Given's Rotation SVD example

Time bar (total: 11.5s)

analyze525.0ms (4.6%)

Memory
-9.2MiB live, 935.5MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%48.6%51.4%0%0%0%0
0%0%48.6%51.4%0%0%0%1
0%0%48.6%51.4%0%0%0%2
0%0%48.6%51.4%0%0%0%3
0%0%48.6%51.4%0%0%0%4
31.3%15.2%33.4%51.4%0%0%0%5
34.4%16.7%31.9%51.4%0%0%0%6
51.6%25.1%23.6%51.4%0%0%0%7
53.1%25.8%22.8%51.4%0%0%0%8
62.5%30.4%18.2%51.4%0%0%0%9
63.7%31%17.7%51.4%0%0%0%10
68.6%33.3%15.3%51.4%0%0%0%11
69.2%33.7%15%51.4%0%0%0%12
Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.2s (19.5%)

Memory
41.7MiB live, 3 805.9MiB allocated
Samples
1.1s6 242×0valid
270.0ms930×2valid
210.0ms377×3valid
161.0ms634×1valid
29.0ms73×4valid
16.0ms28×5exit
Precisions
Click to see histograms. Total time spent on operations: 1.3s
ival-mult: 346.0ms (25.8% of total)
const: 288.0ms (21.5% of total)
ival-sqrt: 225.0ms (16.8% of total)
ival-add: 170.0ms (12.7% of total)
ival-div: 100.0ms (7.5% of total)
ival-<: 78.0ms (5.8% of total)
adjust: 59.0ms (4.4% of total)
ival-fabs: 50.0ms (3.7% of total)
exact: 12.0ms (0.9% of total)
ival-and: 11.0ms (0.8% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

preprocess66.0ms (0.6%)

Memory
22.9MiB live, 59.1MiB allocated
Algorithm
2×egg-herbie
Rules
248×distribute-lft-neg-in
218×unsub-neg
196×associate-*r*
196×associate-*l*
166×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

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

(abs p)

explain252.0ms (2.2%)

Memory
-10.6MiB live, 549.1MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
770-0-(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
370-0-(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
120-0-(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-rescue770
↳(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))overflow77
↳(*.f64 (*.f64 #s(literal 4 binary64) p) p)overflow77
+.f64(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))cancellation370
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-rescue120
↳(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)))))))underflow4
↳(*.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))))))underflow16
↳(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))underflow16
↳(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))underflow14
↳(*.f64 (*.f64 #s(literal 4 binary64) p) p)underflow53
Confusion
Predicted +Predicted -
+490
-77130
Precision
0.3888888888888889
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+4900
-770130
Precision?
0.3888888888888889
Recall?
1.0
Freqs
test
numberfreq
0130
1126
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
52.0ms410×0valid
11.0ms54×1valid
8.0ms32×2valid
6.0ms14×3valid
1.0ms2×4valid
Compiler

Compiled 230 to 60 computations (73.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-add: 16.0ms (33.8% of total)
ival-mult: 14.0ms (29.5% of total)
ival-sqrt: 9.0ms (19% of total)
ival-div: 5.0ms (10.6% of total)
adjust: 2.0ms (4.2% of total)
exact: 1.0ms (2.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
3.3MiB live, 3.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶82.2%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0%)

Memory
20.2MiB live, 20.2MiB allocated
Algorithm
1×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×*-lowering-*.f32
32×*-lowering-*.f64
18×accelerator-lowering-fma.f32
18×accelerator-lowering-fma.f64
12×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01494
12994
23694
33894
43994
03986
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1/2
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
1
(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
x
(sqrt (+ (* (* 4 p) p) (* x x)))
(+ (* (* 4 p) p) (* x x))
(* (* 4 p) p)
(* 4 p)
4
p
(* x x)
Outputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64)))
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))))
1
#s(literal 1 binary64)
(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
(/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))
x
(sqrt (+ (* (* 4 p) p) (* x x)))
(sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))
(+ (* (* 4 p) p) (* x x))
(fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))
(* (* 4 p) p)
(*.f64 #s(literal 4 binary64) (*.f64 p p))
(* 4 p)
(*.f64 #s(literal 4 binary64) p)
4
#s(literal 4 binary64)
p
(* x x)
(*.f64 x x)

localize136.0ms (1.2%)

Memory
-18.9MiB live, 135.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
✓accuracy95.6%
(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)))))))
✓accuracy86.7%
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
✓accuracy72.1%
(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
Samples
78.0ms16×2valid
20.0ms205×0valid
18.0ms27×1valid
2.0ms7×3valid
0.0ms1×4valid
Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 107.0ms
ival-div: 90.0ms (83.9% of total)
ival-mult: 8.0ms (7.5% of total)
ival-sqrt: 5.0ms (4.7% of total)
ival-add: 3.0ms (2.8% of total)
adjust: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory
26.6MiB live, 26.6MiB allocated
Counts
5 → 120
Calls
Call 1
Inputs
#<alt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))>
#<alt (+ (* (* 4 p) p) (* x x))>
#<alt (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))>
#<alt (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))>
#<alt (sqrt (+ (* (* 4 p) p) (* x x)))>
Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt (pow x 2)>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))>
#<alt (+ (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))))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* -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))))>
#<alt (+ (* -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)))))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<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))>
#<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))>
#<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))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<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))))))>
#<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))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))>
#<alt (+ (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))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))>
#<alt (+ (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)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))>
#<alt (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))>
#<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))>
#<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))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))>
#<alt (+ 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)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ x p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))>
#<alt (+ 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)))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
Calls

30 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
1.0ms
x
@inf
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
1.0ms
x
@-inf
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1.0ms
p
@0
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1.0ms
x
@inf
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

rewrite325.0ms (2.8%)

Memory
-25.1MiB live, 501.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 862×accelerator-lowering-fma.f32
4 862×accelerator-lowering-fma.f64
3 532×*-lowering-*.f32
3 532×*-lowering-*.f64
2 388×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01466
16866
249266
3694866
0847359
Stop Event
1×iter limit
1×node limit
Counts
5 → 276
Calls
Call 1
Inputs
(* 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)))
Outputs
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (/.f64 (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #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 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #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 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))))))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (-.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (fma.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/8 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(/.f64 (fma.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64)) (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(/.f64 (neg.f64 (fma.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))) (neg.f64 (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))) (neg.f64 (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
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(*.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(*.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 3 binary64)))) (fma.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) (*.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)))))) (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))) (+.f64 (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))) (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p)))))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p)))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (fma.f64 (*.f64 p p) #s(literal -4 binary64) (*.f64 x x)))) (sqrt.f64 (fma.f64 (*.f64 p p) #s(literal -4 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 #s(literal -16 binary64) (*.f64 p (*.f64 p (*.f64 p p)))))) (sqrt.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))))))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
(pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
(*.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))) (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 p p) #s(literal -4 binary64) (*.f64 x x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 p p) #s(literal -4 binary64) (*.f64 x x)))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
(*.f64 (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))

simplify432.0ms (3.8%)

Memory
-9.9MiB live, 624.3MiB allocated
Algorithm
1×egg-herbie
Rules
9 590×accelerator-lowering-fma.f32
9 590×accelerator-lowering-fma.f64
6 900×*-lowering-*.f32
6 900×*-lowering-*.f64
4 472×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04342482
113252377
246062304
080752141
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (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))))
(* 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))))
(* 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))
(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)))))
(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 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))))))))
(* (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 (/ (* 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))
(* (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))))))))
(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))))))
(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 (* 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
(+ 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))))))
(* 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))
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))))))
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)))))
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)))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
Outputs
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 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #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 x (fma.f64 x (*.f64 x (fma.f64 #s(literal 3/512 binary64) (*.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
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 #s(literal -1/4 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (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 #s(literal -1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) (*.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 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.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 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 p p) (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64))))) (*.f64 #s(literal -256 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))))) (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 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.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
#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 (*.f64 p p) (fma.f64 (*.f64 p p) (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #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 (*.f64 p p) (fma.f64 p (*.f64 p (fma.f64 #s(literal -10 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
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 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #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 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (pow.f64 p #s(literal 5 binary64))) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/32 binary64) (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) #s(literal 1/2 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 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.f64 p p))) 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 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) (/.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.f64 p p))) p))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(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 x (sqrt.f64 #s(literal 1/2 binary64))) p) (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 x (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (/.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 p p))) (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 x (fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)) (/.f64 (*.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -3/128 binary64)) (*.f64 p (*.f64 p p)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (*.f64 p p))))
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x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 p (*.f64 p (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 p p) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))) 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 (*.f64 p p) (fma.f64 (*.f64 p p) (fma.f64 (*.f64 p p) (/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 2 binary64) x)) x)
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) #s(literal 2 binary64)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 2 binary64))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 p (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (neg.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) #s(literal 2 binary64))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 2 binary64))) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64)))) (neg.f64 p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p) (*.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (*.f64 x x) (fma.f64 (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) #s(literal -1/64 binary64) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (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 p (*.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 p #s(literal 2 binary64)))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (*.f64 #s(literal 2 binary64) x) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(* 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 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (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)))))))
(*.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))) (neg.f64 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 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) x))

eval109.0ms (0.9%)

Memory
6.6MiB live, 120.6MiB allocated
Compiler

Compiled 15 528 to 1 955 computations (87.4% saved)

prune61.0ms (0.5%)

Memory
17.7MiB live, 178.0MiB allocated
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New38214396
Fresh000
Picked101
Done000
Total38314397
Accuracy
99.8%
Counts
397 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.3%
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
▶22.6%
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
55.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
▶81.8%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
82.2%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
28.7%
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
53.4%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
12.9%
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) (*.f64 p p)) (*.f64 x x)))
▶16.2%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
▶82.2%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
40.0%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))))))
79.5%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
38.8%
(sqrt.f64 #s(literal 1 binary64))
▶57.7%
(sqrt.f64 #s(literal 1/2 binary64))
Compiler

Compiled 510 to 302 computations (40.8% saved)

simplify195.0ms (1.7%)

Memory
-17.8MiB live, 143.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
✓cost-diff0
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))
✓cost-diff0
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 p p)
✓cost-diff0
(/.f64 (*.f64 p p) (*.f64 x x))
✓cost-diff1152
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
✓cost-diff1216
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
Rules
1 464×accelerator-lowering-fma.f32
1 464×accelerator-lowering-fma.f64
1 316×*-lowering-*.f32
1 316×*-lowering-*.f64
1 090×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027257
154253
2113253
3261253
4445253
5533253
6669253
7812253
8906253
91156253
102018253
113096253
123420253
133632253
143795253
153841253
163942253
174149253
184249253
194249253
204249253
214297253
224591253
04591238
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))
(/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
1/2
(/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
1
(+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
x
(sqrt (+ (* x x) (* p (* 4 p))))
(+ (* x x) (* p (* 4 p)))
(* p (* 4 p))
p
(* 4 p)
4
(sqrt 1/2)
1/2
(sqrt (/ (* p p) (* x x)))
(/ (* p p) (* x x))
(* p p)
p
(* x x)
x
(/ (* (sqrt 1/2) (* (sqrt 2) p)) (neg x))
(* (sqrt 1/2) (* (sqrt 2) p))
(sqrt 1/2)
1/2
(* (sqrt 2) p)
(sqrt 2)
2
p
(neg x)
x
(* (sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (sqrt 1/2))
(sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
(+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
1
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
x
(sqrt (+ (* x x) (* p (* 4 p))))
(+ (* x x) (* p (* 4 p)))
(* p (* 4 p))
p
(* 4 p)
4
(sqrt 1/2)
1/2
Outputs
(sqrt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64)))
(/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))))
1
#s(literal 1 binary64)
(+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
(/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))
x
(sqrt (+ (* x x) (* p (* 4 p))))
(sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))
(+ (* x x) (* p (* 4 p)))
(fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))
(* p (* 4 p))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
p
(* 4 p)
(*.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (/ (* p p) (* x x)))
(fabs.f64 (/.f64 p x))
(/ (* p p) (* x x))
(/.f64 (*.f64 p p) (*.f64 x x))
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)
x
(/ (* (sqrt 1/2) (* (sqrt 2) p)) (neg x))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (sqrt.f64 #s(literal 2 binary64)))) x))
(* (sqrt 1/2) (* (sqrt 2) p))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (sqrt.f64 #s(literal 2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (sqrt 2) p)
(*.f64 p (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
p
(neg x)
(neg.f64 x)
x
(* (sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))))
(+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))
1
#s(literal 1 binary64)
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
(/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))
x
(sqrt (+ (* x x) (* p (* 4 p))))
(sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))
(+ (* x x) (* p (* 4 p)))
(fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))
(* p (* 4 p))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
p
(* 4 p)
(*.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize161.0ms (1.4%)

Memory
18.2MiB live, 283.7MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy99.4%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy95.6%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))
✓accuracy86.7%
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
✓accuracy72.1%
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(neg.f64 x)
✓accuracy99.4%
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))
✓accuracy99.2%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 p p)
✓accuracy84.8%
(/.f64 (*.f64 p p) (*.f64 x x))
✓accuracy69.2%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy99.9%
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
✓accuracy95.6%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
✓accuracy86.7%
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
✓accuracy72.1%
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
Samples
59.0ms205×0valid
10.0ms17×2valid
9.0ms27×1valid
4.0ms7×3valid
Compiler

Compiled 250 to 29 computations (88.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-div: 22.0ms (41.5% of total)
ival-sqrt: 14.0ms (26.4% of total)
ival-mult: 11.0ms (20.8% of total)
ival-add: 3.0ms (5.7% of total)
adjust: 1.0ms (1.9% of total)
exact: 1.0ms (1.9% of total)
ival-neg: 1.0ms (1.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series34.0ms (0.3%)

Memory
-5.4MiB live, 74.8MiB allocated
Counts
17 → 324
Calls
Call 1
Inputs
#<alt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))>
#<alt (sqrt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))>
#<alt (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))>
#<alt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))>
#<alt (sqrt 1/2)>
#<alt (sqrt (/ (* p p) (* x x)))>
#<alt (/ (* p p) (* x x))>
#<alt (* p p)>
#<alt (* x x)>
#<alt (/ (* (sqrt 1/2) (* (sqrt 2) p)) (neg x))>
#<alt (* (sqrt 1/2) (* (sqrt 2) p))>
#<alt (* (sqrt 2) p)>
#<alt (* (sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (sqrt 1/2))>
#<alt (sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))>
#<alt (/ x (sqrt (+ (* x x) (* p (* 4 p)))))>
#<alt (sqrt (+ (* x x) (* p (* 4 p))))>
#<alt (neg x)>
Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))>
#<alt (+ (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))))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* -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))))>
#<alt (+ (* -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)))))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<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))>
#<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))>
#<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))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<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))))))>
#<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))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))>
#<alt (+ (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))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))>
#<alt (+ (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)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ x p)))>
#<alt (+ 1 (* x (- (* 1/4 (/ x (pow p 2))) (* 1/2 (/ 1 p)))))>
#<alt (+ 1 (* x (- (* x (+ (* -1/16 (/ x (pow p 3))) (* 1/4 (/ 1 (pow p 2))))) (* 1/2 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 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))))>
#<alt (- (+ 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))))))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (* (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)))))>
#<alt (* (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))))))>
#<alt (* (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))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (+ (* -1 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1/2 (* (pow p 2) (+ (* (pow p 2) (- (* 5/2 (/ (pow p 2) (pow x 6))) (/ 1 (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ x p)))>
#<alt (- (+ 1 (* 1/4 (/ (pow x 2) (pow p 2)))) (* 1/2 (/ x p)))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1/16 (pow x 3)) (* 1/8 (pow x 3))) (pow p 3)))) (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/2 (/ x p))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (* -1 (/ (- (* -1/4 (/ (pow x 2) p)) (* 1/2 x)) p)))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1/16 (/ (pow x 3) p)) (* 1/8 (/ (pow x 3) p))) (* -1/4 (pow x 2))) p)) (* 1/2 x)) p)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))>
#<alt (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))>
#<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))>
#<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))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))>
#<alt (+ 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)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ x p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))>
#<alt (+ 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)))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (* (sqrt 1/2) (sqrt 2)))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (* p (sqrt 2))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))>
#<alt (+ (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))))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* -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))))>
#<alt (+ (* -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)))))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<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))>
#<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))>
#<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))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<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))))))>
#<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))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))>
#<alt (+ (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))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))>
#<alt (+ (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)))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2))))))>
#<alt (+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 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 (/ (- (* -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)))))))>
#<alt (* -1 (/ (* p (sqrt 2)) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 2)))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 (/ (- (* 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 2))))) x))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))>
#<alt (+ (sqrt 2) (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 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 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (sqrt 2))))) (/ 1 (* (pow x 2) (sqrt 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (* 1/4 (/ x p))))>
#<alt (+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ x p)) (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (pow p 3))))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (/ x p)))>
#<alt (+ 1 (* -1 (/ (+ (* 1/32 (/ (pow x 2) p)) (* 1/4 x)) p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) p)) (* -1/32 (pow x 2))) p)) (* 1/4 x)) p)))>
#<alt (* 1/2 (/ x p))>
#<alt (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt (* 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))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt -1>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)>
#<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))))) 1)>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<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))))))>
#<alt (* 1/2 (/ x p))>
#<alt (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)>
#<alt (/ (+ (* -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)>
#<alt (/ (+ (* -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)>
#<alt (* -1/2 (/ x p))>
#<alt (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))>
#<alt (* -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))>
#<alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
Calls

81 calls:

TimeVariablePointExpression
4.0ms
p
@inf
(/ (* p p) (* x x))
1.0ms
p
@0
(/ (* (sqrt 1/2) (* (sqrt 2) p)) (neg x))
1.0ms
x
@-inf
(/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
1.0ms
x
@0
(/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
1.0ms
x
@0
(/ (* (sqrt 1/2) (* (sqrt 2) p)) (neg x))

rewrite363.0ms (3.2%)

Memory
-42.1MiB live, 644.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 614×*-lowering-*.f32
4 614×*-lowering-*.f64
4 252×accelerator-lowering-fma.f32
4 252×accelerator-lowering-fma.f64
3 440×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027163
1129148
2856144
08652133
Stop Event
1×iter limit
1×node limit
Counts
17 → 760
Calls
Call 1
Inputs
(/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
(sqrt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))
(/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
(+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
(sqrt 1/2)
(sqrt (/ (* p p) (* x x)))
(/ (* p p) (* x x))
(* p p)
(* x x)
(/ (* (sqrt 1/2) (* (sqrt 2) p)) (neg x))
(* (sqrt 1/2) (* (sqrt 2) p))
(* (sqrt 2) p)
(* (sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (sqrt 1/2))
(sqrt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
(sqrt (+ (* x x) (* p (* 4 p))))
(neg x)
Outputs
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64)))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(+.f64 (*.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) x #s(literal 1/2 binary64))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 (/.f64 x (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 (/.f64 x (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 2 binary64))
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(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))))))
(/.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 p #s(literal 4 binary64)) (*.f64 p (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x (neg.f64 x))))))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))))) (sqrt.f64 (fma.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64)) (*.f64 (*.f64 x x) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))) (sqrt.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64)))))) (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 p #s(literal 4 binary64)) (*.f64 p (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x (neg.f64 x)))))))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))))) (sqrt.f64 (neg.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 p p) (*.f64 (*.f64 p p) #s(literal 16 binary64)) (neg.f64 (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x (neg.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64)))))) (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 p #s(literal 4 binary64)) (*.f64 p (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x (neg.f64 x)))))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))))) (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))))
(pow.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 p #s(literal 4 binary64)) (*.f64 p (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x (neg.f64 x))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 p #s(literal 4 binary64)) (*.f64 p (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x (neg.f64 x)))))))))
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) #s(literal 64 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 p #s(literal 4 binary64)) (*.f64 p (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x (neg.f64 x)))))))))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -4 binary64))))))
(*.f64 (pow.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) #s(literal 1/4 binary64)))
(+.f64 #s(literal 0 binary64) (neg.f64 x))
(-.f64 #s(literal 0 binary64) x)
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) x)
(-.f64 (/.f64 #s(literal 0 binary64) x) x)
(neg.f64 x)
(neg.f64 (/.f64 x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (neg.f64 (*.f64 x (*.f64 x x)))))
(/.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 x x) (neg.f64 x))
(/.f64 (neg.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 x (neg.f64 x)) x)
(/.f64 (*.f64 x (*.f64 x x)) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 x (neg.f64 x)) #s(literal 1 binary64)) x)
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x (*.f64 x x)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (neg.f64 (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 x #s(literal -1 binary64))
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (*.f64 x (neg.f64 x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (neg.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)))
(*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x))

simplify468.0ms (4.1%)

Memory
18.1MiB live, 806.9MiB allocated
Algorithm
1×egg-herbie
Rules
9 260×accelerator-lowering-fma.f32
9 260×accelerator-lowering-fma.f64
6 652×*-lowering-*.f32
6 652×*-lowering-*.f64
3 958×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06705716
120955417
273695319
084355012
Stop Event
1×iter limit
1×node limit
Counts
324 → 324
Calls
Call 1
Inputs
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* 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))))))))
(* (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 (/ (* 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))
(* (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))))))))
(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))))))
(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 (* x (- (* 1/4 (/ x (pow p 2))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (- (* x (+ (* -1/16 (/ x (pow p 3))) (* 1/4 (/ 1 (pow p 2))))) (* 1/2 (/ 1 p)))))
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))))))
(* 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))))))))
1/2
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* (pow p 2) (+ (* -1 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1/2 (* (pow p 2) (+ (* (pow p 2) (- (* 5/2 (/ (pow p 2) (pow x 6))) (/ 1 (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1/2 (/ x p)))
(- (+ 1 (* 1/4 (/ (pow x 2) (pow p 2)))) (* 1/2 (/ x p)))
(- (+ 1 (* -1 (/ (+ (* -1/16 (pow x 3)) (* 1/8 (pow x 3))) (pow p 3)))) (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/2 (/ x p))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* -1 (/ (- (* -1/4 (/ (pow x 2) p)) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1/16 (/ (pow x 3) p)) (* 1/8 (/ (pow x 3) p))) (* -1/4 (pow x 2))) p)) (* 1/2 x)) p)))
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
(+ 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))))))
(* 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))
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))))))
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)))))
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)))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ (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))
(/ (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))
(/ (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))
(/ (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))
(/ (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 p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 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))))))))
(* (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 (/ (* 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))
(* (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))))))))
(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))))))
(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 (* 1/4 (/ x p)))
(+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))
(+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 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 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 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 (/ (- (* -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)))))))
(* -1 (/ (* p (sqrt 2)) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 (/ (- (* 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 2))))) x))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 2))))))
(+ (sqrt 2) (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 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 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (sqrt 2))))) (/ 1 (* (pow x 2) (sqrt 2))))))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (* 1/4 (/ x p))))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ x p)) (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (pow p 3))))))
1
(+ 1 (* -1/4 (/ x p)))
(+ 1 (* -1 (/ (+ (* 1/32 (/ (pow x 2) p)) (* 1/4 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) p)) (* -1/32 (pow x 2))) p)) (* 1/4 x)) 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))))
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))))))
-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
(+ 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 (/ 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)
(* -1/2 (/ x p))
(* -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))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
Outputs
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 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (*.f64 x (/.f64 x (*.f64 p (*.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) #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 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 3/512 binary64) (/.f64 (*.f64 x x) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 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 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(fma.f64 #s(literal -1/4 binary64) (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 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x))))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
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#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 p p) (fma.f64 p (*.f64 p (/.f64 #s(literal 6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #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 (*.f64 p p) (fma.f64 (*.f64 p p) (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -20 binary64) (/.f64 #s(literal 6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(* 1/2 (/ x p))
(*.f64 #s(literal 1/2 binary64) (/.f64 x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/16 binary64) (*.f64 p p)) (*.f64 #s(literal 1/2 binary64) 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)
(/.f64 (-.f64 (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/16 binary64) (*.f64 p p)) (*.f64 #s(literal 1/2 binary64) x)) (/.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 (*.f64 p p) (*.f64 p p)))) 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)
(/.f64 (-.f64 (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/16 binary64) (*.f64 p p)) (*.f64 #s(literal 1/2 binary64) x)) (fma.f64 x (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (fma.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 p #s(literal 6 binary64))))) p)
(* -1/2 (/ x p))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) p)
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/16 binary64) (*.f64 p p)) (*.f64 #s(literal 1/2 binary64) x)) (neg.f64 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))
(/.f64 (-.f64 (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/16 binary64) (*.f64 p p)) (*.f64 #s(literal 1/2 binary64) x)) (/.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 (*.f64 p p) (*.f64 p p)))) (neg.f64 p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(/.f64 (-.f64 (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/16 binary64) (*.f64 p p)) (*.f64 #s(literal 1/2 binary64) x)) (fma.f64 x (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (fma.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 p #s(literal 6 binary64))))) (neg.f64 p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p) (*.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x (/.f64 x (*.f64 p (*.f64 p p)))) #s(literal -1/64 binary64) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (/.f64 (*.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 p #s(literal 2 binary64)))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(*.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.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))))
(* 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 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(neg.f64 (*.f64 x (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)))))))
(*.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))) (neg.f64 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 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) x))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (*.f64 p p) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 p p) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)) 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 (*.f64 p p) (fma.f64 (*.f64 p p) (fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 2 binary64) x)) x)
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (fma.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 p (+.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(neg.f64 (*.f64 p (fma.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64))) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (+.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64)))) (neg.f64 p))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

eval250.0ms (2.2%)

Memory
48.5MiB live, 412.8MiB allocated
Compiler

Compiled 34 366 to 3 642 computations (89.4% saved)

prune167.0ms (1.5%)

Memory
-20.5MiB live, 403.1MiB allocated
Pruning

18 alts after pruning (15 fresh and 3 done)

PrunedKeptTotal
New1 330101 340
Fresh459
Picked235
Done000
Total1 336181 354
Accuracy
99.9%
Counts
1 354 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
22.8%
(/.f64 (neg.f64 p) x)
5.0%
(/.f64 p x)
81.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))))
53.3%
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
40.0%
(*.f64 (sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓81.8%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
▶82.2%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
28.7%
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
▶53.4%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
12.9%
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (*.f64 p p)) (*.f64 x x)))
▶82.2%
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
✓16.2%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
▶54.7%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
31.2%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
40.0%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))))))
79.5%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
▶38.8%
(sqrt.f64 #s(literal 1 binary64))
✓57.7%
(sqrt.f64 #s(literal 1/2 binary64))
Compiler

Compiled 715 to 364 computations (49.1% saved)

simplify254.0ms (2.2%)

Memory
23.9MiB live, 450.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))
✓cost-diff0
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))
✓cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓cost-diff640
(sqrt.f64 #s(literal 1 binary64))
✓cost-diff192
(/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)))))
✓cost-diff320
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
✓cost-diff3648
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))
✓cost-diff4480
(pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64))
Rules
6 648×accelerator-lowering-fma.f32
6 648×accelerator-lowering-fma.f64
5 252×*-lowering-*.f32
5 252×*-lowering-*.f64
2 304×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037436
181420
2183381
3542378
41758374
53098374
64411374
77905374
08024341
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt (/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))))
(/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))))
(+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8)
(pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3)
(/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))
(* 1/2 x)
1/2
x
(sqrt (+ (* x x) (* p (* p 4))))
(+ (* x x) (* p (* p 4)))
(* p (* p 4))
p
(* p 4)
4
3
1/8
(+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))
(- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))
1/4
(* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)
(sqrt 1)
1
(sqrt (+ (* 1/4 (/ x p)) 1/2))
(+ (* 1/4 (/ x p)) 1/2)
1/4
(/ x p)
x
p
1/2
(sqrt (/ 1/2 (+ (* (/ x p) -1/2) 1)))
(/ 1/2 (+ (* (/ x p) -1/2) 1))
1/2
(+ (* (/ x p) -1/2) 1)
(/ x p)
x
p
-1/2
1
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2))
(+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2)
(/ x (sqrt (+ (* x x) (* p (* p 4)))))
x
(sqrt (+ (* x x) (* p (* p 4))))
(+ (* x x) (* p (* p 4)))
(* p (* p 4))
p
(* p 4)
4
1/2
Outputs
(sqrt (/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1 binary64)) (-.f64 (fma.f64 x (/.f64 x (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))))))
(/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))))
(*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1 binary64)) (-.f64 (fma.f64 x (/.f64 x (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8)
(fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/8 binary64))
(pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3)
(/.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))
(/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x
(sqrt (+ (* x x) (* p (* p 4))))
(sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))
(+ (* x x) (* p (* p 4)))
(fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))
(* p (* p 4))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
p
(* p 4)
(*.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
3
#s(literal 3 binary64)
1/8
#s(literal 1/8 binary64)
(+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/4 binary64))
(- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))
(fma.f64 x (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)
(/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))
(sqrt 1)
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(sqrt (+ (* 1/4 (/ x p)) 1/2))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(+ (* 1/4 (/ x p)) 1/2)
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
1/4
#s(literal 1/4 binary64)
(/ x p)
(/.f64 x p)
x
p
1/2
#s(literal 1/2 binary64)
(sqrt (/ 1/2 (+ (* (/ x p) -1/2) 1)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 x (/.f64 #s(literal -1/2 binary64) p) #s(literal 1 binary64))))
(/ 1/2 (+ (* (/ x p) -1/2) 1))
(/.f64 #s(literal 1/2 binary64) (fma.f64 x (/.f64 #s(literal -1/2 binary64) p) #s(literal 1 binary64)))
1/2
#s(literal 1/2 binary64)
(+ (* (/ x p) -1/2) 1)
(fma.f64 x (/.f64 #s(literal -1/2 binary64) p) #s(literal 1 binary64))
(/ x p)
(/.f64 x p)
x
p
-1/2
#s(literal -1/2 binary64)
1
#s(literal 1 binary64)
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64)))
(+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2)
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64))
(/ x (sqrt (+ (* x x) (* p (* p 4)))))
(/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))
x
(sqrt (+ (* x x) (* p (* p 4))))
(sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))
(+ (* x x) (* p (* p 4)))
(fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))
(* p (* p 4))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
p
(* p 4)
(*.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
1/2
#s(literal 1/2 binary64)

localize131.0ms (1.1%)

Memory
-63.9MiB live, 226.9MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 p #s(literal 4 binary64))
✓accuracy100.0%
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓accuracy72.1%
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))
✓accuracy100.0%
(fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓accuracy100.0%
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1 binary64))
✓accuracy100.0%
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
✓accuracy100.0%
(/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)))))
✓accuracy99.8%
(pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64))
✓accuracy72.1%
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))
Samples
35.0ms133×0valid
31.0ms123×0invalid
Compiler

Compiled 406 to 39 computations (90.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 46.0ms
ival-mult: 13.0ms (28.3% of total)
ival-add: 9.0ms (19.6% of total)
ival-sqrt: 9.0ms (19.6% of total)
ival-div: 8.0ms (17.4% of total)
ival-pow: 5.0ms (10.9% of total)
ival-sub: 1.0ms (2.2% of total)
exact: 1.0ms (2.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series74.0ms (0.6%)

Memory
-20.2MiB live, 137.4MiB allocated
Counts
17 → 372
Calls
Call 1
Inputs
#<alt (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3)>
#<alt (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))>
#<alt (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)>
#<alt (/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))))>
#<alt (sqrt 1)>
#<alt (sqrt (+ (* 1/4 (/ x p)) 1/2))>
#<alt (+ (* 1/4 (/ x p)) 1/2)>
#<alt (/ x p)>
#<alt (sqrt (/ 1/2 (+ (* (/ x p) -1/2) 1)))>
#<alt (/ 1/2 (+ (* (/ x p) -1/2) 1))>
#<alt (+ (* (/ x p) -1/2) 1)>
#<alt (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2))>
#<alt (+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2)>
#<alt (/ x (sqrt (+ (* x x) (* p (* p 4)))))>
#<alt (sqrt (+ (* x x) (* p (* p 4))))>
#<alt (sqrt (/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))))>
#<alt (* p 4)>
Outputs
#<alt (* 1/64 (/ (pow x 3) (pow p 3)))>
#<alt (* (pow x 3) (+ (* -1/8192 (/ (* (pow x 2) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 9))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 3) (+ (* (pow x 2) (+ (* -1/2 (* (pow p 3) (* (pow x 2) (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12)))))))) (* -1/8192 (/ (+ (* 16 (pow p 4)) (* 32 (pow p 4))) (pow p 9))))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 3) (+ (* (pow x 2) (+ (* -1/8192 (/ (+ (* 16 (pow p 4)) (* 32 (pow p 4))) (pow p 9))) (* (pow x 2) (+ (* -1/2 (* (pow p 3) (* (pow x 2) (+ (* -1/64 (/ (* (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12)))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 6))) (+ (* -1/262144 (/ (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 18))) (+ (* 1/4096 (/ 1 (pow p 12))) (* 1/128 (/ (* (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12))))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 6))))))))) (* -1/2 (* (pow p 3) (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12))))))))))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt 1/8>
#<alt (+ 1/8 (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))>
#<alt (+ 1/8 (+ (* -1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2)))))>
#<alt (+ 1/8 (+ (* -1/16 (/ (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6))))) (pow x 6))) (+ (* -1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))))>
#<alt -1/8>
#<alt (- (* 1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))) 1/8)>
#<alt (- (+ (* 1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* 1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2)))) 1/8)>
#<alt (- (+ (* 1/16 (/ (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6))))) (pow x 6))) (+ (* 1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* 1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))) 1/8)>
#<alt 1/8>
#<alt (+ 1/8 (* -3/4 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/8 (* (pow p 2) (- (* -1/16 (* (pow p 2) (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10))))))) (* 3/4 (/ 1 (pow x 2))))))>
#<alt (+ 1/8 (* (pow p 2) (- (* (pow p 2) (+ (* -1/16 (* (pow p 2) (* (pow x 6) (+ (* -12 (/ (+ (* 16 (pow x 2)) (* 32 (pow x 2))) (pow x 14))) (+ (* -1 (/ (* (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 48 (/ 1 (pow x 10)))) (+ (* 4 (pow x 4)) (* 8 (pow x 4)))) (pow x 6))) (+ (* 6 (/ (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))) (pow x 2))) (* 64 (/ 1 (pow x 12))))))))) (* -1/16 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))))) (* 3/4 (/ 1 (pow x 2))))))>
#<alt (* 1/64 (/ (pow x 3) (pow p 3)))>
#<alt (/ (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))) (pow p 3))>
#<alt (/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3)))) (pow p 3))>
#<alt (/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/64 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* -1/262144 (* (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* 1/4096 (pow x 6)) (* 1/128 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4)))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))))))) (pow p 6))) (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))))) (pow p 3))>
#<alt (* -1/64 (/ (pow x 3) (pow p 3)))>
#<alt (* -1 (/ (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))) (pow p 3)))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3)))) (pow p 3)))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/64 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* -1/262144 (* (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* 1/4096 (pow x 6)) (* 1/128 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4)))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))))))) (pow p 6))) (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))))) (pow p 3)))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/8 (/ x p)))>
#<alt (+ 1/4 (* x (- (* 1/16 (/ x (pow p 2))) (* 1/8 (/ 1 p)))))>
#<alt (+ 1/4 (* x (- (* x (+ (* 1/64 (/ x (pow p 3))) (* 1/16 (/ 1 (pow p 2))))) (* 1/8 (/ 1 p)))))>
#<alt 1/4>
#<alt (- (+ 1/4 (* -1 (/ (pow p 2) (pow x 2)))) (* -1/2 (/ (pow p 2) (pow x 2))))>
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#<alt 1/4>
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#<alt 1>
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#<alt 1>
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#<alt 1/2>
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#<alt 1/2>
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#<alt (sqrt 1/2)>
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#<alt (* 2 p)>
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#<alt x>
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#<alt (* -1 x)>
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#<alt x>
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#<alt (* 2 p)>
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#<alt (* -2 p)>
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#<alt (sqrt 1/2)>
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#<alt 1>
#<alt (+ 1 (* 1/2 (/ (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))) (pow x 2))))>
#<alt (+ 1 (+ (* 1/2 (/ (- (* -1/4 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (+ (* 1/4 (pow (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))) 2)) (+ (* 4 (* (- (* -1 (pow p 2)) (* -1/2 (pow p 2))) (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))))) (* 4 (- (* 4 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))) (pow x 2)))))>
#<alt (+ 1 (+ (* 1/2 (/ (- (* -1/4 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/2 (* (- (* -1/4 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (+ (* 1/4 (pow (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))) 2)) (+ (* 4 (* (- (* -1 (pow p 2)) (* -1/2 (pow p 2))) (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))))) (* 4 (- (* 4 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))))) (+ (* 4 (* (- (* -1 (pow p 2)) (* -1/2 (pow p 2))) (- (* -1/4 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (+ (* 4 (* (- (* -1 (pow p 2)) (* -1/2 (pow p 2))) (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))))) (* 4 (- (* 4 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))))) (+ (* 4 (* (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))) (- (* 4 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (* 4 (- (* -16 (pow p 6)) (* -1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (+ (* 1/4 (pow (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))) 2)) (+ (* 4 (* (- (* -1 (pow p 2)) (* -1/2 (pow p 2))) (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))))) (* 4 (- (* 4 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 4 (pow p 2)) (* 8 (pow p 2)))) (* 4 (- (* -1 (pow p 2)) (* -1/2 (pow p 2))))) (pow x 2))))))>
#<alt (* -1 (* (/ (sqrt 1/12) x) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))>
#<alt (* -1 (/ (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (* (pow x 2) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (* (sqrt 1/12) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (+ (* 1/4 (/ (pow (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) 2) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))))))) (* (pow x 4) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (* (pow x 2) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (* (sqrt 1/12) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -64 (* (pow p 6) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/4 (pow (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) 2)) (* 1/2 (* (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -16 (pow p 6)) (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (+ (* 1/2 (/ (* (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (+ (* 1/4 (/ (pow (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) 2) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))))))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (+ (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))))))))) (* 4/3 (* (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))))) (* (pow x 6) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (+ (* 1/4 (/ (pow (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) 2) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))))))) (* (pow x 4) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (* (pow x 2) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (* (sqrt 1/12) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 1/2 (* (pow p 2) (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 49/4 (/ 1 (pow x 4)))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* 1/2 (* (pow p 2) (- (+ (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 16 (pow x 2)) (* 32 (pow x 2))) (pow x 14))) (+ (* -1 (/ (* (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 48 (/ 1 (pow x 10)))) (+ (* 4 (pow x 4)) (* 8 (pow x 4)))) (pow x 6))) (+ (* 6 (/ (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))) (pow x 2))) (* 64 (/ 1 (pow x 12)))))))) (* 54 (/ 1 (pow x 6)))) (+ (* -2 (/ (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 12 (/ 1 (pow x 4)))) (pow x 2))) (* -1/2 (/ (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 49/4 (/ 1 (pow x 4)))) (pow x 2))))))) (* 1/2 (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 49/4 (/ 1 (pow x 4))))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2))))) (pow (sqrt 1/2) 2))) (+ (* 1/32 (pow x 3)) (* 1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* p (sqrt 1/2))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2))))) (pow (sqrt 1/2) 2))) (+ (* 1/32 (pow x 3)) (* 1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))))) (* p (sqrt 1/2))))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
#<alt (* 4 p)>
Calls

93 calls:

TimeVariablePointExpression
5.0ms
p
@inf
(* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)
5.0ms
x
@-inf
(/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))))
4.0ms
p
@0
(pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3)
4.0ms
x
@-inf
(sqrt (/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))))
3.0ms
x
@inf
(/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))))

rewrite642.0ms (5.6%)

Memory
3.9MiB live, 438.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 906×*-lowering-*.f32
5 906×*-lowering-*.f64
4 286×/-lowering-/.f32
4 286×/-lowering-/.f64
3 414×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037203
1226198
21890198
09588179
Stop Event
1×iter limit
1×node limit
Counts
17 → 785
Calls
Call 1
Inputs
(pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3)
(+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))
(* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)
(/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2))))
(sqrt 1)
(sqrt (+ (* 1/4 (/ x p)) 1/2))
(+ (* 1/4 (/ x p)) 1/2)
(/ x p)
(sqrt (/ 1/2 (+ (* (/ x p) -1/2) 1)))
(/ 1/2 (+ (* (/ x p) -1/2) 1))
(+ (* (/ x p) -1/2) 1)
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2))
(+ (* (/ x (sqrt (+ (* x x) (* p (* p 4))))) 1/2) 1/2)
(/ x (sqrt (+ (* x x) (* p (* p 4)))))
(sqrt (+ (* x x) (* p (* p 4))))
(sqrt (/ (+ (pow (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 3) 1/8) (+ (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4)))))) (- 1/4 (* (/ (* 1/2 x) (sqrt (+ (* x x) (* p (* p 4))))) 1/2)))))
(* p 4)
Outputs
(exp.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal 3/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 3/2 binary64) (*.f64 (log.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 3/2 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 3 binary64))))
(neg.f64 (pow.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 3 binary64)))
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(pow.f64 (exp.f64 (log.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))) (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))))))))
(*.f64 (sqrt.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #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 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #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 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.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 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64)) (fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (-.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64)) (-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64)) (fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/64 binary64)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (-.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/8 binary64)) (-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))))))) (sqrt.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (/.f64 (*.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)

simplify685.0ms (5.9%)

Memory
28.1MiB live, 659.5MiB allocated
Algorithm
1×egg-herbie
Rules
8 496×*-lowering-*.f32
8 496×*-lowering-*.f64
7 640×accelerator-lowering-fma.f32
7 640×accelerator-lowering-fma.f64
6 126×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0142310940
1455510698
0963910070
Stop Event
1×iter limit
1×node limit
Counts
372 → 372
Calls
Call 1
Inputs
(* 1/64 (/ (pow x 3) (pow p 3)))
(* (pow x 3) (+ (* -1/8192 (/ (* (pow x 2) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 9))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 3) (+ (* (pow x 2) (+ (* -1/2 (* (pow p 3) (* (pow x 2) (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12)))))))) (* -1/8192 (/ (+ (* 16 (pow p 4)) (* 32 (pow p 4))) (pow p 9))))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 3) (+ (* (pow x 2) (+ (* -1/8192 (/ (+ (* 16 (pow p 4)) (* 32 (pow p 4))) (pow p 9))) (* (pow x 2) (+ (* -1/2 (* (pow p 3) (* (pow x 2) (+ (* -1/64 (/ (* (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12)))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 6))) (+ (* -1/262144 (/ (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 18))) (+ (* 1/4096 (/ 1 (pow p 12))) (* 1/128 (/ (* (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12))))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 6))))))))) (* -1/2 (* (pow p 3) (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12))))))))))) (* 1/64 (/ 1 (pow p 3)))))
1/8
(+ 1/8 (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))
(+ 1/8 (+ (* -1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2)))))
(+ 1/8 (+ (* -1/16 (/ (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6))))) (pow x 6))) (+ (* -1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))))
-1/8
(- (* 1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))) 1/8)
(- (+ (* 1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* 1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2)))) 1/8)
(- (+ (* 1/16 (/ (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6))))) (pow x 6))) (+ (* 1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* 1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))) 1/8)
1/8
(+ 1/8 (* -3/4 (/ (pow p 2) (pow x 2))))
(+ 1/8 (* (pow p 2) (- (* -1/16 (* (pow p 2) (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10))))))) (* 3/4 (/ 1 (pow x 2))))))
(+ 1/8 (* (pow p 2) (- (* (pow p 2) (+ (* -1/16 (* (pow p 2) (* (pow x 6) (+ (* -12 (/ (+ (* 16 (pow x 2)) (* 32 (pow x 2))) (pow x 14))) (+ (* -1 (/ (* (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 48 (/ 1 (pow x 10)))) (+ (* 4 (pow x 4)) (* 8 (pow x 4)))) (pow x 6))) (+ (* 6 (/ (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))) (pow x 2))) (* 64 (/ 1 (pow x 12))))))))) (* -1/16 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))))) (* 3/4 (/ 1 (pow x 2))))))
(* 1/64 (/ (pow x 3) (pow p 3)))
(/ (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))) (pow p 3))
(/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3)))) (pow p 3))
(/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/64 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* -1/262144 (* (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* 1/4096 (pow x 6)) (* 1/128 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4)))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))))))) (pow p 6))) (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))))) (pow p 3))
(* -1/64 (/ (pow x 3) (pow p 3)))
(* -1 (/ (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))) (pow p 3)))
(* -1 (/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3)))) (pow p 3)))
(* -1 (/ (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/64 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* -1/262144 (* (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))) (+ (* 1/4096 (pow x 6)) (* 1/128 (* (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4)))))) (+ (* 16 (pow x 2)) (* 32 (pow x 2))))))))) (pow p 6))) (+ (* -1/2 (/ (* (pow x 3) (+ (* -1/262144 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (+ (* 1/1048576 (pow (+ (* 16 (pow x 2)) (* 32 (pow x 2))) 2)) (* 1/4096 (+ (* 4 (pow x 4)) (* 8 (pow x 4))))))) (pow p 4))) (+ (* -1/8192 (/ (* (pow x 3) (+ (* 16 (pow x 2)) (* 32 (pow x 2)))) (pow p 2))) (* 1/64 (pow x 3))))) (pow p 3)))
1/4
(+ 1/4 (* -1/8 (/ x p)))
(+ 1/4 (* x (- (* 1/16 (/ x (pow p 2))) (* 1/8 (/ 1 p)))))
(+ 1/4 (* x (- (* x (+ (* 1/64 (/ x (pow p 3))) (* 1/16 (/ 1 (pow p 2))))) (* 1/8 (/ 1 p)))))
1/4
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1
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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
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1
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1
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(* 2 p)
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x
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x
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(sqrt 1/2)
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1
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(* -1 (* (/ (sqrt 1/12) x) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))
(* -1 (/ (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (* (pow x 2) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (* (sqrt 1/12) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) x))
(* -1 (/ (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (+ (* 1/4 (/ (pow (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) 2) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))))))) (* (pow x 4) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (* (pow x 2) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (* (sqrt 1/12) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) x))
(* -1 (/ (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -64 (* (pow p 6) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (* 64 (pow p 6)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/4 (pow (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) 2)) (* 1/2 (* (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -16 (pow p 6)) (* 1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (+ (* 1/2 (/ (* (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (+ (* 1/4 (/ (pow (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) 2) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))))))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (+ (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))))))))) (* 4/3 (* (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))))) (* (pow x 6) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6)))))) (+ (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* 4 (pow p 4)) (* 1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (+ (* 1/4 (/ (pow (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) 2) (* (pow (sqrt 1/12) 2) (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))) (* 4/3 (* (- (* -1 (pow p 2)) (* 1/2 (pow p 2))) (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2))))))))))) (* (pow x 4) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (+ (* 1/2 (* (/ (- (* 1/12 (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))))) (* 1/9 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (- (* -1 (pow p 2)) (* 1/2 (pow p 2)))))) (* (pow x 2) (sqrt 1/12))) (sqrt (/ 1 (+ (* 4 (pow p 2)) (* 8 (pow p 2))))))) (* (sqrt 1/12) (sqrt (+ (* 4 (pow p 2)) (* 8 (pow p 2)))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 1/2 (* (pow p 2) (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 49/4 (/ 1 (pow x 4)))))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* 1/2 (* (pow p 2) (- (+ (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 16 (pow x 2)) (* 32 (pow x 2))) (pow x 14))) (+ (* -1 (/ (* (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 48 (/ 1 (pow x 10)))) (+ (* 4 (pow x 4)) (* 8 (pow x 4)))) (pow x 6))) (+ (* 6 (/ (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))) (pow x 2))) (* 64 (/ 1 (pow x 12)))))))) (* 54 (/ 1 (pow x 6)))) (+ (* -2 (/ (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 12 (/ 1 (pow x 4)))) (pow x 2))) (* -1/2 (/ (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 49/4 (/ 1 (pow x 4)))) (pow x 2))))))) (* 1/2 (- (* -1/4 (* (pow x 6) (+ (* -12 (/ (+ (* 4 (pow x 4)) (* 8 (pow x 4))) (pow x 14))) (* 84 (/ 1 (pow x 10)))))) (* 49/4 (/ 1 (pow x 4))))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2))))) (pow (sqrt 1/2) 2))) (+ (* 1/32 (pow x 3)) (* 1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* p (sqrt 1/2))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2))))) (pow (sqrt 1/2) 2))) (+ (* 1/32 (pow x 3)) (* 1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))))) (* p (sqrt 1/2))))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
Outputs
(* 1/64 (/ (pow x 3) (pow p 3)))
(/.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x x))) (*.f64 p (*.f64 p p)))
(* (pow x 3) (+ (* -1/8192 (/ (* (pow x 2) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 9))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal -1/8192 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64))) (pow.f64 p #s(literal 9 binary64))) (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 3) (+ (* (pow x 2) (+ (* -1/2 (* (pow p 3) (* (pow x 2) (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12)))))))) (* -1/8192 (/ (+ (* 16 (pow p 4)) (* 32 (pow p 4))) (pow p 9))))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 x x)) (fma.f64 #s(literal -1/262144 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) #s(literal 2 binary64)) (pow.f64 p #s(literal 18 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) #s(literal 2 binary64)) (pow.f64 p #s(literal 18 binary64))) #s(literal 1/1048576 binary64) (/.f64 (*.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 p p) #s(literal 12 binary64))) (pow.f64 p #s(literal 12 binary64)))))) (/.f64 (*.f64 #s(literal -1/8192 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64))) (pow.f64 p #s(literal 9 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 3) (+ (* (pow x 2) (+ (* -1/8192 (/ (+ (* 16 (pow p 4)) (* 32 (pow p 4))) (pow p 9))) (* (pow x 2) (+ (* -1/2 (* (pow p 3) (* (pow x 2) (+ (* -1/64 (/ (* (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12)))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 6))) (+ (* -1/262144 (/ (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 18))) (+ (* 1/4096 (/ 1 (pow p 12))) (* 1/128 (/ (* (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12))))) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (pow p 6))))))))) (* -1/2 (* (pow p 3) (+ (* -1/262144 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (+ (* 1/1048576 (/ (pow (+ (* 16 (pow p 4)) (* 32 (pow p 4))) 2) (pow p 18))) (* 1/4096 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow p 12))))))))))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 x x)) (fma.f64 #s(literal -1/64 binary64) (*.f64 (fma.f64 #s(literal -1/262144 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) #s(literal 2 binary64)) (pow.f64 p #s(literal 18 binary64))) (/.f64 (*.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 p p) #s(literal 12 binary64))) (pow.f64 p #s(literal 12 binary64)))) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 #s(literal -1/262144 binary64) (/.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) (*.f64 (*.f64 p p) #s(literal 12 binary64))) (pow.f64 p #s(literal 18 binary64))) (fma.f64 #s(literal 1/128 binary64) (*.f64 (fma.f64 #s(literal -1/262144 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) #s(literal 2 binary64)) (pow.f64 p #s(literal 18 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) #s(literal 2 binary64)) (pow.f64 p #s(literal 18 binary64))) #s(literal 1/1048576 binary64) (/.f64 (*.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 p p) #s(literal 12 binary64))) (pow.f64 p #s(literal 12 binary64))))) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) (pow.f64 p #s(literal 6 binary64)))) (/.f64 #s(literal 1/4096 binary64) (pow.f64 p #s(literal 12 binary64)))))) (*.f64 (*.f64 p (*.f64 p p)) (fma.f64 #s(literal -1/262144 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) #s(literal 2 binary64)) (pow.f64 p #s(literal 18 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) #s(literal 2 binary64)) (pow.f64 p #s(literal 18 binary64))) #s(literal 1/1048576 binary64) (/.f64 (*.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 p p) #s(literal 12 binary64))) (pow.f64 p #s(literal 12 binary64)))))))) (/.f64 (*.f64 #s(literal -1/8192 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64))) (pow.f64 p #s(literal 9 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p)))))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))
(fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)) (*.f64 x x)) #s(literal 1/8 binary64))
(+ 1/8 (+ (* -1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2)))))
(fma.f64 #s(literal -1/16 binary64) (+.f64 (/.f64 (-.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 144 binary64)) #s(literal 1/4 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64))) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 144 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)) (*.f64 x x))) #s(literal 1/8 binary64))
(+ 1/8 (+ (* -1/16 (/ (+ (* -1 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4)))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (+ (* -1 (* (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 1/2 (* (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (+ (* 4 (pow p 2)) (* 8 (pow p 2))))) (* 64 (pow p 6))))) (pow x 6))) (+ (* -1/16 (/ (+ (* -1 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 1/4 (pow (+ (* 4 (pow p 2)) (* 8 (pow p 2))) 2)) (+ (* 16 (pow p 4)) (* 32 (pow p 4))))) (pow x 4))) (* -1/16 (/ (+ (* 4 (pow p 2)) (* 8 (pow p 2))) (pow x 2))))))
(+.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)) (-.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 144 binary64))) (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64)) (*.f64 (*.f64 p p) #s(literal 12 binary64))))) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)) (-.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 144 binary64)) #s(literal 1/4 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64))) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 144 binary64))))))) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal -1/16 binary64) (+.f64 (/.f64 (-.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 144 binary64)) #s(literal 1/4 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 48 binary64))) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 144 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)) (*.f64 x x))))))
-1/8
#s(literal -1/8 binary64)
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1/8
#s(literal 1/8 binary64)
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1/4
#s(literal 1/4 binary64)
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1/4
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3/4
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1/4
#s(literal 1/4 binary64)
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1/2
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1/2
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1/2
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1
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1/2
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1
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-1
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(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (*.f64 (*.f64 p p) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2))))) (pow (sqrt 1/2) 2))) (+ (* 1/32 (pow x 3)) (* 1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))) #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/32 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 0 binary64))))) (*.f64 (*.f64 p (*.f64 p p)) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (*.f64 (*.f64 p p) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal -1/8 binary64) (/.f64 x (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (* p (sqrt 1/2))))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (+ (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))) (* 1/8 (pow x 2))))) (pow (sqrt 1/2) 2))) (+ (* 1/32 (pow x 3)) (* 1/2 (* x (+ (* -1/8 (pow x 2)) (* 1/8 (pow x 2))))))) (* p (sqrt 1/2))))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))) #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/32 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 0 binary64))))) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))

eval237.0ms (2.1%)

Memory
7.7MiB live, 560.7MiB allocated
Compiler

Compiled 95 901 to 5 305 computations (94.5% saved)

prune166.0ms (1.4%)

Memory
3.4MiB live, 440.2MiB allocated
Pruning

20 alts after pruning (15 fresh and 5 done)

PrunedKeptTotal
New1 42591 434
Fresh4610
Picked325
Done033
Total1 432201 452
Accuracy
99.9%
Counts
1 452 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶29.1%
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
22.8%
(/.f64 (neg.f64 p) x)
5.0%
(/.f64 p x)
▶81.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))))
53.3%
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
16.7%
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/12 binary64)) x) (neg.f64 (sqrt.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)))))
✓81.8%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
▶6.0%
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶79.5%
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓82.2%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓53.4%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
53.4%
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
12.9%
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (*.f64 p p)) (*.f64 x x)))
18.8%
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/16 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (*.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (neg.f64 (*.f64 x #s(literal 1/4 binary64))))) (*.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
66.4%
(sqrt.f64 (/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
✓16.2%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
31.2%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
55.2%
(sqrt.f64 (-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64)))))
✓57.7%
(sqrt.f64 #s(literal 1/2 binary64))
▶38.8%
#s(literal 1 binary64)
Compiler

Compiled 841 to 408 computations (51.5% saved)

simplify322.0ms (2.8%)

Memory
-15.8MiB live, 475.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
✓cost-diff0
(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
✓cost-diff0
(fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 (*.f64 p p) (*.f64 x x))
✓cost-diff0
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64))
✓cost-diff768
(fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓cost-diff1152
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 p p)
✓cost-diff0
(/.f64 (*.f64 p p) (*.f64 x x))
✓cost-diff0
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))
✓cost-diff0
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))))
Rules
12 126×accelerator-lowering-fma.f32
12 126×accelerator-lowering-fma.f64
4 832×*-lowering-*.f32
4 832×*-lowering-*.f64
2 482×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034254
168252
2129248
3257246
4456242
5987242
62562242
73910242
85274242
97865242
08385203
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))))
1
(sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))))
(/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))
2
(+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))
(/ x (sqrt (+ (* x x) (* p (* p 4)))))
x
(sqrt (+ (* x x) (* p (* p 4))))
(+ (* x x) (* p (* p 4)))
(* p (* p 4))
p
(* p 4)
4
1
(+ (* -1/2 (/ (* p p) (* x x))) 1)
-1/2
(/ (* p p) (* x x))
(* p p)
p
(* x x)
x
1
(sqrt (+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2))
(+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2)
(+ (* 2 (/ (* p p) (* x x))) -1)
2
(/ (* p p) (* x x))
(* p p)
p
(* x x)
x
-1
1/2
(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
(+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2)
(/ x (+ (* 2 (/ (* p p) x)) x))
x
(+ (* 2 (/ (* p p) x)) x)
2
(/ (* p p) x)
(* p p)
p
1/2
Outputs
(/ 1 (sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))))
1
#s(literal 1 binary64)
(sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
2
#s(literal 2 binary64)
(+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))
(/ x (sqrt (+ (* x x) (* p (* p 4)))))
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
x
(sqrt (+ (* x x) (* p (* p 4))))
(sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))
(+ (* x x) (* p (* p 4)))
(fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))
(* p (* p 4))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
p
(* p 4)
(*.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
1
#s(literal 1 binary64)
(+ (* -1/2 (/ (* p p) (* x x))) 1)
(fma.f64 p (/.f64 (*.f64 p #s(literal -1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64))
-1/2
#s(literal -1/2 binary64)
(/ (* p p) (* x x))
(/.f64 (*.f64 p p) (*.f64 x x))
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)
x
1
#s(literal 1 binary64)
(sqrt (+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2))
(fabs.f64 (/.f64 p x))
(+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2)
(/.f64 (*.f64 p p) (*.f64 x x))
(+ (* 2 (/ (* p p) (* x x))) -1)
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64))
2
#s(literal 2 binary64)
(/ (* p p) (* x x))
(/.f64 (*.f64 p p) (*.f64 x x))
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)
x
-1
#s(literal -1 binary64)
1/2
#s(literal 1/2 binary64)
(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64)))
(+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2)
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64))
(/ x (+ (* 2 (/ (* p p) x)) x))
(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
x
(+ (* 2 (/ (* p p) x)) x)
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
2
#s(literal 2 binary64)
(/ (* p p) x)
(/.f64 (*.f64 p p) x)
(* p p)
(*.f64 p p)
p
1/2
#s(literal 1/2 binary64)

localize159.0ms (1.4%)

Memory
26.7MiB live, 259.8MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓accuracy94.9%
(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
✓accuracy94.0%
(/.f64 (*.f64 p p) x)
✓accuracy100.0%
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64))
✓accuracy84.8%
(/.f64 (*.f64 p p) (*.f64 x x))
✓accuracy73.4%
(fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓accuracy69.2%
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓accuracy100.0%
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 p p)
✓accuracy84.8%
(/.f64 (*.f64 p p) (*.f64 x x))
✓accuracy99.1%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))))
✓accuracy95.6%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))
✓accuracy86.7%
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))
✓accuracy72.1%
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))
Samples
34.0ms50×2valid
31.0ms135×0valid
20.0ms45×1valid
17.0ms21×3valid
5.0ms5×4valid
Compiler

Compiled 245 to 36 computations (85.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 77.0ms
ival-mult: 20.0ms (25.9% of total)
ival-div: 19.0ms (24.6% of total)
ival-add: 14.0ms (18.1% of total)
ival-sqrt: 12.0ms (15.5% of total)
adjust: 10.0ms (12.9% of total)
exact: 1.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series53.0ms (0.5%)

Memory
-14.2MiB live, 71.3MiB allocated
Counts
17 → 384
Calls
Call 1
Inputs
#<alt (/ 1 (sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))))>
#<alt (sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))))>
#<alt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))>
#<alt (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))>
#<alt (+ (* -1/2 (/ (* p p) (* x x))) 1)>
#<alt (/ (* p p) (* x x))>
#<alt (* p p)>
#<alt (* x x)>
#<alt (sqrt (+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2))>
#<alt (+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2)>
#<alt (+ (* 2 (/ (* p p) (* x x))) -1)>
#<alt (sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))>
#<alt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2)>
#<alt (/ x (+ (* 2 (/ (* p p) x)) x))>
#<alt (+ (* 2 (/ (* p p) x)) x)>
#<alt (sqrt (+ (* x x) (* p (* p 4))))>
#<alt (/ (* p p) x)>
Outputs
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* 1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2)))>
#<alt (+ (* x (+ (* -1/32 (/ x (* (pow p 2) (sqrt 2)))) (* 1/4 (/ 1 (* p (sqrt 2)))))) (/ 1 (sqrt 2)))>
#<alt (+ (* x (+ (* x (- (* -3/128 (/ x (* (pow p 3) (sqrt 2)))) (* 1/32 (/ 1 (* (pow p 2) (sqrt 2)))))) (* 1/4 (/ 1 (* p (sqrt 2)))))) (/ 1 (sqrt 2)))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (pow (sqrt 2) 2))))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (pow (sqrt 2) 2)))) (* 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) (pow (sqrt 2) 2)))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (pow (sqrt 2) 2)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (pow (sqrt 2) 2))))) (* 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) (pow (sqrt 2) 2))))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (pow (sqrt 2) 2))))) (+ (* 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) (pow (sqrt 2) 2))))) (* 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) (pow (sqrt 2) 2)))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))) (/ 1 (* (pow x 2) (pow (sqrt 2) 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 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))))) (pow (sqrt 2) 2))) (* 1/2 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (/ 1 (* (pow x 2) (pow (sqrt 2) 2))))))>
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* 1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2)))>
#<alt (+ (* -1/32 (/ (pow x 2) (* (pow p 2) (sqrt 2)))) (+ (* 1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2))))>
#<alt (+ (* -1/32 (/ (pow x 2) (* (pow p 2) (sqrt 2)))) (+ (* 1/4 (/ x (* p (sqrt 2)))) (+ (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (* (pow p 3) (sqrt 2)))) (/ 1 (sqrt 2)))))>
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* -1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2)))>
#<alt (+ (* -1 (/ (+ (* 1/32 (/ (pow x 2) (* p (sqrt 2)))) (* 1/4 (/ x (sqrt 2)))) p)) (/ 1 (sqrt 2)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (* p (sqrt 2)))) (* -1/32 (/ (pow x 2) (sqrt 2)))) p)) (* 1/4 (/ x (sqrt 2)))) p)) (/ 1 (sqrt 2)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/4 (/ (* x (sqrt 2)) p)))>
#<alt (+ (sqrt 2) (* x (+ (* -1/4 (/ (sqrt 2) p)) (* 3/32 (/ (* x (sqrt 2)) (pow p 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/4 (/ (sqrt 2) p)) (* x (+ (* -1/128 (/ (* x (sqrt 2)) (pow p 3))) (* 3/32 (/ (sqrt 2) (pow p 2))))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/2 (pow p 4)) (+ (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/16 (/ (pow p 4) (pow (sqrt 1/2) 2)))))) (* (pow x 4) (sqrt 1/2)))) (+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2))))>
#<alt (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/2 (pow p 4)) (+ (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/16 (/ (pow p 4) (pow (sqrt 1/2) 2)))))) (* (pow x 4) (sqrt 1/2)))) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/4 (/ (* (pow p 2) (+ (* -1/2 (pow p 4)) (+ (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/16 (/ (pow p 4) (pow (sqrt 1/2) 2)))))) (pow (sqrt 1/2) 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) (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))))) (* (pow x 6) (sqrt 1/2)))) (+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2)))))>
#<alt (* -1 (/ (* x (* (sqrt 1/2) (sqrt 2))) p))>
#<alt (* -1 (* x (+ (* -1/16 (/ (* (sqrt 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* (pow p 3) (* (pow x 2) (sqrt 1/2))))) (/ (* (sqrt 1/2) (sqrt 2)) p))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (* (sqrt 2) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/256 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow (sqrt 1/2) 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) (sqrt 1/2)))) (+ (* -1/16 (/ (* (sqrt 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* (pow p 3) (* (pow x 2) (sqrt 1/2))))) (/ (* (sqrt 1/2) (sqrt 2)) p)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (* (sqrt 2) (+ (* -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))) (+ (* 1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/256 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow (sqrt 1/2) 2)))) (* 1/8 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (* (pow p 2) (pow (sqrt 1/2) 2)))) (* 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) (sqrt 1/2)))) (+ (* -1/2 (/ (* p (* (sqrt 2) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/256 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow (sqrt 1/2) 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) (sqrt 1/2)))) (+ (* -1/16 (/ (* (sqrt 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* (pow p 3) (* (pow x 2) (sqrt 1/2))))) (/ (* (sqrt 1/2) (sqrt 2)) p))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 2) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt 1/2) 2)))) (/ 1 (pow x 4))))) (sqrt 1/2))) (* 1/4 (/ (sqrt 2) (* (pow x 2) (sqrt 1/2)))))))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* 1/4 (/ (sqrt 2) (* (pow x 2) (sqrt 1/2)))) (* (pow p 2) (+ (* -1/2 (/ (* (sqrt 2) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt 1/2) 2)))) (/ 1 (pow x 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow p 2) (* (sqrt 2) (- (* 5/2 (/ 1 (pow x 6))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt 1/2) 2)))) (/ 1 (pow x 4))) (* (pow x 2) (pow (sqrt 1/2) 2))))))) (sqrt 1/2))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/4 (/ (* x (sqrt 2)) p)))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))) (pow p 2))) (* -1/4 (/ (* x (sqrt 2)) p))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))) (pow p 2))) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/16 (pow x 3)) (+ (* 1/8 (pow x 3)) (* 1/4 (* x (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))))))) (pow p 3))) (* -1/4 (/ (* x (sqrt 2)) p)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/4 (/ (* x (sqrt 2)) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1/4 (* x (sqrt 2))) (* 1/2 (/ (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))) p))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2))))) (* 1/2 (/ (* (sqrt 2) (+ (* -1/16 (pow x 3)) (+ (* 1/8 (pow x 3)) (* 1/4 (* x (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))))))) p))) p)) (* -1/4 (* x (sqrt 2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))>
#<alt (+ 2 (* x (- (* x (+ (* -1/8 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))>
#<alt (/ (pow x 2) (pow p 2))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (/ 1 (pow p 2))) (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2))))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (* (pow p 4) (pow x 4))))))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))>
#<alt (- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))>
#<alt 2>
#<alt (+ 2 (/ x p))>
#<alt (+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))>
#<alt (+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))>
#<alt (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 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))))))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))>
#<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))>
#<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))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))>
#<alt (+ 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)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ x p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))>
#<alt (+ 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)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt -1>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))>
#<alt (/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))>
#<alt (/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))>
#<alt -1>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt -1>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* -1/2 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow x 2) (- (* 1/16 (/ 1 (pow p 6))) (* -1/8 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -4 (pow p 6)) (* -1/2 (* (pow p 2) (- (* 2 (pow p 4)) (* 1/4 (pow p 4)))))) (pow x 6))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (+ (* -1/2 (/ (+ (* 1/2 (* (pow p 2) (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))) (* -1/2 (/ (pow p 2) (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 7/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -25/16 (/ (pow p 2) (pow x 6))) (* 7/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1/2 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))>
#<alt (+ 1/2 (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -4 (/ (pow p 6) (pow x 6))) (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 2 (/ (pow p 4) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* -4 (/ (pow p 6) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 8))) (* 1/8 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))>
#<alt (/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))>
#<alt (/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (/ (+ (* 2 (pow p 2)) (pow x 2)) x)>
#<alt (/ (+ (* 2 (pow p 2)) (pow x 2)) x)>
#<alt (/ (+ (* 2 (pow p 2)) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
Calls

96 calls:

TimeVariablePointExpression
12.0ms
p
@inf
(/ x (+ (* 2 (/ (* p p) x)) x))
10.0ms
x
@-inf
(/ 1 (sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))))
2.0ms
x
@-inf
(sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))))
1.0ms
x
@inf
(sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))))
1.0ms
x
@-inf
(/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))

rewrite327.0ms (2.8%)

Memory
-12.3MiB live, 620.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 808×/-lowering-/.f32
4 808×/-lowering-/.f64
4 388×accelerator-lowering-fma.f32
4 388×accelerator-lowering-fma.f64
4 084×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034198
1199183
21547182
08592167
Stop Event
1×iter limit
1×node limit
Counts
17 → 480
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))))
(sqrt (/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))))
(/ 2 (+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4)))))))
(+ 1 (/ x (sqrt (+ (* x x) (* p (* p 4))))))
(+ (* -1/2 (/ (* p p) (* x x))) 1)
(/ (* p p) (* x x))
(* p p)
(* x x)
(sqrt (+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2))
(+ (* (+ (* 2 (/ (* p p) (* x x))) -1) 1/2) 1/2)
(+ (* 2 (/ (* p p) (* x x))) -1)
(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
(+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2)
(/ x (+ (* 2 (/ (* p p) x)) x))
(+ (* 2 (/ (* p p) x)) x)
(sqrt (+ (* x x) (* p (* p 4))))
(/ (* p p) x)
Outputs
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64)))))))
(sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))) (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
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(/.f64 (sqrt.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p))) #s(literal 64 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p))) #s(literal 64 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))
(pow.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))) (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p))) #s(literal 64 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p))) #s(literal 64 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))
(*.f64 (pow.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 x (*.f64 p p))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (*.f64 p p) (neg.f64 x)))
(neg.f64 (/.f64 (*.f64 p p) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 p p)) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 p p)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (*.f64 p p)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (*.f64 p p) #s(literal 1 binary64))))
(/.f64 (*.f64 p p) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (*.f64 p p))))
(/.f64 (neg.f64 (*.f64 p p)) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (*.f64 p p))) (neg.f64 (neg.f64 x)))
(/.f64 (*.f64 (*.f64 p p) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 p p)))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (*.f64 (*.f64 p p) #s(literal 1 binary64))) (neg.f64 x))
(pow.f64 (/.f64 x (*.f64 p p)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) x))
(*.f64 p (/.f64 p x))
(*.f64 (*.f64 p p) (/.f64 #s(literal 1 binary64) x))
(*.f64 (neg.f64 (*.f64 p p)) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (/.f64 p x) p)
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 p p))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) #s(literal -1 binary64)))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 (neg.f64 p) x))
(*.f64 (/.f64 (neg.f64 p) #s(literal -1 binary64)) (/.f64 p x))

simplify428.0ms (3.7%)

Memory
44.8MiB live, 829.8MiB allocated
Algorithm
1×egg-herbie
Rules
10 520×accelerator-lowering-fma.f32
10 520×accelerator-lowering-fma.f64
8 340×*-lowering-*.f32
8 340×*-lowering-*.f64
4 738×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08616393
127746033
085395693
Stop Event
1×iter limit
1×node limit
Counts
384 → 384
Calls
Call 1
Inputs
(/ 1 (sqrt 2))
(+ (* 1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2)))
(+ (* x (+ (* -1/32 (/ x (* (pow p 2) (sqrt 2)))) (* 1/4 (/ 1 (* p (sqrt 2)))))) (/ 1 (sqrt 2)))
(+ (* x (+ (* x (- (* -3/128 (/ x (* (pow p 3) (sqrt 2)))) (* 1/32 (/ 1 (* (pow p 2) (sqrt 2)))))) (* 1/4 (/ 1 (* p (sqrt 2)))))) (/ 1 (sqrt 2)))
1
(+ 1 (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))))
(+ 1 (+ (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (pow (sqrt 2) 2))))))
(+ 1 (+ (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (pow (sqrt 2) 2)))) (* 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) (pow (sqrt 2) 2)))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (pow (sqrt 2) 2)))))) x))
(* -1 (/ (+ p (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (pow (sqrt 2) 2))))) (* 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) (pow (sqrt 2) 2))))))) x))
(* -1 (/ (+ p (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (pow (sqrt 2) 2))))) (+ (* 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) (pow (sqrt 2) 2))))) (* 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) (pow (sqrt 2) 2)))))))) x))
1
(+ 1 (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))))
(+ 1 (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))) (/ 1 (* (pow x 2) (pow (sqrt 2) 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 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))))) (pow (sqrt 2) 2))) (* 1/2 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (/ 1 (* (pow x 2) (pow (sqrt 2) 2))))))
(/ 1 (sqrt 2))
(+ (* 1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2)))
(+ (* -1/32 (/ (pow x 2) (* (pow p 2) (sqrt 2)))) (+ (* 1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2))))
(+ (* -1/32 (/ (pow x 2) (* (pow p 2) (sqrt 2)))) (+ (* 1/4 (/ x (* p (sqrt 2)))) (+ (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (* (pow p 3) (sqrt 2)))) (/ 1 (sqrt 2)))))
(/ 1 (sqrt 2))
(+ (* -1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2)))
(+ (* -1 (/ (+ (* 1/32 (/ (pow x 2) (* p (sqrt 2)))) (* 1/4 (/ x (sqrt 2)))) p)) (/ 1 (sqrt 2)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (* p (sqrt 2)))) (* -1/32 (/ (pow x 2) (sqrt 2)))) p)) (* 1/4 (/ x (sqrt 2)))) p)) (/ 1 (sqrt 2)))
(sqrt 2)
(+ (sqrt 2) (* -1/4 (/ (* x (sqrt 2)) p)))
(+ (sqrt 2) (* x (+ (* -1/4 (/ (sqrt 2) p)) (* 3/32 (/ (* x (sqrt 2)) (pow p 2))))))
(+ (sqrt 2) (* x (+ (* -1/4 (/ (sqrt 2) p)) (* x (+ (* -1/128 (/ (* x (sqrt 2)) (pow p 3))) (* 3/32 (/ (sqrt 2) (pow p 2))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/2 (pow p 4)) (+ (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/16 (/ (pow p 4) (pow (sqrt 1/2) 2)))))) (* (pow x 4) (sqrt 1/2)))) (+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/2 (pow p 4)) (+ (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/16 (/ (pow p 4) (pow (sqrt 1/2) 2)))))) (* (pow x 4) (sqrt 1/2)))) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/4 (/ (* (pow p 2) (+ (* -1/2 (pow p 4)) (+ (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/16 (/ (pow p 4) (pow (sqrt 1/2) 2)))))) (pow (sqrt 1/2) 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) (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))))) (* (pow x 6) (sqrt 1/2)))) (+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* x (* (sqrt 1/2) (sqrt 2))) p))
(* -1 (* x (+ (* -1/16 (/ (* (sqrt 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* (pow p 3) (* (pow x 2) (sqrt 1/2))))) (/ (* (sqrt 1/2) (sqrt 2)) p))))
(* -1 (* x (+ (* -1/2 (/ (* p (* (sqrt 2) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/256 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow (sqrt 1/2) 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) (sqrt 1/2)))) (+ (* -1/16 (/ (* (sqrt 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* (pow p 3) (* (pow x 2) (sqrt 1/2))))) (/ (* (sqrt 1/2) (sqrt 2)) p)))))
(* -1 (* x (+ (* -1/2 (/ (* p (* (sqrt 2) (+ (* -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))) (+ (* 1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/256 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow (sqrt 1/2) 2)))) (* 1/8 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (* (pow p 2) (pow (sqrt 1/2) 2)))) (* 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) (sqrt 1/2)))) (+ (* -1/2 (/ (* p (* (sqrt 2) (+ (* -1/32 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/256 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow (sqrt 1/2) 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) (sqrt 1/2)))) (+ (* -1/16 (/ (* (sqrt 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* (pow p 3) (* (pow x 2) (sqrt 1/2))))) (/ (* (sqrt 1/2) (sqrt 2)) p))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* 1/4 (/ (* (pow p 2) (sqrt 2)) (* (pow x 2) (sqrt 1/2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 2) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt 1/2) 2)))) (/ 1 (pow x 4))))) (sqrt 1/2))) (* 1/4 (/ (sqrt 2) (* (pow x 2) (sqrt 1/2)))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* 1/4 (/ (sqrt 2) (* (pow x 2) (sqrt 1/2)))) (* (pow p 2) (+ (* -1/2 (/ (* (sqrt 2) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt 1/2) 2)))) (/ 1 (pow x 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow p 2) (* (sqrt 2) (- (* 5/2 (/ 1 (pow x 6))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt 1/2) 2)))) (/ 1 (pow x 4))) (* (pow x 2) (pow (sqrt 1/2) 2))))))) (sqrt 1/2))))))))
(sqrt 2)
(+ (sqrt 2) (* -1/4 (/ (* x (sqrt 2)) p)))
(+ (sqrt 2) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))) (pow p 2))) (* -1/4 (/ (* x (sqrt 2)) p))))
(+ (sqrt 2) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))) (pow p 2))) (+ (* -1/2 (/ (* (sqrt 2) (+ (* -1/16 (pow x 3)) (+ (* 1/8 (pow x 3)) (* 1/4 (* x (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))))))) (pow p 3))) (* -1/4 (/ (* x (sqrt 2)) p)))))
(sqrt 2)
(+ (sqrt 2) (* 1/4 (/ (* x (sqrt 2)) p)))
(+ (sqrt 2) (* -1 (/ (+ (* -1/4 (* x (sqrt 2))) (* 1/2 (/ (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))) p))) p)))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt 2) (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2))))) (* 1/2 (/ (* (sqrt 2) (+ (* -1/16 (pow x 3)) (+ (* 1/8 (pow x 3)) (* 1/4 (* x (+ (* -1/4 (pow x 2)) (* 1/16 (pow x 2)))))))) p))) p)) (* -1/4 (* x (sqrt 2)))) p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))
(+ 2 (* x (- (* x (+ (* -1/8 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))
1
(+ 1 (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))
(/ (pow x 2) (pow p 2))
(* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (/ 1 (pow p 2))) (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2))))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (* (pow p 4) (pow x 4))))))))
1
(+ 1 (/ (pow p 2) (pow x 2)))
(+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
2
(+ 2 (* -1 (/ x p)))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
(- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
2
(+ 2 (/ x p))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))
(+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))
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
(+ 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))))))
(* 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))
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))))))
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)))))
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)))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (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))
(/ (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))
(/ (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))
(/ (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))
(/ (pow p 2) (pow x 2))
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ (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))
(/ (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))
(/ (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))
(/ (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))
(/ (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
(- (* 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) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* 2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* -1 (pow x 2)) (* 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))) 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)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* -1/2 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow x 2) (- (* 1/16 (/ 1 (pow p 6))) (* -1/8 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -4 (pow p 6)) (* -1/2 (* (pow p 2) (- (* 2 (pow p 4)) (* 1/4 (pow p 4)))))) (pow x 6))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (+ (* -1/2 (/ (+ (* 1/2 (* (pow p 2) (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))) (* -1/2 (/ (pow p 2) (pow x 2))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 7/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -25/16 (/ (pow p 2) (pow x 6))) (* 7/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))
(+ 1/2 (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -4 (/ (pow p 6) (pow x 6))) (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 2 (/ (pow p 4) (pow x 4)))) (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -4 (/ (pow p 6) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 8))) (* 1/8 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* 2 (/ (pow p 2) x)))
(* 2 (/ (pow p 2) x))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* 2 (/ (pow p 2) x))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* 2 (/ (pow p 2) x))
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
x
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
Outputs
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (/ x (* p (sqrt 2)))) (/ 1 (sqrt 2)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (+ (* -1/32 (/ x (* (pow p 2) (sqrt 2)))) (* 1/4 (/ 1 (* p (sqrt 2)))))) (/ 1 (sqrt 2)))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (+ (* x (- (* -3/128 (/ x (* (pow p 3) (sqrt 2)))) (* 1/32 (/ 1 (* (pow p 2) (sqrt 2)))))) (* 1/4 (/ 1 (* p (sqrt 2)))))) (/ 1 (sqrt 2)))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -3/128 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 p (*.f64 p p)))) (/.f64 #s(literal -1/32 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 p p)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (pow p 2) (* (pow x 2) (pow (sqrt 2) 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (pow (sqrt 2) 2))))))
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#s(literal -1 binary64)
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(sqrt 1/2)
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
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(sqrt 1/2)
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(sqrt 1/2)
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
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(+ 1/2 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))
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1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
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1
#s(literal 1 binary64)
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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
#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 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64)))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -8 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 #s(literal -4 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))))
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 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64)))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -8 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 #s(literal -4 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))))
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) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 p p) (fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 p p) (fma.f64 (*.f64 p p) (fma.f64 (/.f64 (*.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -8 binary64) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 1/2 binary64))) (*.f64 p p))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 p p))) (*.f64 p p))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 p p)))) (*.f64 p p))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
(/.f64 (-.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 p #s(literal 6 binary64))) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 p p)) (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 4 binary64))))) (*.f64 p p))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 1/2 binary64))) (*.f64 p p))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 p p))) (*.f64 p p))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 p p)))) (*.f64 p p))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
(/.f64 (-.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 p #s(literal 6 binary64))) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 p p)) (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 4 binary64))))) (*.f64 p p))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(* 2 (/ (pow p 2) x))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x)
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 (/.f64 x (*.f64 p p)) (/.f64 #s(literal 2 binary64) x)))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 (/.f64 x (*.f64 p p)) (/.f64 #s(literal 2 binary64) x)))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 (/.f64 x (*.f64 p p)) (/.f64 #s(literal 2 binary64) x)))
(* 2 (/ (pow p 2) x))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x)
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 (/.f64 x (*.f64 p p)) (/.f64 #s(literal 2 binary64) x)))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 (/.f64 x (*.f64 p p)) (/.f64 #s(literal 2 binary64) x)))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 (/.f64 x (*.f64 p p)) (/.f64 #s(literal 2 binary64) x)))
(* 2 (/ (pow p 2) x))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 p p) (*.f64 x x)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 p p) (*.f64 x x)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 p p) (*.f64 x x)) x)
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (*.f64 #s(literal 2 binary64) x) x)
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (*.f64 #s(literal 2 binary64) x) x)
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (*.f64 #s(literal 2 binary64) x) x)
x
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(*.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(*.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(*.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p) (*.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 (*.f64 x x) (fma.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) (*.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 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (/.f64 (*.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 #s(literal 2 binary64) p))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (*.f64 #s(literal 2 binary64) x) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 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 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(neg.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (*.f64 #s(literal 2 binary64) x) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)))) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))))) x))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (*.f64 p p) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 p p) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)) 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 (*.f64 p p) (fma.f64 (*.f64 p p) (fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 p p) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 2 binary64) x)) x)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) #s(literal 2 binary64)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (fma.f64 #s(literal -1/64 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 p (+.f64 #s(literal 2 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal 1/512 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) #s(literal 2 binary64)) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (fma.f64 #s(literal -1/64 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64))) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (+.f64 #s(literal 2 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal 1/512 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))))) (neg.f64 p))
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)

eval204.0ms (1.8%)

Memory
-17.3MiB live, 251.9MiB allocated
Compiler

Compiled 23 957 to 2 878 computations (88% saved)

prune116.0ms (1%)

Memory
-18.3MiB live, 255.6MiB allocated
Pruning

22 alts after pruning (13 fresh and 9 done)

PrunedKeptTotal
New9784982
Fresh1910
Picked145
Done055
Total980221 002
Accuracy
99.9%
Counts
1 002 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓29.1%
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
29.1%
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
22.8%
(/.f64 (neg.f64 p) x)
5.0%
(/.f64 p x)
52.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))))
31.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))
56.9%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
53.3%
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
16.7%
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/12 binary64)) x) (neg.f64 (sqrt.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)))))
✓81.8%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓6.0%
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓79.5%
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓82.2%
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓53.4%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
53.4%
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
12.9%
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (*.f64 p p)) (*.f64 x x)))
18.8%
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/16 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (*.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (neg.f64 (*.f64 x #s(literal 1/4 binary64))))) (*.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
66.4%
(sqrt.f64 (/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
✓16.2%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
55.2%
(sqrt.f64 (-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64)))))
✓57.7%
(sqrt.f64 #s(literal 1/2 binary64))
✓38.8%
#s(literal 1 binary64)
Compiler

Compiled 1 257 to 431 computations (65.7% saved)

regimes76.0ms (0.7%)

Memory
2.9MiB live, 118.0MiB allocated
Counts
38 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/12 binary64)) x) (neg.f64 (sqrt.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)))))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #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)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) (*.f64 p p)) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (*.f64 p p)) (*.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(sqrt.f64 (-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/16 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (*.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (neg.f64 (*.f64 x #s(literal 1/4 binary64))))) (*.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) #s(literal -1/4 binary64)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
Calls

7 calls:

13.0ms
x
12.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
12.0ms
(*.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
p
9.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Results
AccuracySegmentsBranch
82.2%1p
82.2%1x
99.9%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)))))))
99.9%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))))))
99.9%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.9%2(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
82.2%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
Compiler

Compiled 80 to 56 computations (30% saved)

regimes43.0ms (0.4%)

Memory
-12.0MiB live, 61.9MiB allocated
Counts
36 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/12 binary64)) x) (neg.f64 (sqrt.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)))))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #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)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) (*.f64 p p)) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (*.f64 p p)) (*.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(sqrt.f64 (-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal -1/2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))) (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))) (fma.f64 x (/.f64 x (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x)) (sqrt.f64 (fma.f64 p (*.f64 p #s(literal 4 binary64)) (*.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))))))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
Calls

4 calls:

11.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
8.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
8.0ms
(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)))))))
8.0ms
(*.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
99.9%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)))))))
99.9%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))))))
99.9%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.9%2(/.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)

regimes27.0ms (0.2%)

Memory
34.5MiB live, 34.5MiB allocated
Counts
27 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/12 binary64)) x) (neg.f64 (sqrt.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)))))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #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)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
Calls

4 calls:

7.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
6.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
6.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
6.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
Results
AccuracySegmentsBranch
99.9%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)))))))
99.9%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))))))
99.9%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.9%2(/.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)

regimes46.0ms (0.4%)

Memory
-17.0MiB live, 28.0MiB allocated
Counts
23 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/12 binary64)) x) (neg.f64 (sqrt.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)))))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
Calls

4 calls:

28.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
6.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
6.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
5.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
Results
AccuracySegmentsBranch
98.6%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)))))))
98.6%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
98.6%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
98.6%2(/.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)

regimes25.0ms (0.2%)

Memory
-5.6MiB live, 31.4MiB allocated
Counts
20 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/12 binary64)) x) (neg.f64 (sqrt.f64 (*.f64 (*.f64 p p) #s(literal 12 binary64)))))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))
Calls

4 calls:

9.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
5.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
5.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
5.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
Results
AccuracySegmentsBranch
99.3%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)))))))
99.3%3(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
99.3%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.3%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)

regimes21.0ms (0.2%)

Memory
-3.5MiB live, 33.6MiB allocated
Counts
17 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
Calls

4 calls:

7.0ms
(*.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))))))
4.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
4.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
Results
AccuracySegmentsBranch
99.3%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)))))))
99.3%3(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
99.3%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.3%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)

regimes13.0ms (0.1%)

Memory
25.3MiB live, 25.3MiB allocated
Counts
11 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) (*.f64 p #s(literal 1/2 binary64))) p))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
Calls

4 calls:

3.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
3.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
3.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
Results
AccuracySegmentsBranch
99.3%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)))))))
99.3%3(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
99.3%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.3%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)

regimes14.0ms (0.1%)

Memory
-14.8MiB live, 21.9MiB allocated
Counts
7 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
Calls

4 calls:

6.0ms
(/.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
(+.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
99.2%3(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
99.2%3(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
99.2%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.2%3(/.f64 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
19.3MiB live, 19.3MiB allocated
Counts
6 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(/.f64 (neg.f64 p) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1 binary64)
Calls

4 calls:

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)))))))
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
98.4%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)))))))
98.4%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))))))
98.4%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
98.4%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)

regimes18.0ms (0.2%)

Memory
-19.0MiB live, 27.9MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
Outputs
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1 binary64)
Calls

7 calls:

6.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms
x
2.0ms
p
2.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
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
65.7%2x
73.8%2p
73.8%2(*.f64 (*.f64 #s(literal 4 binary64) p) p)
79.4%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)))))))
79.4%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))))))
79.4%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
79.4%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)

regimes10.0ms (0.1%)

Memory
-17.9MiB live, 20.9MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

7 calls:

3.0ms
p
1.0ms
x
1.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
1.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
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))))))
Results
AccuracySegmentsBranch
38.8%1x
38.8%1p
38.8%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
38.8%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)))))))
38.8%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))))))
38.8%1(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
38.8%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)

bsearch1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-0.9999999999998586
-0.9998921678051318
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-0.9999999999998586
-0.9998921678051318
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-0.9999999999998586
-0.9998921678051318
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-0.5319397674414901
-1.7591104193218213e-6
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
3.9623098517112735e-6
0.9999967572082491
0.0ms
-0.9998921678051318
-0.5319397674414901
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
3.9623098517112735e-6
0.9999967572082491
0.0ms
-0.9998921678051318
-0.5319397674414901
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
3.9623098517112735e-6
0.9999967572082491
0.0ms
-0.9998921678051318
-0.5319397674414901
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
3.9623098517112735e-6
0.9999967572082491
0.0ms
-0.9998921678051318
-0.5319397674414901
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
3.9623098517112735e-6
0.9999967572082491
0.0ms
-0.9998921678051318
-0.5319397674414901
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.9623098517112735e-6
0.9999967572082491
Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify13.0ms (0.1%)

Memory
23.0MiB live, 23.0MiB allocated
Algorithm
1×egg-herbie
Rules
26×*-commutative_binary64
26×+-commutative_binary64
18×sub-neg_binary64
16×neg-sub0_binary64
16×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
080441
1102441
2122441
3141441
4152441
5156441
Stop Event
1×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 -4503149267407759/4503599627370496 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #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 -4503149267407759/4503599627370496 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -4503149267407759/4503599627370496 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #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 -1/2 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #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)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #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)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #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)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
#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 -4503149267407759/4503599627370496 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -4503149267407759/4503599627370496 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -4503149267407759/4503599627370496 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -4503149267407759/4503599627370496 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -4503149267407759/4503599627370496 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -4503149267407759/4503599627370496 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #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 -1/2 binary64)) (/.f64 (neg.f64 p) x) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -1/2 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #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)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (/.f64 (fma.f64 x x (*.f64 #s(literal -1/2 binary64) (*.f64 p p))) (*.f64 x x))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))))
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(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #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)) (/.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 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -5404319552844595/9007199254740992 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.5s (12.8%)

Memory
-6.0MiB live, 905.6MiB allocated
Rules
10 520×accelerator-lowering-fma.f32
10 520×accelerator-lowering-fma.f64
9 590×accelerator-lowering-fma.f32
9 590×accelerator-lowering-fma.f64
8 496×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08616393
127746033
085395693
0142310940
1455510698
0963910070
027163
1129148
2856144
08652133
037203
1226198
21890198
09588179
01466
16866
249266
3694866
0847359
04342482
113252377
246062304
080752141
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 829 to 368 computations (55.6% saved)

preprocess118.0ms (1%)

Memory
14.0MiB live, 170.3MiB allocated
Compiler

Compiled 1 124 to 260 computations (76.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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