s(alt (*.f64 p (/.f64 p (*.f64 x x))) (patch (*.f64 p (/.f64 p (*.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 p (*.f64 x x)) (patch (/.f64 p (*.f64 x x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) (patch #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (patch (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))) (patch (sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (patch (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (patch (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 p p) (*.f64 x x)) (patch (/.f64 (*.f64 p p) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #<representation binary64>) () ())
Outputs
#s(alt (* -1 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow p 2))) (taylor 0 p) (#s(alt (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())) ())
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#s(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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (patch (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow p 2) (pow x 2))) 2) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (*.f64 p p) (*.f64 x x)) (patch (/.f64 (*.f64 p p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (*.f64 p p) (*.f64 x x)) (patch (/.f64 (*.f64 p p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (*.f64 p p) (*.f64 x x)) (patch (/.f64 (*.f64 p p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (*.f64 p p) (*.f64 x x)) (patch (/.f64 (*.f64 p p) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 2 (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
24.0ms
x
@-inf
((- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))) (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x)))))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* p (/ p (* x x))) (/ p (* x x)) (sqrt (+ (* (/ 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)))) (+ (* (/ (* p p) (* x x)) 2) -1) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (+ (* (* p 4) p) (* x x))) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
9.0ms
x
@inf
((- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))) (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x)))))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* p (/ p (* x x))) (/ p (* x x)) (sqrt (+ (* (/ 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)))) (+ (* (/ (* p p) (* x x)) 2) -1) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (+ (* (* p 4) p) (* x x))) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
3.0ms
p
@0
((- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))) (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x)))))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* p (/ p (* x x))) (/ p (* x x)) (sqrt (+ (* (/ 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)))) (+ (* (/ (* p p) (* x x)) 2) -1) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (+ (* (* p 4) p) (* x x))) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
3.0ms
p
@inf
((- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))) (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x)))))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* p (/ p (* x x))) (/ p (* x x)) (sqrt (+ (* (/ 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)))) (+ (* (/ (* p p) (* x x)) 2) -1) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (+ (* (* p 4) p) (* x x))) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
2.0ms
x
@0
((- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))) (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x))))))) (* 1/2 (- (/ -1 (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))) (/ (* x x) (* (- 1 (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x))) (+ (* (* p 4) p) (* x x)))))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* p (/ p (* x x))) (/ p (* x x)) (sqrt (+ (* (/ 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)))) (+ (* (/ (* p p) (* x x)) 2) -1) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (+ (* (* p 4) p) (* x x))) (+ -1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

simplify330.0ms (3.5%)

Memory
5.2MiB live, 440.0MiB allocated
Algorithm
egg-herbie
Rules
7 420×lower-*.f64
7 420×lower-*.f32
7 232×lower-fma.f64
7 232×lower-fma.f32
5 028×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0153221715
1503621411
0875119978
Stop Event
iter limit
node limit
Counts
528 → 524
Calls
Call 1
Inputs
(* -1 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow p 2)))
(/ (- (* 2 (pow p 2)) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(/ (- (* (pow p 2) (+ 2 (* -2 (/ (pow p 2) (pow x 2))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(/ (- (* (pow p 2) (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* (/ (sqrt -1/2) p) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))
(/ (+ (* -1 (* (* (pow p 2) (sqrt -1/2)) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))) p)
(/ (+ (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* (pow p 2) (+ (* -1 (* (sqrt -1/2) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* 1/2 (* (* (pow p 2) (* (sqrt -1/2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))))))) p)
(/ (+ (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* (pow p 2) (+ (* -1 (* (sqrt -1/2) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* (pow p 2) (+ (* -1/2 (* (* (pow p 2) (* (sqrt -1/2) (+ (* -1 (/ (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 6 (/ 1 (pow x 4)))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* 1/2 (* (* (sqrt -1/2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))))))))) p)
(* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow p 2)))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2)) (pow p 2))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (* (pow p 2) (+ 1 (* -1 (/ (pow p 2) (pow x 2)))))) (pow p 2))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (* (pow p 2) (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))))) (pow p 2))
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 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
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)))))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
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))))))
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
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(* 2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* 32 (/ (pow p 2) (pow x 6))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -128 (/ (pow p 2) (pow x 8))) (* 32 (/ 1 (pow x 6))))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
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1
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1/2
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(sqrt 1/2)
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1/2
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1
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-1
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1
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1
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(* (sqrt -1) (sqrt -1/2))
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1/2
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(sqrt 1/2)
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(sqrt 1/2)
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1/2
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(sqrt 1/2)
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1/2
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1/2
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(sqrt 1/2)
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1/2
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1
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-1
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(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
1
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1
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1/2
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(sqrt 1/2)
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1
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1
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1
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1
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1
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1
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-1
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1
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x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
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x
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(/ (pow p 2) (pow x 2))
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(* -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 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(/ (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))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(* -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))
(/ (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
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -8 (/ (pow p 4) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* -8 (/ (pow p 4) (pow x 2))) (+ (* 2 (pow p 2)) (* 32 (/ (pow p 6) (pow x 4))))) (pow x 2))
(/ (+ (* -128 (/ (pow p 8) (pow x 6))) (+ (* -8 (/ (pow p 4) (pow x 2))) (+ (* 2 (pow p 2)) (* 32 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* 1/2 (/ (* (- (* -8 (pow p 4)) (* -2 (pow p 4))) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* (pow p 2) (pow (sqrt 2) 2))))))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4)))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2)))) (pow x 2))
(* 4 (/ (pow p 2) (pow x 2)))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4))))) (pow x 2))
(/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -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 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))))))))
-2
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
Outputs
(* -1 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow p 2)))
(/.f64 #s(literal 0 binary64) (*.f64 p p))
(/ (- (* 2 (pow p 2)) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(/.f64 (fma.f64 (*.f64 p p) #s(literal 2 binary64) #s(literal 0 binary64)) (*.f64 p p))
(/ (- (* (pow p 2) (+ 2 (* -2 (/ (pow p 2) (pow x 2))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(/.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal 2 binary64)) (*.f64 p p) #s(literal 0 binary64)) (*.f64 p p))
(/ (- (* (pow p 2) (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2))
(/.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 2 binary64)) (*.f64 p p) #s(literal 0 binary64)) (*.f64 p p))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -20 binary64) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(* (/ (sqrt -1/2) p) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))
(*.f64 (sqrt.f64 #s(literal 0 binary64)) (/.f64 (sqrt.f64 #s(literal -1/2 binary64)) p))
(/ (+ (* -1 (* (* (pow p 2) (sqrt -1/2)) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))) p)
(/.f64 (fma.f64 (neg.f64 (*.f64 p p)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))) p)
(/ (+ (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* (pow p 2) (+ (* -1 (* (sqrt -1/2) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* 1/2 (* (* (pow p 2) (* (sqrt -1/2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))))))) p)
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 p p)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))))) (*.f64 p p) (*.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))) p)
(/ (+ (* (sqrt -1/2) (sqrt (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* (pow p 2) (+ (* -1 (* (sqrt -1/2) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* (pow p 2) (+ (* -1/2 (* (* (pow p 2) (* (sqrt -1/2) (+ (* -1 (/ (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))) (* 6 (/ 1 (pow x 4)))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))))))) (* 1/2 (* (* (sqrt -1/2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))) (sqrt (/ 1 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))))))))))) p)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 p p))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))))) (*.f64 p p) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))))) (*.f64 p p) (*.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))) p)
(* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2))) (pow p 2)))
(/.f64 #s(literal 0 binary64) (*.f64 p p))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (pow p 2)) (pow p 2))
(/.f64 (fma.f64 p p #s(literal 0 binary64)) (*.f64 p p))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (* (pow p 2) (+ 1 (* -1 (/ (pow p 2) (pow x 2)))))) (pow p 2))
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x))) (*.f64 p p) #s(literal 0 binary64)) (*.f64 p p))
(/ (+ (* -1/2 (+ (* -1/2 (pow x 2)) (* 1/2 (pow x 2)))) (* (pow p 2) (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))))) (pow p 2))
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64)) (*.f64 p p) #s(literal 0 binary64)) (*.f64 p p))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 11/8 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -69/16 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (neg.f64 (*.f64 p p)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
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(* (sqrt -1) (sqrt -1/2))
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1/2
#s(literal 1/2 binary64)
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(sqrt 1/2)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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(* 2 p)
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#s(literal -1 binary64)
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1/2
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(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (*.f64 x x)) #s(literal -16 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 64 binary64) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) (*.f64 x x))
(/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 8 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -256 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (*.f64 x x)) #s(literal -16 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 64 binary64) (*.f64 #s(literal 4 binary64) (*.f64 p p))))) (*.f64 x x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(neg.f64 (fma.f64 x (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) 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))))))))
(neg.f64 (fma.f64 x (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 4 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x)))) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(neg.f64 (fma.f64 x (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) 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))))))))
(neg.f64 (fma.f64 x (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 4 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x)))) x))
-2
#s(literal -2 binary64)
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -2 binary64))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -2 binary64)))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
(fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (-.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 p p)) #s(literal 2 binary64) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) #s(literal 2 binary64)))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal 2 binary64))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(-.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x)))
(- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
(-.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 p p)) #s(literal 2 binary64) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/2 binary64) #s(literal 2 binary64)) (fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))))

rewrite273.0ms (2.9%)

Memory
21.2MiB live, 379.6MiB allocated
Rules
4 584×lower-/.f32
4 566×lower-/.f64
4 156×lower-fma.f32
4 150×lower-fma.f64
3 794×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059452
097472
1383456
22657311
09351304
Stop Event
iter limit
node limit
iter limit
Counts
22 → 850
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x))))
(*.f64 p (/.f64 p (*.f64 x x)))
(/.f64 p (*.f64 x x))
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 (*.f64 p p) (*.f64 x x))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
Outputs
(*.f64 (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (+.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64)) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64))) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64)))
(*.f64 (*.f64 (fma.f64 (/.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
(*.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) #s(literal -3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (fma.f64 (/.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))))
(*.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (/.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))) (*.f64 (fma.f64 (/.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) x (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64)))) #s(literal -1 binary64))
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(-.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))) (/.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x) (neg.f64 (-.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))) (/.f64 (*.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))) (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (+.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
(+.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))

eval326.0ms (3.4%)

Memory
-16.4MiB live, 510.6MiB allocated
Compiler

Compiled 71 465 to 5 022 computations (93% saved)

prune233.0ms (2.5%)

Memory
-20.0MiB live, 551.7MiB allocated
Pruning

20 alts after pruning (11 fresh and 9 done)

PrunedKeptTotal
New1 41561 421
Fresh459
Picked055
Done044
Total1 419201 439
Accuracy
99.9%
Counts
1 439 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
79.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
79.7%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
77.6%
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
6.6%
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
50.8%
(sqrt.f64 (/.f64 (*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))))
52.4%
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
12.9%
(sqrt.f64 (/.f64 #s(approx (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (*.f64 (fma.f64 #s(literal -8 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (*.f64 p p))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
50.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) (*.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
49.9%
(sqrt.f64 #s(approx (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
28.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
12.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
11.4%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p)) (*.f64 x x))))
16.0%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
18.8%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
53.6%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
49.6%
#s(approx (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
25.6%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
38.4%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Compiler

Compiled 954 to 408 computations (57.2% saved)

simplify138.0ms (1.5%)

Memory
11.8MiB live, 202.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (neg.f64 x) x)
cost-diff0
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))))
cost-diff0
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
cost-diff2880
(fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))
cost-diff0
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)))
cost-diff0
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
cost-diff640
(fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p))
cost-diff0
(/.f64 #s(literal 1 binary64) (*.f64 x x))
cost-diff0
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))
cost-diff0
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
cost-diff320
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))
cost-diff0
(neg.f64 p)
cost-diff0
(/.f64 (neg.f64 p) x)
cost-diff0
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff0
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
cost-diff1408
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
Rules
12 278×lower-fma.f32
12 270×lower-fma.f64
4 038×lower-*.f32
4 020×lower-*.f64
1 718×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058630
094620
1177595
2385580
31135580
43078580
54802547
08021540
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)
#s(literal 1/2 binary64)
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(/.f64 (neg.f64 p) x)
(neg.f64 p)
p
x
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x
(*.f64 p p)
p
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))
(fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p))
(*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)))
(*.f64 (*.f64 p p) (*.f64 p p))
(*.f64 p p)
p
(/.f64 #s(literal -12 binary64) (*.f64 x x))
#s(literal -12 binary64)
(*.f64 x x)
x
#s(literal 1/4 binary64)
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))))
#s(literal 1/2 binary64)
(fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
#s(literal 1 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)
(/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))
#s(literal -1 binary64)
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
x
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
p
(*.f64 x x)
#s(literal 1/2 binary64)
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(/.f64 (neg.f64 p) x)
(neg.f64 p)
p
x
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p (*.f64 x x)) p)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p (*.f64 x x)) p))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))
(*.f64 (/.f64 p (*.f64 x x)) p)
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x
(*.f64 p p)
p
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p (*.f64 x x)) (fma.f64 (*.f64 (/.f64 #s(literal -3 binary64) (*.f64 x x)) p) (*.f64 p p) p))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p (*.f64 x x)) (fma.f64 (*.f64 (/.f64 #s(literal -3 binary64) (*.f64 x x)) p) (*.f64 p p) p)))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))
(*.f64 (/.f64 p (*.f64 x x)) (fma.f64 (*.f64 (/.f64 #s(literal -3 binary64) (*.f64 x x)) p) (*.f64 p p) p))
(fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p))
(*.f64 (fma.f64 (*.f64 (/.f64 #s(literal -3 binary64) (*.f64 x x)) p) p #s(literal 1 binary64)) (*.f64 p p))
(*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)))
(*.f64 (*.f64 #s(literal -12 binary64) (*.f64 p p)) (*.f64 (/.f64 p (*.f64 x x)) p))
(*.f64 (*.f64 p p) (*.f64 p p))
(*.f64 (*.f64 (*.f64 p p) p) p)
(*.f64 p p)
p
(/.f64 #s(literal -12 binary64) (*.f64 x x))
#s(literal -12 binary64)
(*.f64 x x)
x
#s(literal 1/4 binary64)
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
(sqrt.f64 (*.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))))
(*.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64))))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
#s(literal 1 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))
(fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))
(fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
p
(*.f64 x x)
(/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
#s(literal -1 binary64)
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))
(-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))

localize269.0ms (2.8%)

Memory
20.0MiB live, 454.9MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy8.254723807951137
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
accuracy8.254723807951137
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
accuracy31.161531238235046
(fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))
accuracy4.560997376042884
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))
accuracy5.36585188626102
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
accuracy15.761588707302995
(fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p))
accuracy47.915288205246476
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)))
accuracy0.234375
(/.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy5.36585188626102
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
accuracy6.2605075546854065
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))
accuracy46.96840349816959
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))
accuracy0
(/.f64 (neg.f64 p) x)
accuracy0
(neg.f64 p)
accuracy47.59309161008346
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
accuracy0.7048044516826061
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
accuracy5.36585188626102
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy7.522607369904728
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy14.63530602503128
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
Samples
79.0ms63×2valid
75.0ms128×0valid
32.0ms49×1valid
18.0ms16×3valid
Compiler

Compiled 600 to 54 computations (91% saved)

Precisions
Click to see histograms. Total time spent on operations: 164.0ms
ival-div: 73.0ms (44.6% of total)
ival-mult: 36.0ms (22% of total)
ival-sqrt: 19.0ms (11.6% of total)
ival-add: 18.0ms (11% of total)
adjust: 13.0ms (7.9% of total)
ival-sub: 2.0ms (1.2% of total)
ival-neg: 2.0ms (1.2% of total)
exact: 1.0ms (0.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series106.0ms (1.1%)

Memory
-23.4MiB live, 133.8MiB allocated
Counts
22 → 492
Calls
Call 1
Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())
#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())
#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (patch (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)) (patch (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))) (patch (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))) #<representation binary64>) () ())
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#s(alt (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))) (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))) #<representation binary64>) () ())
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#s(alt (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)) (patch (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)) #<representation binary64>) () ())
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Outputs
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#s(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)))))) (taylor 0 p) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 p) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 p) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 p) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)) #<representation binary64>) () ())) ())
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#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))) #<representation binary64>) () ())) ())
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Calls

6 calls:

TimeVariablePointExpression
10.0ms
p
@inf
((/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (* (/ 1 (* x x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ 1 (* x x)) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))) (sqrt (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))))) (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1)))) (* (neg x) x) (sqrt (+ (* (* 4 p) p) (* x x))) (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
7.0ms
p
@0
((/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (* (/ 1 (* x x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ 1 (* x x)) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))) (sqrt (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))))) (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1)))) (* (neg x) x) (sqrt (+ (* (* 4 p) p) (* x x))) (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
6.0ms
x
@inf
((/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (* (/ 1 (* x x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ 1 (* x x)) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))) (sqrt (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))))) (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1)))) (* (neg x) x) (sqrt (+ (* (* 4 p) p) (* x x))) (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
5.0ms
x
@-inf
((/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (* (/ 1 (* x x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ 1 (* x x)) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))) (sqrt (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))))) (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1)))) (* (neg x) x) (sqrt (+ (* (* 4 p) p) (* x x))) (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
3.0ms
x
@0
((/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (* (/ 1 (* x x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ 1 (* x x)) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))) (sqrt (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1))))) (* 1/2 (+ (* (* (neg x) x) (/ 1 (* (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (+ (* (* 4 p) p) (* x x))))) (/ -1 (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1)))) (* (neg x) x) (sqrt (+ (* (* 4 p) p) (* x x))) (+ (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) -1) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

simplify289.0ms (3%)

Memory
0.1MiB live, 472.3MiB allocated
Algorithm
egg-herbie
Rules
8 070×lower-*.f64
8 070×lower-*.f32
7 612×lower-fma.f64
7 612×lower-fma.f32
5 882×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0131120192
1432219871
0910118537
Stop Event
iter limit
node limit
Counts
492 → 490
Calls
Call 1
Inputs
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))))))
1
(+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (+ (* -9/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 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))))))
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))))))
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
(+ 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))))))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
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)))))
(pow p 2)
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
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)))))
(/ (pow p 2) (pow x 2))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
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)))))
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 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* 2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* -6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* 20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 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 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (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))))))
(+ (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 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)))))))
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)))))
(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)))))))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
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)))))
(* -3 (/ (pow p 4) (pow x 2)))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
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)))))
(* -3 (/ (pow p 4) (pow x 4)))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/4 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ (pow x 2) (pow p 2))) (* 1/2 (/ x p)))))
(+ 1 (+ (* -1/4 (/ (pow x 2) (pow p 2))) (+ (* -1/8 (/ (pow x 3) (pow p 3))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (+ (* 1/8 (/ (pow x 3) (pow p 3))) (+ (* 1/4 (/ (pow x 2) (pow p 2))) (* 1/2 (/ x p))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (+ (* -1/4 (pow x 2)) (* 1/4 (pow x 2))) (* 1/16 (pow x 2)))) (pow p 2)))))
(+ (sqrt 1/2) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (+ (* 1/2 (/ (* (sqrt 1/2) (- (+ (* -1/4 (pow x 2)) (* 1/4 (pow x 2))) (* 1/16 (pow x 2)))) (pow p 2))) (* 1/2 (/ (* (sqrt 1/2) (- (+ (* -1/8 (pow x 3)) (+ (* -1/16 (pow x 3)) (* 1/8 (pow x 3)))) (* 1/4 (* x (- (+ (* -1/4 (pow x 2)) (* 1/4 (pow x 2))) (* 1/16 (pow x 2))))))) (pow p 3))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* 1/4 (/ x p)) (* 1/2 (/ (+ (* -1/4 (pow x 2)) (* 1/4 (pow x 2))) (pow p 2)))))
(+ 1/2 (+ (* 1/4 (/ x p)) (+ (* 1/2 (/ (+ (* -1/4 (pow x 2)) (* 1/4 (pow x 2))) (pow p 2))) (* 1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* -1/16 (pow x 3)) (* 1/8 (pow x 3)))) (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))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
-1
(- (* 1/2 (/ x p)) 1)
(- (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))) 1)
(- (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))) 1)
1
(+ 1 (* -1/2 (/ x p)))
(- (+ 1 (* 1/16 (/ (pow x 3) (pow p 3)))) (* 1/2 (/ x p)))
(- (+ 1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(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)))
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(sqrt 2)
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1
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(sqrt 1/2)
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1/2
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1
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(sqrt 2)
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1/2
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(sqrt 1/2)
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1/2
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1
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(sqrt 1/2)
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1/2
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(* -1 (pow x 2))
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(* -1 (pow x 2))
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-1
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1
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1
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1
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1
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1
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1
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(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
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1
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1
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(/ (pow p 2) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
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(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
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)))))))
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (- (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -2 (pow p 2))) (pow x 2))
(/ (- (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))))) (pow x 2))
(/ (- (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
(* -1 (/ p x))
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(* -1 (/ (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/2 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (+ (* -1/8 (* (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* 1/8 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (+ (* 1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (+ (* 1/2 (/ (* (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 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(pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))) (* (pow p 2) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))))))))))))))) (* (pow x 6) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (+ (* 1/4 (/ (pow (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) 2) (* (pow (sqrt -1) 2) (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))))))) (* (pow x 4) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (+ (* -1/2 (* (/ (* (sqrt -1/2) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4)))))) (* (pow x 2) (sqrt -1))) (sqrt (/ 1 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))))))) (* (* (sqrt -1) (sqrt -1/2)) (sqrt (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))))))) x))
(* 1/2 (/ (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2))) (pow x 2)))
(/ (+ (* 1/2 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))) (* 1/2 (/ (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) (pow x 2)))) (pow x 2))
(/ (+ (* 1/2 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))) (+ (* 1/2 (/ (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))))) (pow x 4))) (* 1/2 (/ (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) (pow x 2))))) (pow x 2))
(/ (+ (* 1/2 (+ (* 1/4 (+ (* -2 (pow p 2)) (* 8 (pow p 2)))) (* 1/2 (pow p 2)))) (+ (* 1/2 (/ (+ (* -1/2 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (+ (* -1/8 (* (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* 1/8 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (+ (* 1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (* (pow p 2) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4)))))))))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -1/2 (* (+ (* -2 (pow p 2)) (* 8 (pow p 2))) (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/8 (* (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -2 (pow p 2)) (* 8 (pow p 2))))) (+ (* 1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 1/4 (+ (* -2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (* (pow p 2) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/2 (pow p 4))))))))) (pow x 4))) (* 1/2 (/ (+ (* -1/8 (pow (+ (* -2 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (+ (* 1/4 (+ (* -8 (pow p 4)) (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))) (* 1/2 (pow p 4))))) (pow x 2)))))) (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -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))))))))
-2
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 11/8 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (+ (* -9/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal -9/8 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 49/16 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -9/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 11/8 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
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)))))
(fma.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -10 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 11/8 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 p)
(neg.f64 p)
(* -1 p)
(neg.f64 p)
(* -1 p)
(neg.f64 p)
(* -1 p)
(neg.f64 p)
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
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x
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
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1
#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
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(* -2 p)
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-1
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1
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(pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64))) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) #s(literal 1/4 binary64) (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (fma.f64 (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64))) (*.f64 p p) (*.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) #s(literal 1/8 binary64)))) (*.f64 p p) (*.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 p p)) (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) #s(literal -1/2 binary64))) #s(literal 1/4 binary64))))))))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 p p) #s(literal 6 binary64))) (fma.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 p #s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 36 binary64)) #s(literal -1/8 binary64))) (fma.f64 (*.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 p #s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64))) (*.f64 (*.f64 p p) #s(literal 6 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 p p)) #s(literal 1/8 binary64) (fma.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) #s(literal 1/8 binary64) (fma.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64))) (*.f64 p p))))))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 36 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 1/8 binary64) (fma.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 p #s(literal 4 binary64)) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal -1/2 binary64))) #s(literal 1/4 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/2 binary64))))) (*.f64 x x)))))) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) x 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))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 4 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x)))) x x))
-2
#s(literal -2 binary64)
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -2 binary64))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -2 binary64)))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
(fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (-.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))) #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(-.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x)))
(- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
(-.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/2 binary64) #s(literal 2 binary64)) (fma.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) (*.f64 x x))))

rewrite185.0ms (2%)

Memory
35.8MiB live, 385.1MiB allocated
Rules
4 946×lower-*.f32
4 928×lower-*.f64
4 152×lower-/.f32
4 134×lower-/.f64
2 108×lower--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058451
094430
1355409
22273409
08638402
Stop Event
iter limit
node limit
iter limit
Counts
22 → 554
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(/.f64 (neg.f64 p) x)
(neg.f64 p)
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))
(fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64)))))
(*.f64 (neg.f64 x) x)
(sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))
Outputs
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/4 binary64)))))))
(*.f64 (sqrt.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/4 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64))) #s(literal 1 binary64))
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(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64))) (*.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64)) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (*.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64)) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))) (neg.f64 (neg.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)))
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))) (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (neg.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (neg.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64))))
(/.f64 (-.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64)) (neg.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64)))
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(fma.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 x (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))) (/.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64))) (/.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (+.f64 (+.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(+.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))

eval266.0ms (2.8%)

Memory
-40.7MiB live, 422.9MiB allocated
Compiler

Compiled 54 626 to 4 061 computations (92.6% saved)

prune191.0ms (2%)

Memory
29.1MiB live, 346.8MiB allocated
Pruning

20 alts after pruning (9 fresh and 11 done)

PrunedKeptTotal
New1 12551 130
Fresh246
Picked235
Done189
Total1 130201 150
Accuracy
99.9%
Counts
1 150 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
79.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
52.9%
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt.f64 #s(literal 2 binary64))))
79.7%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
77.6%
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
6.6%
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
50.8%
(sqrt.f64 (/.f64 (*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))))
52.4%
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
50.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) (*.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
52.4%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
49.9%
(sqrt.f64 #s(approx (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
28.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
11.4%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p)) (*.f64 x x))))
13.9%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (*.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 p p))) (*.f64 x x))))
53.6%
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
49.6%
#s(approx (/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
24.6%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (-.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 x p)) (*.f64 x x)))
25.6%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
25.6%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (*.f64 p (/.f64 #s(literal -1 binary64) x)))
38.4%
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Compiler

Compiled 1 383 to 408 computations (70.5% saved)

regimes140.0ms (1.5%)

Memory
-34.9MiB live, 91.8MiB allocated
Counts
37 → 2
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (*.f64 p (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (-.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 x p)) (*.f64 x x)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (*.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x)))
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (*.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 p p))) (*.f64 x x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 (*.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))))) (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal -1 binary64))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(sqrt.f64 (/.f64 #s(approx (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (*.f64 (fma.f64 #s(literal -8 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (*.f64 p p))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (*.f64 (/.f64 x (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) p) p) (*.f64 #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 p p)) (*.f64 x x))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))) (*.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))) (/.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))) (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
Outputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64)))
Calls

7 calls:

51.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
34.0ms
p
17.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
10.0ms
x
9.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Results
AccuracySegmentsBranch
79.7%1p
85.3%2x
99.8%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)))))))
99.8%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))))))
99.8%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.8%2(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
79.7%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
Compiler

Compiled 80 to 56 computations (30% saved)

regimes27.0ms (0.3%)

Memory
5.8MiB live, 39.2MiB allocated
Counts
20 → 3
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (*.f64 p (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (-.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 x p)) (*.f64 x x)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 p (/.f64 p (*.f64 x x)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (*.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (/ 1 (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2)))) (fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x)))
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
Outputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Calls

4 calls:

10.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
5.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
5.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
5.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
Results
AccuracySegmentsBranch
98.8%3(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
98.8%3(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
98.8%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
98.8%3(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes9.0ms (0.1%)

Memory
18.9MiB live, 18.9MiB allocated
Counts
6 → 3
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (*.f64 p (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2) 1/2))) (sqrt.f64 #s(literal 2 binary64))))
Outputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Calls

4 calls:

2.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
2.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
2.0ms
(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
97.5%3(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
97.5%3(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
97.5%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
97.5%3(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes15.0ms (0.2%)

Memory
-5.2MiB live, 31.4MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
Outputs
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Calls

7 calls:

4.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
2.0ms
x
2.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
2.0ms
p
2.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
Results
AccuracySegmentsBranch
69.9%2p
69.9%2(*.f64 (*.f64 #s(literal 4 binary64) p) p)
62.5%2x
75.5%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
75.5%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
75.5%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
75.5%2(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Compiler

Compiled 80 to 56 computations (30% saved)

regimes9.0ms (0.1%)

Memory
22.7MiB live, 22.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Outputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Calls

7 calls:

1.0ms
x
1.0ms
p
1.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
1.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
1.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Results
AccuracySegmentsBranch
38.4%1x
38.4%1p
38.4%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
38.4%1(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
38.4%1(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
38.4%1(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
38.4%1(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Compiler

Compiled 80 to 56 computations (30% saved)

bsearch4.0ms (0%)

Memory
-34.3MiB live, 1.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-0.9999999999943615
-0.9999887438050786
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
2.1582325552766917e-7
1.0
0.0ms
-0.902818649552741
-0.5045390673812059
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
2.1582325552766917e-7
1.0
0.0ms
-0.902818649552741
-0.5045390673812059
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch12.0ms (0.1%)

Memory
21.7MiB live, 21.7MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
11.0ms
2.1582325552766917e-7
1.0
Samples
6.0ms144×0valid
Compiler

Compiled 121 to 100 computations (17.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-add: 1.0ms (37% of total)
ival-mult: 1.0ms (37% of total)
ival-sqrt: 1.0ms (37% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify8.0ms (0.1%)

Memory
13.0MiB live, 13.0MiB allocated
Algorithm
egg-herbie
Rules
10×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058309
169309
275309
380309
483309
584309
Stop Event
saturated
Calls
Call 1
Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -9007109182748445/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 944473296573929/2361183241434822606848 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 944473296573929/2361183241434822606848 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -9007109182748445/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -9007109182748445/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 944473296573929/2361183241434822606848 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -5404319552844595/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 944473296573929/2361183241434822606848 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 944473296573929/2361183241434822606848 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal -5404319552844595/9007199254740992 binary64)) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 944473296573929/2361183241434822606848 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

soundness498.0ms (5.3%)

Memory
-1.7MiB live, 477.6MiB allocated
Rules
9 590×lower-fma.f64
9 590×lower-fma.f32
6 992×lower-fma.f64
6 992×lower-fma.f32
6 964×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04342486
113252377
246112304
080842141
0146020510
1478820185
0819618822
01466
02366
17766
250166
3696766
0849259
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 665 to 279 computations (58% saved)

preprocess93.0ms (1%)

Memory
-40.4MiB live, 166.9MiB allocated
Compiler

Compiled 432 to 166 computations (61.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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