Given's Rotation SVD example

Time bar (total: 10.9s)

analyze434.0ms (4%)

Memory
32.3MiB live, 625.6MiB 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)

sample2.3s (20.7%)

Memory
37.9MiB live, 3 305.9MiB allocated
Samples
1.1s6 217×0valid
340.0ms1 024×2valid
185.0ms416×3valid
130.0ms599×1valid
Precisions
Click to see histograms. Total time spent on operations: 1.5s
ival-mult: 436.0ms (29.8% of total)
const: 334.0ms (22.9% of total)
ival-sqrt: 246.0ms (16.8% of total)
ival-add: 129.0ms (8.8% of total)
ival-div: 116.0ms (7.9% of total)
adjust: 75.0ms (5.1% of total)
ival-fabs: 54.0ms (3.7% of total)
ival-<: 46.0ms (3.1% of total)
ival-and: 11.0ms (0.8% of total)
exact: 10.0ms (0.7% of total)
ival-assert: 4.0ms (0.3% of total)
Bogosity

preprocess64.0ms (0.6%)

Memory
16.2MiB live, 54.8MiB allocated
Algorithm
1×egg-herbie
Rules
252×distribute-lft-neg-in
218×unsub-neg
198×associate-*r*
196×associate-*l*
162×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

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

(abs p)

explain241.0ms (2.2%)

Memory
9.4MiB live, 434.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
650-0-(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
380-0-(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
350-3(3.850551048072816e-170 -4.1026927394391004e-13)(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-rescue650
↳(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))overflow65
↳(*.f64 (*.f64 #s(literal 4 binary64) p) p)overflow65
+.f64(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))cancellation380
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-rescue320
↳(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)))))))underflow5
↳(*.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))))))underflow37
↳(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))underflow37
↳(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))underflow19
↳(*.f64 (*.f64 #s(literal 4 binary64) p) p)underflow64
Confusion
Predicted +Predicted -
+700
-65121
Precision
0.5185185185185185
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+7000
-650121
Precision?
0.5185185185185185
Recall?
1.0
Freqs
test
numberfreq
0121
1135
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
33.0ms364×0valid
18.0ms70×2valid
12.0ms30×3valid
8.0ms48×1valid
Compiler

Compiled 230 to 60 computations (73.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-mult: 13.0ms (27.5% of total)
ival-sqrt: 12.0ms (25.4% of total)
ival-add: 8.0ms (16.9% of total)
adjust: 7.0ms (14.8% of total)
ival-div: 6.0ms (12.7% 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
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶74.3%
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify8.0ms (0.1%)

Memory
-22.3MiB live, 14.0MiB 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×lower-*.f32
24×lower-*.f64
18×lower-fma.f64
18×lower-fma.f32
12×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

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

localize69.0ms (0.6%)

Memory
-20.7MiB live, 150.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
✓accuracy88.0%
(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)))))))
✓accuracy86.6%
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
✓accuracy76.5%
(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
Samples
33.0ms182×0valid
8.0ms35×2valid
5.0ms15×3valid
4.0ms24×1valid
Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 6.0ms (28.2% of total)
ival-sqrt: 5.0ms (23.5% of total)
ival-add: 4.0ms (18.8% of total)
ival-div: 3.0ms (14.1% of total)
adjust: 2.0ms (9.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series22.0ms (0.2%)

Memory
-24.4MiB live, 49.5MiB allocated
Counts
5 → 120
Calls
Call 1
Inputs
#<alt (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))>
#<alt (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))>
#<alt (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))>
#<alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))>
#<alt (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 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
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
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
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))))))

rewrite388.0ms (3.6%)

Memory
8.2MiB live, 570.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 862×lower-fma.f64
4 862×lower-fma.f32
3 532×lower-*.f32
3 524×lower-*.f64
2 388×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

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

simplify358.0ms (3.3%)

Memory
39.3MiB live, 708.5MiB allocated
Algorithm
1×egg-herbie
Rules
9 590×lower-fma.f64
9 590×lower-fma.f32
6 900×lower-*.f64
6 900×lower-*.f32
4 472×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04342482
113252377
246062304
080752141
Stop Event
1×iter limit
1×node limit
Counts
120 → 118
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))

eval62.0ms (0.6%)

Memory
-19.8MiB live, 129.5MiB allocated
Compiler

Compiled 15 512 to 1 954 computations (87.4% saved)

prune60.0ms (0.6%)

Memory
20.8MiB live, 136.1MiB allocated
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New38410394
Fresh000
Picked101
Done000
Total38510395
Accuracy
99.7%
Counts
395 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
31.1%
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
74.3%
(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)))
▶24.2%
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
▶49.3%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
12.8%
(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)))
16.1%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
▶74.3%
(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)))))))))
▶70.9%
(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)))))
33.6%
(sqrt.f64 #s(literal 1 binary64))
▶52.8%
(sqrt.f64 #s(literal 1/2 binary64))
Compiler

Compiled 260 to 176 computations (32.3% saved)

simplify349.0ms (3.2%)

Memory
11.1MiB live, 434.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))
✓cost-diff0
(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)))))
✓cost-diff128
(*.f64 p (/.f64 #s(literal 2 binary64) x))
✓cost-diff128
(*.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))))
✓cost-diff0
(/.f64 p (*.f64 x x))
✓cost-diff0
(neg.f64 p)
✓cost-diff0
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #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-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
9 818×lower-fma.f32
9 810×lower-fma.f64
2 198×lower-*.f32
2 188×lower-*.f64
1 646×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
032231
060227
199227
2151227
3221227
4285227
5341227
6468227
7704227
81160227
92733227
104519227
116149227
127397227
08010223
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(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 1/2 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))))))))
#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)))))))
#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 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
x
(sqrt.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 p (*.f64 #s(literal 4 binary64) p))
p
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
#s(literal 1/4 binary64)
(/.f64 x p)
x
p
#s(literal 1/2 binary64)
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(neg.f64 p)
p
(/.f64 p (*.f64 x x))
(*.f64 x x)
x
#s(literal 1 binary64)
(sqrt.f64 (*.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)))))
(*.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))))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))
#s(literal 1 binary64)
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
x
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
p
(*.f64 p (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
Outputs
(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)))))))))
(sqrt.f64 (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)))
(/.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))))))))
(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))
#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 #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 1 binary64) (/.f64 x (sqrt.f64 (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 p #s(literal 4 binary64)))))))
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))))
x
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64)))))
(fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))
(fma.f64 x x (*.f64 p (*.f64 p #s(literal 4 binary64))))
(*.f64 p (*.f64 #s(literal 4 binary64) p))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
p
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
#s(literal 1/4 binary64)
(/.f64 x p)
x
p
#s(literal 1/2 binary64)
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(neg.f64 p)
p
(/.f64 p (*.f64 x x))
(*.f64 x x)
x
#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 x (/.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 p p) (/.f64 p x) x)) #s(literal 1/2 binary64)))
(*.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))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 p p) (/.f64 p x) x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))
(+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 p p) (/.f64 p x) x)))
#s(literal 1 binary64)
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
(/.f64 x (fma.f64 (+.f64 p p) (/.f64 p x) x))
x
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
(fma.f64 (+.f64 p p) (/.f64 p x) x)
p
(*.f64 p (/.f64 #s(literal 2 binary64) x))
(/.f64 (+.f64 p p) x)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)

localize110.0ms (1%)

Memory
13.3MiB live, 248.1MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.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))))
✓accuracy100.0%
(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)))))
✓accuracy100.0%
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
✓accuracy99.9%
(*.f64 p (/.f64 #s(literal 2 binary64) x))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
✓accuracy100.0%
(neg.f64 p)
✓accuracy99.9%
(/.f64 p (*.f64 x x))
✓accuracy100.0%
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
✓accuracy100.0%
(/.f64 x p)
✓accuracy98.1%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 #s(literal 4 binary64) p)
✓accuracy100.0%
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
✓accuracy100.0%
(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)))))))))
✓accuracy100.0%
(/.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))))))))
Samples
47.0ms198×0invalid
19.0ms58×0valid
Compiler

Compiled 249 to 37 computations (85.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 46.0ms
ival-div: 14.0ms (30.7% of total)
ival-mult: 13.0ms (28.5% of total)
ival-sqrt: 9.0ms (19.7% of total)
ival-add: 7.0ms (15.3% of total)
exact: 1.0ms (2.2% of total)
ival-neg: 1.0ms (2.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series48.0ms (0.4%)

Memory
-14.1MiB live, 104.0MiB allocated
Counts
20 → 420
Calls
Call 1
Inputs
#<alt (/.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))))))))>
#<alt (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)))))))))>
#<alt (/.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)))))))>
#<alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))>
#<alt (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))>
#<alt (/.f64 x p)>
#<alt (sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))>
#<alt (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))>
#<alt (neg.f64 p)>
#<alt (/.f64 p (*.f64 x x))>
#<alt (*.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))))>
#<alt (*.f64 p (/.f64 #s(literal 2 binary64) x))>
#<alt (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)))))>
#<alt (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))>
#<alt (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))>
#<alt (*.f64 #s(literal 4 binary64) p)>
#<alt (*.f64 x x)>
#<alt (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) 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 (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 (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))>
#<alt (* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* -1/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (- (* -1/16 (/ (pow p 2) (pow x 6))) (* 1/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (/ (* p (sqrt -1)) x)>
#<alt (* p (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))>
#<alt (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))>
#<alt (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow x 5) (* (pow p 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))))>
#<alt (* -1 (/ (* p (sqrt -1)) x))>
#<alt (* -1 (* p (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))>
#<alt (* -1 (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))))>
#<alt (* -1 (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow x 5) (* (pow p 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))))>
#<alt (/ (* p (sqrt -1)) x)>
#<alt (/ (+ (* 1/2 (/ (pow x 2) (* p (sqrt -1)))) (* p (sqrt -1))) x)>
#<alt (/ (+ (* p (sqrt -1)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* p (sqrt -1))))))) x)>
#<alt (/ (+ (* p (sqrt -1)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (* (pow p 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow p 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* p (sqrt -1))))))) x)>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* -1/8 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/8 (/ (pow p 4) (pow x 4))) (* -1/16 (/ (pow p 6) (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* -1/8 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/8 (/ (pow p 4) (pow x 4))) (* -1/16 (/ (pow p 6) (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (* -1 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))>
#<alt (* -1 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))>
#<alt (* -1 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt (/ p (pow x 2))>
#<alt 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 (+ (* -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 (* (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 (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (+ (* -5/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 4))) (* 1/4 (/ (sqrt 1/2) (pow p 2))))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (pow p 2))) (* (pow x 2) (+ (* -5/32 (/ (sqrt 1/2) (pow p 4))) (* 13/128 (/ (* (pow x 2) (sqrt 1/2)) (pow p 6))))))))>
#<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) (+ (* -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) (+ (* -4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 8 (pow p 6)) (/ (* (pow p 2) (+ (* -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 (* (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) (- (* 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) (- (* -8 (pow p 6)) (* -1 (/ (* (pow p 2) (- (* 4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))>
#<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) (- (* 4 (/ 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 (/ (- (* 4 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 8 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 4 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/4 (* (pow x 2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4))))) (* -1/8 (pow x 6)))) (pow p 6))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/4 (* (pow x 2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4))))) (* -1/8 (pow x 6)))) (pow p 6))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2))))))>
#<alt (+ 1 (* (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 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 2 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 2 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 2 (+ (* -8 (/ (pow p 6) (pow x 6))) (+ (* -2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 4) (pow x 4))))))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 2 (* (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>
#<alt (+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* 1/2 (/ (pow x 2) (pow p 2)))))>
#<alt (- (+ 1 (+ (* 1/8 (/ (pow x 6) (pow p 6))) (* 1/2 (/ (pow x 2) (pow p 2))))) (* 1/4 (/ (pow x 4) (pow p 4))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* 1/2 (/ (pow x 2) (pow p 2)))))>
#<alt (- (+ 1 (+ (* 1/8 (/ (pow x 6) (pow p 6))) (* 1/2 (/ (pow x 2) (pow p 2))))) (* 1/4 (/ (pow x 4) (pow p 4))))>
#<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 (* 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)>
#<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 (* 1/2 (/ (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))>
Calls

105 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/ x (+ (* p (* p (/ 2 x))) x))
2.0ms
x
@0
(sqrt (+ (* 1/4 (/ x p)) 1/2))
2.0ms
p
@0
(sqrt (+ (* 1/4 (/ x p)) 1/2))
2.0ms
x
@inf
(sqrt (* 1/2 (+ 1 (/ x (+ (* p (* p (/ 2 x))) x)))))
2.0ms
p
@-inf
(* 1/2 (+ 1 (/ x (+ (* p (* p (/ 2 x))) x))))

rewrite468.0ms (4.3%)

Memory
-33.6MiB live, 527.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 376×lower-*.f32
4 366×lower-*.f64
4 258×lower-/.f32
4 244×lower-/.f64
3 642×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
032178
060174
1224174
21531174
08155170
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 513
Calls
Call 1
Inputs
(/.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))))))))
(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) (+.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 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(/.f64 x p)
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(neg.f64 p)
(/.f64 p (*.f64 x x))
(*.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))))
(*.f64 p (/.f64 #s(literal 2 binary64) x))
(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)))))
(+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
(*.f64 #s(literal 4 binary64) p)
(*.f64 x x)
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
Outputs
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64))
(+.f64 (*.f64 (/.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 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))
(fma.f64 (/.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))
(neg.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 #s(literal 4 binary64) (*.f64 p p)))))))))
(/.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 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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))))
(/.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 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.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)))))))) (+.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))))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (+.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))))))))) (neg.f64 (+.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)))))))))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))) (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (/.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)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 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) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)))
(*.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))
(*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))))
(exp.f64 (*.f64 (log.f64 (fma.f64 #s(literal 1/2 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)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 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 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 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 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 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 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.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 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)))))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))))))
(pow.f64 (fma.f64 #s(literal 1/2 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))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 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))
(pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 #s(literal 1/2 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))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 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 1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64)) #s(literal 1/4 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 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (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)))))))))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.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)))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
(*.f64 (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
(exp.f64 (*.f64 (log1p.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal -1 binary64)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 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) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))))
(neg.f64 (/.f64 #s(literal -1 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) (+.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 (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (/.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 (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))))
(pow.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 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.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) (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 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) (+.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))
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(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) x)) (neg.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x))) (neg.f64 (neg.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x))))
(/.f64 (neg.f64 (*.f64 x #s(literal 1 binary64))) (neg.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)))))
(pow.f64 (/.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x) x) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)))
(*.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)))
(*.f64 (/.f64 x (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)))
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)) x)
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)))
(*.f64 (/.f64 x (fma.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x)) (*.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x))))
(*.f64 (/.f64 x (fma.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x)) (*.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x))))))
(*.f64 (/.f64 x (*.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x) (-.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) x))) (-.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) x))
(*.f64 (/.f64 x (*.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x) (-.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 p (*.f64 p p)) (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x)) (*.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x))))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x) (-.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) x))) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 2 binary64)) x) x))))

simplify659.0ms (6.1%)

Memory
14.9MiB live, 920.5MiB allocated
Algorithm
1×egg-herbie
Rules
11 178×lower-fma.f64
11 178×lower-fma.f32
8 502×lower-*.f64
8 502×lower-*.f32
5 092×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09766799
130276597
086716211
Stop Event
1×iter limit
1×node limit
Counts
420 → 418
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)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* 1/2 (sqrt (/ x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))
(* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))
(* 1/2 (sqrt (/ x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 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))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* -1/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (- (* -1/16 (/ (pow p 2) (pow x 6))) (* 1/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(/ (* p (sqrt -1)) x)
(* p (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))
(* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))
(* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow x 5) (* (pow p 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))))
(* -1 (/ (* p (sqrt -1)) x))
(* -1 (* p (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))
(* -1 (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))))
(* -1 (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow x 5) (* (pow p 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))))
(/ (* p (sqrt -1)) x)
(/ (+ (* 1/2 (/ (pow x 2) (* p (sqrt -1)))) (* p (sqrt -1))) x)
(/ (+ (* p (sqrt -1)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* p (sqrt -1))))))) x)
(/ (+ (* p (sqrt -1)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (* (pow p 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow p 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* p (sqrt -1))))))) x)
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* -1/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/8 (/ (pow p 4) (pow x 4))) (* -1/16 (/ (pow p 6) (pow x 6))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* -1/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/8 (/ (pow p 4) (pow x 4))) (* -1/16 (/ (pow p 6) (pow x 6))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(* -1 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* -1 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* -1 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 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 (+ (* -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 (* (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))))))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* -5/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 4))) (* 1/4 (/ (sqrt 1/2) (pow p 2))))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (pow p 2))) (* (pow x 2) (+ (* -5/32 (/ (sqrt 1/2) (pow p 4))) (* 13/128 (/ (* (pow x 2) (sqrt 1/2)) (pow p 6))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -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) (+ (* -4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 8 (pow p 6)) (/ (* (pow p 2) (+ (* -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)))))
(* (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) (- (* 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) (- (* -8 (pow p 6)) (* -1 (/ (* (pow p 2) (- (* 4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 4 (/ 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 (/ (- (* 4 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 8 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 4 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/4 (* (pow x 2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4))))) (* -1/8 (pow x 6)))) (pow p 6))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/4 (* (pow x 2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4))))) (* -1/8 (pow x 6)))) (pow p 6))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))))
1
(+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))
(+ 1 (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2))))))
(+ 1 (* (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))))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 4) (pow x 4)))))
(+ 2 (+ (* -8 (/ (pow p 6) (pow x 6))) (+ (* -2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 4) (pow x 4))))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))
(+ 1 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* 1/2 (/ (pow x 2) (pow p 2)))))
(- (+ 1 (+ (* 1/8 (/ (pow x 6) (pow p 6))) (* 1/2 (/ (pow x 2) (pow p 2))))) (* 1/4 (/ (pow x 4) (pow p 4))))
1
(+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))
(+ 1 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* 1/2 (/ (pow x 2) (pow p 2)))))
(- (+ 1 (+ (* 1/8 (/ (pow x 6) (pow p 6))) (* 1/2 (/ (pow x 2) (pow p 2))))) (* 1/4 (/ (pow x 4) (pow p 4))))
(* 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))))))))
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(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)
(* 1/2 (/ (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))
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 (*.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 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.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) (+.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 p (*.f64 p (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (-.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))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #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))
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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2
#s(literal 2 binary64)
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2
#s(literal 2 binary64)
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1
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1
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(sqrt 1/2)
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(+ 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 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 p p))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (/.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 #s(literal 1/2 binary64) (*.f64 x x) (/.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 #s(literal 1/2 binary64) (*.f64 x x))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 p p)) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (pow.f64 p #s(literal 4 binary64))))) (*.f64 p p))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 p p))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (/.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 #s(literal 1/2 binary64) (*.f64 x x) (/.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 #s(literal 1/2 binary64) (*.f64 x x))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 p p)) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (pow.f64 p #s(literal 4 binary64))))) (*.f64 p p))

eval126.0ms (1.2%)

Memory
21.2MiB live, 287.2MiB allocated
Compiler

Compiled 21 605 to 3 040 computations (85.9% saved)

prune102.0ms (0.9%)

Memory
-4.6MiB live, 271.1MiB allocated
Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New9247931
Fresh145
Picked235
Done000
Total92714941
Accuracy
99.8%
Counts
941 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
24.6%
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
▶31.1%
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
70.9%
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶74.3%
(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)))
✓49.3%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
12.8%
(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)))
▶16.1%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
51.4%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶26.4%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
15.7%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 p p))))
15.7%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x)))))
✓74.3%
(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)))))))))
✓52.8%
(sqrt.f64 #s(literal 1/2 binary64))
▶33.6%
#s(literal 1 binary64)
Compiler

Compiled 335 to 223 computations (33.4% saved)

simplify400.0ms (3.7%)

Memory
-8.1MiB live, 203.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓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 1/2 binary64))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
✓cost-diff320
(/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #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 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
✓cost-diff0
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
✓cost-diff0
(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))
✓cost-diff0
(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)))
Rules
2 272×lower-fma.f32
2 266×lower-fma.f64
1 908×lower-*.f32
1 896×lower-*.f64
1 156×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026175
048175
181171
2158171
3341169
4537169
5635169
6771169
7915169
81009169
91295169
102434169
113386169
123794169
134071169
144240169
154306169
164598169
174744169
184803169
194803169
204803169
214904169
224990169
235026169
245026169
255026169
265058169
275254169
285254169
295310169
305600169
05600167
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(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)))
(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))
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
x
(sqrt.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 p (*.f64 #s(literal 4 binary64) p))
p
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
p
(neg.f64 x)
x
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
Outputs
(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 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p 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 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
x
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
(sqrt.f64 (fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p))))
(fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))
(fma.f64 x x (*.f64 #s(literal 4 binary64) (*.f64 p p)))
(*.f64 p (*.f64 #s(literal 4 binary64) p))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
p
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(fabs.f64 (/.f64 p x))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(*.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (neg.f64 x)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))
(*.f64 p (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
(*.f64 p (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
p
(neg.f64 x)
x
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 p (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 p (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x

localize125.0ms (1.1%)

Memory
29.6MiB live, 256.7MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 p p)
✓accuracy99.7%
(/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64)))
✓accuracy88.8%
(/.f64 (*.f64 p p) (*.f64 x x))
✓accuracy84.0%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(neg.f64 x)
✓accuracy99.3%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
✓accuracy99.3%
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 p p)
✓accuracy88.8%
(/.f64 (*.f64 p p) (*.f64 x x))
✓accuracy65.4%
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
✓accuracy100.0%
(/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))
✓accuracy88.0%
(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)))
✓accuracy86.7%
(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))
✓accuracy76.5%
(sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))
Samples
50.0ms182×0valid
14.0ms34×2valid
8.0ms16×3valid
7.0ms24×1valid
Compiler

Compiled 187 to 30 computations (84% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-mult: 20.0ms (35.5% of total)
ival-sqrt: 18.0ms (31.9% of total)
ival-div: 8.0ms (14.2% of total)
ival-add: 5.0ms (8.9% of total)
adjust: 4.0ms (7.1% of total)
exact: 1.0ms (1.8% of total)
ival-neg: 1.0ms (1.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series27.0ms (0.2%)

Memory
-13.1MiB live, 61.2MiB allocated
Counts
16 → 300
Calls
Call 1
Inputs
#<alt (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)))>
#<alt (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))>
#<alt (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p)))))>
#<alt (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 #s(literal 4 binary64) p))))>
#<alt (sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))>
#<alt (/.f64 (*.f64 p p) (*.f64 x x))>
#<alt (*.f64 p p)>
#<alt (*.f64 x x)>
#<alt (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))>
#<alt (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)>
#<alt (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))>
#<alt (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))>
#<alt (neg.f64 x)>
Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
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#<alt (* 2 p)>
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#<alt (* x (+ (* (pow x 2) (+ (* -1 (/ (sqrt 1/2) (* (pow p 3) (sqrt 2)))) (* (pow x 2) (+ (* -1/2 (/ (* p (* (pow x 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 2 (/ 1 (pow p 6))) (/ 1 (* (pow p 6) (pow (sqrt 2) 2)))) (* (pow p 2) (pow (sqrt 2) 2)))) (* 2 (/ 1 (pow p 8))))))) (sqrt 2))) (* 1/2 (/ (* p (* (sqrt 1/2) (- (* 2 (/ 1 (pow p 6))) (/ 1 (* (pow p 6) (pow (sqrt 2) 2)))))) (sqrt 2))))))) (/ (* (sqrt 1/2) (sqrt 2)) p)))>
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#<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) (+ (* -2 (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) (+ (* -2 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 2 (pow p 6)) (/ (* (pow p 2) (+ (* -2 (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 (* (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) (+ (* -2 (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) (+ (* -2 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 2 (pow p 6)) (/ (* (pow p 2) (+ (* -2 (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 1/2>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* 1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (+ (* 1/2 (/ 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)) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 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

75 calls:

TimeVariablePointExpression
3.0ms
p
@inf
(sqrt (/ 1/2 (+ (* 1/2 (/ (* p p) (* x x))) 1/2)))
2.0ms
p
@0
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
2.0ms
p
@0
(/ (* (sqrt 1/2) (* (sqrt 2) p)) (neg x))
1.0ms
x
@-inf
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
1.0ms
x
@0
(sqrt (/ 1/2 (+ (* 1/2 (/ (* p p) (* x x))) 1/2)))

rewrite343.0ms (3.1%)

Memory
18.5MiB live, 502.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 238×lower-fma.f32
5 232×lower-fma.f64
5 068×lower-*.f32
5 056×lower-*.f64
3 644×lower-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
025130
047130
1158109
2992105
08554105
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
16 → 559
Calls
Call 1
Inputs
(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)))
(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))
(/.f64 x (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))))
(sqrt.f64 (/.f64 (*.f64 p p) (*.f64 x x)))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
(*.f64 x x)
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p))
(sqrt.f64 #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
(/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))
(neg.f64 x)
Outputs
(exp.f64 (*.f64 (log.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/4 binary64)))) (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal -1/4 binary64))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #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 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal -1/4 binary64)))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal -1/4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/4 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/4 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal 1/4 binary64)) (*.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal -1/4 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64))
(+.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))))) (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64))
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(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x))))))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/4 binary64)))))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (-.f64 (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))))))
(*.f64 #s(literal 1 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (fma.f64 p (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/4 binary64))))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 x (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))))
(*.f64 (fma.f64 p (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1/2 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) x) x)
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 0 binary64))))
(neg.f64 x)
(neg.f64 (/.f64 x #s(literal 1 binary64)))
(/.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 #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 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (neg.f64 (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 0 binary64))))
(*.f64 x #s(literal -1 binary64))
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 (*.f64 x (neg.f64 x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)))
(*.f64 (neg.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x))

simplify320.0ms (2.9%)

Memory
-27.4MiB live, 580.6MiB allocated
Algorithm
1×egg-herbie
Rules
7 242×lower-fma.f64
7 242×lower-fma.f32
7 036×lower-*.f64
7 036×lower-*.f32
2 534×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06204488
119454315
267644290
081074071
Stop Event
1×iter limit
1×node limit
Counts
300 → 298
Calls
Call 1
Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(* 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))))))))
(/ 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))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (/ (pow p 2) (pow x 4)) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -1 (/ (pow p 2) (pow x 6))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))))
(/ (pow x 2) (pow p 2))
(/ (+ (* -1 (/ (pow x 4) (pow p 2))) (pow x 2)) (pow p 2))
(/ (- (+ (/ (pow x 6) (pow p 4)) (pow x 2)) (/ (pow x 4) (pow p 2))) (pow p 2))
(/ (- (+ (* -1 (/ (pow x 8) (pow p 6))) (pow x 2)) (+ (* -1 (/ (pow x 6) (pow p 4))) (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (pow x 2) (pow p 2))
(/ (+ (* -1 (/ (pow x 4) (pow p 2))) (pow x 2)) (pow p 2))
(/ (- (+ (/ (pow x 6) (pow p 4)) (pow x 2)) (/ (pow x 4) (pow p 2))) (pow p 2))
(/ (- (+ (* -1 (/ (pow x 8) (pow p 6))) (pow x 2)) (+ (* -1 (/ (pow x 6) (pow p 4))) (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (pow x 2) (pow p 2))
(* (pow x 2) (+ (* -1 (/ (pow x 2) (pow p 4))) (/ 1 (pow p 2))))
(* (pow x 2) (+ (* (pow x 2) (- (/ (pow x 2) (pow p 6)) (/ 1 (pow p 4)))) (/ 1 (pow p 2))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow p 8))) (/ 1 (pow p 6)))) (/ 1 (pow p 4)))) (/ 1 (pow p 2))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -1 (/ (pow p 6) (pow x 6)))) (+ (* -1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -1 (/ (pow p 6) (pow x 6)))) (+ (* -1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 2 (/ 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 (/ (- (* 2 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 2 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 2 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(/ (* x (* (sqrt 1/2) (sqrt 2))) p)
(/ (+ (* -1 (/ (* (pow x 3) (sqrt 1/2)) (* (pow p 2) (sqrt 2)))) (* x (* (sqrt 1/2) (sqrt 2)))) p)
(/ (+ (* -1 (/ (* (pow x 3) (sqrt 1/2)) (* (pow p 2) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -2 (pow x 6)) (/ (pow x 6) (pow (sqrt 2) 2)))) (* (pow p 4) (* x (sqrt 2))))) (* x (* (sqrt 1/2) (sqrt 2))))) p)
(/ (+ (* -1 (/ (* (pow x 3) (sqrt 1/2)) (* (pow p 2) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -2 (pow x 6)) (/ (pow x 6) (pow (sqrt 2) 2)))) (* (pow p 4) (* x (sqrt 2))))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 2 (pow x 8)) (/ (* (pow x 2) (+ (* -2 (pow x 6)) (/ (pow x 6) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow p 6) (* x (sqrt 2))))) (* x (* (sqrt 1/2) (sqrt 2)))))) p)
(* -1 (/ (* x (* (sqrt 1/2) (sqrt 2))) p))
(* -1 (/ (+ (* -1 (/ (* (pow x 3) (sqrt 1/2)) (* (pow p 2) (sqrt 2)))) (* x (* (sqrt 1/2) (sqrt 2)))) p))
(* -1 (/ (+ (* -1 (/ (* (pow x 3) (sqrt 1/2)) (* (pow p 2) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -2 (pow x 6)) (/ (pow x 6) (pow (sqrt 2) 2)))) (* (pow p 4) (* x (sqrt 2))))) (* x (* (sqrt 1/2) (sqrt 2))))) p))
(* -1 (/ (+ (* -1 (/ (* (pow x 3) (sqrt 1/2)) (* (pow p 2) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -2 (pow x 6)) (/ (pow x 6) (pow (sqrt 2) 2)))) (* (pow p 4) (* x (sqrt 2))))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 2 (pow x 8)) (/ (* (pow x 2) (+ (* -2 (pow x 6)) (/ (pow x 6) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow p 6) (* x (sqrt 2))))) (* x (* (sqrt 1/2) (sqrt 2)))))) p))
(/ (* x (* (sqrt 1/2) (sqrt 2))) p)
(* x (+ (* -1 (/ (* (pow x 2) (sqrt 1/2)) (* (pow p 3) (sqrt 2)))) (/ (* (sqrt 1/2) (sqrt 2)) p)))
(* x (+ (* (pow x 2) (+ (* -1 (/ (sqrt 1/2) (* (pow p 3) (sqrt 2)))) (* 1/2 (/ (* p (* (pow x 2) (* (sqrt 1/2) (- (* 2 (/ 1 (pow p 6))) (/ 1 (* (pow p 6) (pow (sqrt 2) 2))))))) (sqrt 2))))) (/ (* (sqrt 1/2) (sqrt 2)) p)))
(* x (+ (* (pow x 2) (+ (* -1 (/ (sqrt 1/2) (* (pow p 3) (sqrt 2)))) (* (pow x 2) (+ (* -1/2 (/ (* p (* (pow x 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 2 (/ 1 (pow p 6))) (/ 1 (* (pow p 6) (pow (sqrt 2) 2)))) (* (pow p 2) (pow (sqrt 2) 2)))) (* 2 (/ 1 (pow p 8))))))) (sqrt 2))) (* 1/2 (/ (* p (* (sqrt 1/2) (- (* 2 (/ 1 (pow p 6))) (/ 1 (* (pow p 6) (pow (sqrt 2) 2)))))) (sqrt 2))))))) (/ (* (sqrt 1/2) (sqrt 2)) p)))
(* (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) (+ (* -2 (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) (+ (* -2 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 2 (pow p 6)) (/ (* (pow p 2) (+ (* -2 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -2 (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) (+ (* -2 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 2 (pow p 6)) (/ (* (pow p 2) (+ (* -2 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
1/2
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(* 1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))
1/2
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
1/2
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 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
(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 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 p p)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 p p) (*.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/128 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 p p))))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64))) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (fma.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)))
(* -1 (/ p x))
(/.f64 p (neg.f64 x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p (*.f64 x x))) p) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) (*.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (*.f64 p (*.f64 (*.f64 x x) (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p (*.f64 x x))) p)) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) (*.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (*.f64 p (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) (*.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p p))) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 p p) (fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64))))) (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)))) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal -64 binary64)))) (*.f64 p (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p (*.f64 x x))) p)) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
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(sqrt 1/2)
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1/2
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1
#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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-1
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(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* 1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* (pow p 2) (+ (* 1/2 (/ 1 (pow p 2))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* 1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))
(/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x x (*.f64 p p))) (*.f64 x x))
(/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x x (*.f64 p p))) (*.f64 x x))
(/ (+ (* 1/2 (pow p 2)) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x x (*.f64 p p))) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 p (*.f64 p (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(* -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)

eval135.0ms (1.2%)

Memory
26.1MiB live, 337.3MiB allocated
Compiler

Compiled 20 300 to 2 564 computations (87.4% saved)

prune155.0ms (1.4%)

Memory
-13.2MiB live, 199.1MiB allocated
Pruning

12 alts after pruning (6 fresh and 6 done)

PrunedKeptTotal
New9925997
Fresh516
Picked235
Done033
Total999121 011
Accuracy
100.0%
Counts
1 011 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶24.6%
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
22.2%
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p (*.f64 x x))) p) (neg.f64 x))
▶31.4%
(/.f64 (neg.f64 p) x)
▶5.4%
(/.f64 p x)
▶31.3%
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
▶70.9%
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓74.3%
(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)))
✓49.3%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓26.4%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
✓74.3%
(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)))))))))
✓52.8%
(sqrt.f64 #s(literal 1/2 binary64))
✓33.6%
#s(literal 1 binary64)
Compiler

Compiled 206 to 134 computations (35% saved)

simplify235.0ms (2.2%)

Memory
1.3MiB live, 81.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 p p)
✓cost-diff0
(/.f64 (*.f64 p p) (*.f64 x x))
✓cost-diff0
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
(/.f64 #s(literal -1 binary64) x)
✓cost-diff192
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
✓cost-diff0
(neg.f64 p)
✓cost-diff0
(/.f64 (neg.f64 p) x)
✓cost-diff0
(/.f64 p x)
✓cost-diff0
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
✓cost-diff0
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
✓cost-diff0
(fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
Rules
1 760×lower-fma.f32
1 754×lower-fma.f64
1 408×lower-*.f32
1 400×lower-*.f64
642×times-frac
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022108
040107
167107
2119107
3162107
4184107
5199107
6267107
7318107
8340107
9394107
10505107
11736107
121220107
132057107
143008107
153464107
163613107
173678107
183703107
193708107
203746107
213930107
224046107
234050107
244050107
254050107
264050107
274090107
284379107
294379107
04379107
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
x
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
p
(*.f64 p (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(/.f64 p x)
p
x
(/.f64 (neg.f64 p) x)
(neg.f64 p)
p
x
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
p
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)
Outputs
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(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)))
(fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(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))
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
x
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
p
(*.f64 p (/.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 p #s(literal 2 binary64)) x)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(/.f64 p x)
p
x
(/.f64 (neg.f64 p) x)
(/.f64 p (neg.f64 x))
(neg.f64 p)
p
x
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(/.f64 p (neg.f64 x))
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
p
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 p (/.f64 (*.f64 p #s(literal -1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 1 binary64)

localize89.0ms (0.8%)

Memory
-13.2MiB live, 107.0MiB allocated
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 p p)
✓accuracy100.0%
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓accuracy88.8%
(/.f64 (*.f64 p p) (*.f64 x x))
✓accuracy100.0%
(/.f64 #s(literal -1 binary64) x)
✓accuracy99.6%
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
✓accuracy100.0%
(/.f64 (neg.f64 p) x)
✓accuracy100.0%
(neg.f64 p)
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓accuracy99.9%
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
✓accuracy99.6%
(*.f64 p (/.f64 #s(literal 2 binary64) x))
✓accuracy97.2%
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
Samples
41.0ms256×0valid
Compiler

Compiled 117 to 27 computations (76.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-mult: 11.0ms (39.4% of total)
ival-div: 10.0ms (35.8% of total)
ival-add: 3.0ms (10.7% of total)
ival-sqrt: 2.0ms (7.2% of total)
exact: 1.0ms (3.6% of total)
ival-neg: 1.0ms (3.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory
17.6MiB live, 17.6MiB allocated
Counts
14 → 288
Calls
Call 1
Inputs
#<alt (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))>
#<alt (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)>
#<alt (/.f64 p x)>
#<alt (/.f64 (neg.f64 p) x)>
#<alt (neg.f64 p)>
#<alt (*.f64 (/.f64 #s(literal -1 binary64) x) p)>
#<alt (/.f64 #s(literal -1 binary64) x)>
#<alt (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))>
#<alt (/.f64 (*.f64 p p) (*.f64 x x))>
#<alt (*.f64 p p)>
#<alt (*.f64 x x)>
#<alt (*.f64 p (/.f64 #s(literal 2 binary64) x))>
Outputs
#<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 (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 p)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt 1>
#<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 (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
#<alt (* 2 (/ p x))>
Calls

72 calls:

TimeVariablePointExpression
1.0ms
x
@0
(sqrt (+ (* (/ x (+ (* p (* p (/ 2 x))) x)) 1/2) 1/2))
1.0ms
p
@inf
(sqrt (+ (* (/ x (+ (* p (* p (/ 2 x))) x)) 1/2) 1/2))
1.0ms
x
@-inf
(sqrt (+ (* (/ x (+ (* p (* p (/ 2 x))) x)) 1/2) 1/2))
0.0ms
x
@inf
(sqrt (+ (* (/ x (+ (* p (* p (/ 2 x))) x)) 1/2) 1/2))
0.0ms
p
@0
(sqrt (+ (* (/ x (+ (* p (* p (/ 2 x))) x)) 1/2) 1/2))

rewrite715.0ms (6.6%)

Memory
-3.5MiB live, 512.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
8 830×lower-fma.f32
8 824×lower-fma.f64
5 976×lower-*.f32
5 968×lower-*.f64
3 762×lower-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02290
04089
114385
289585
0845285
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
14 → 651
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(neg.f64 p)
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(/.f64 #s(literal -1 binary64) x)
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(/.f64 (*.f64 p p) (*.f64 x x))
(*.f64 p p)
(*.f64 x x)
(*.f64 p (/.f64 #s(literal 2 binary64) x))
Outputs
(exp.f64 (*.f64 (log.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))) #s(literal 1/2 binary64)))
(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)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))))) (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (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))) (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) (-.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/4 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))) #s(literal -1/4 binary64))) (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))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))) #s(literal -1/4 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 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)))) #s(literal 1/8 binary64)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))) #s(literal -1/4 binary64)))) (neg.f64 (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)))))
(pow.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)) #s(literal 1/2 binary64))
(pow.f64 (pow.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)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.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)) (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))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.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)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1 binary64))))
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(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x)))))) (fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1/8 binary64) #s(literal 1 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)) #s(literal 6 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))))))) (fma.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p)))) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))) (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x))))))))
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1/8 binary64) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x)))))) (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x)))))) (-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1/8 binary64) #s(literal -1 binary64))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 x (*.f64 x (*.f64 x x))))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 p x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (*.f64 (log.f64 p) #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p p) (*.f64 x (neg.f64 x))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 x))) (/.f64 (*.f64 p p) (*.f64 x (neg.f64 x))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) p)) (/.f64 (neg.f64 p) (/.f64 (*.f64 x x) p)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 x p)) (/.f64 (/.f64 p (neg.f64 x)) (/.f64 x p)))
(neg.f64 (/.f64 (*.f64 p p) (*.f64 x (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 p) (/.f64 (*.f64 x x) p)))
(neg.f64 (/.f64 (/.f64 p (neg.f64 x)) (/.f64 x p)))
(neg.f64 (*.f64 (/.f64 (*.f64 p p) (*.f64 x (neg.f64 x))) #s(literal 1 binary64)))
(neg.f64 (*.f64 (neg.f64 p) (/.f64 p (*.f64 x x))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x (neg.f64 x)))))
(neg.f64 (*.f64 (/.f64 p (*.f64 x x)) (neg.f64 p)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (*.f64 p p))))
(/.f64 p (/.f64 (*.f64 x x) p))
(/.f64 (/.f64 p x) (/.f64 x p))
(/.f64 (neg.f64 p) (/.f64 (*.f64 x (neg.f64 x)) p))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (*.f64 p p))))
(/.f64 (/.f64 p (neg.f64 x)) (/.f64 x (neg.f64 p)))
(/.f64 (*.f64 p p) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 p p)))
(/.f64 (*.f64 p (neg.f64 p)) (*.f64 x (neg.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (*.f64 p p)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
(/.f64 (/.f64 (*.f64 p p) x) x)
(/.f64 (/.f64 p (*.f64 x x)) (/.f64 #s(literal 1 binary64) p))
(/.f64 (/.f64 (*.f64 p (neg.f64 p)) x) (neg.f64 x))
(/.f64 (/.f64 (*.f64 p (neg.f64 p)) #s(literal -1 binary64)) (*.f64 x x))
(/.f64 (*.f64 (/.f64 (*.f64 p p) x) #s(literal 1 binary64)) x)
(/.f64 (*.f64 (*.f64 p (neg.f64 p)) #s(literal 1 binary64)) (*.f64 x (neg.f64 x)))
(/.f64 (*.f64 (/.f64 (*.f64 p (neg.f64 p)) x) #s(literal 1 binary64)) (neg.f64 x))
(/.f64 (/.f64 (/.f64 (*.f64 p (neg.f64 p)) x) #s(literal -1 binary64)) x)
(pow.f64 (/.f64 p x) #s(literal 2 binary64))
(pow.f64 (/.f64 x p) #s(literal -2 binary64))
(pow.f64 (/.f64 (*.f64 x x) (*.f64 p p)) #s(literal -1 binary64))
(*.f64 p (/.f64 p (*.f64 x x)))
(*.f64 p (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (neg.f64 x)) p)))
(*.f64 (neg.f64 p) (*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 p x)))
(*.f64 (neg.f64 p) (*.f64 p (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 p p) (*.f64 x (neg.f64 x))))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 p) (/.f64 p (*.f64 x x))))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 p (neg.f64 p)) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 p (neg.f64 x)) (/.f64 #s(literal 1 binary64) p)))
(*.f64 (/.f64 p (neg.f64 x)) (/.f64 p (neg.f64 x)))
(*.f64 (*.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (*.f64 p p) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 2 binary64)))
(*.f64 (*.f64 p p) (*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 p (neg.f64 x)) #s(literal 2 binary64)))
(*.f64 (*.f64 p (neg.f64 p)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(*.f64 (*.f64 p (neg.f64 p)) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (*.f64 p p) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 p x) (/.f64 #s(literal 1 binary64) p)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 p p))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 p (/.f64 #s(literal 1 binary64) p)))
(*.f64 (/.f64 (*.f64 p p) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p (*.f64 x x)) p)
(*.f64 (/.f64 p (*.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) p)))
(*.f64 (/.f64 (*.f64 p (neg.f64 p)) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (*.f64 p (neg.f64 p)))
(*.f64 (/.f64 (neg.f64 p) #s(literal -1 binary64)) (/.f64 p (*.f64 x x)))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 (neg.f64 p) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 p x) #s(literal 1 binary64)) (/.f64 p x))
(*.f64 (pow.f64 (/.f64 p x) #s(literal 1 binary64)) (pow.f64 (/.f64 p x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 x x) (*.f64 p p)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (*.f64 x x) (*.f64 p p)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 (*.f64 p p) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 (/.f64 p (*.f64 x x)) #s(literal -1 binary64)) (neg.f64 p))
(*.f64 (*.f64 (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) p)
(*.f64 (/.f64 (/.f64 p x) (neg.f64 x)) (neg.f64 p))
(+.f64 #s(literal 0 binary64) (*.f64 p p))
(+.f64 (*.f64 (neg.f64 p) #s(literal 0 binary64)) (*.f64 p p))
(exp.f64 (*.f64 (log.f64 p) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 p (neg.f64 p)))
(fma.f64 (neg.f64 p) #s(literal 0 binary64) (*.f64 p p))
(neg.f64 (*.f64 p (neg.f64 p)))
(/.f64 (*.f64 (neg.f64 p) (*.f64 p (neg.f64 p))) p)
(/.f64 (*.f64 (neg.f64 p) (neg.f64 (*.f64 p (*.f64 p p)))) (fma.f64 p p #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 p (neg.f64 p)) (neg.f64 p)) p)
(/.f64 (*.f64 (neg.f64 (*.f64 p (*.f64 p p))) (neg.f64 p)) (fma.f64 p p #s(literal 0 binary64)))
(pow.f64 p #s(literal 2 binary64))
(pow.f64 (neg.f64 p) #s(literal 2 binary64))
(pow.f64 (*.f64 p p) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 p)) #s(literal 2 binary64))
(*.f64 p p)
(*.f64 (neg.f64 p) (neg.f64 p))
(*.f64 #s(literal -1 binary64) (*.f64 p (neg.f64 p)))
(*.f64 (*.f64 p p) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 p p))
(*.f64 (*.f64 p (neg.f64 p)) #s(literal -1 binary64))
(*.f64 (exp.f64 (log.f64 p)) (exp.f64 (log.f64 p)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 (neg.f64 p) (*.f64 x #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 p) (*.f64 x #s(literal 1/2 binary64))))
(neg.f64 (*.f64 (neg.f64 p) (/.f64 #s(literal 2 binary64) x)))
(neg.f64 (*.f64 (/.f64 #s(literal -2 binary64) x) p))
(neg.f64 (*.f64 p (/.f64 #s(literal -2 binary64) x)))
(neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 p (neg.f64 x))))
(neg.f64 (*.f64 (/.f64 #s(literal 2 binary64) x) (neg.f64 p)))
(neg.f64 (/.f64 (*.f64 p #s(literal 2 binary64)) (neg.f64 x)))
(neg.f64 (/.f64 (*.f64 p #s(literal -2 binary64)) x))
(/.f64 p (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 2 binary64) (/.f64 x p))
(/.f64 (/.f64 p x) #s(literal 1/2 binary64))
(/.f64 (neg.f64 p) (*.f64 x #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (*.f64 p #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 p #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (*.f64 p #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -2 binary64) (/.f64 x (neg.f64 p)))
(/.f64 (*.f64 p #s(literal 2 binary64)) x)
(/.f64 (*.f64 p #s(literal -2 binary64)) (neg.f64 x))
(/.f64 (/.f64 p #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 (*.f64 p #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (*.f64 p #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(/.f64 (/.f64 (*.f64 p #s(literal -2 binary64)) #s(literal -1 binary64)) x)
(pow.f64 (/.f64 x (*.f64 p #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) (/.f64 p x))
(*.f64 (/.f64 #s(literal 2 binary64) x) p)
(*.f64 (/.f64 p x) #s(literal 2 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 p) (/.f64 #s(literal 2 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (neg.f64 p) #s(literal 1/2 binary64)))
(*.f64 (/.f64 p (neg.f64 x)) #s(literal -2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 p (*.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal -2 binary64) (/.f64 p (neg.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 p #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 p #s(literal 1/2 binary64)))
(*.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 p #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) x))
(*.f64 (/.f64 p #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x))
(*.f64 (*.f64 (*.f64 p #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64)) (neg.f64 p))

simplify404.0ms (3.7%)

Memory
-35.7MiB live, 498.3MiB allocated
Algorithm
1×egg-herbie
Rules
9 034×lower-fma.f64
9 034×lower-fma.f32
5 596×lower-*.f64
5 596×lower-*.f32
2 558×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02762637
18142584
224932558
358662526
082222386
Stop Event
1×iter limit
1×node limit
Counts
288 → 285
Calls
Call 1
Inputs
(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)))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
1
(+ 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)
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (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)))))))
(fma.f64 (*.f64 x x) (fma.f64 (+.f64 (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 #s(literal -1/16 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (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)))))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 p p)) (/.f64 #s(literal 1/16 binary64) (pow.f64 p #s(literal 6 binary64)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -1/64 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 #s(literal -1/16 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -7/4 binary64) (/.f64 (*.f64 p p) (*.f64 x x))) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -7/4 binary64) (/.f64 (*.f64 p p) (*.f64 x x))) (fma.f64 (fma.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 7/4 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -7/4 binary64) (/.f64 (*.f64 p p) (*.f64 x x))) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 p (/.f64 p (*.f64 x x)) (fma.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -7/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -7/4 binary64))) (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))))) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 7/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 p (*.f64 p (fma.f64 p (/.f64 (*.f64 p #s(literal 7/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (*.f64 p p) (fma.f64 (*.f64 p p) (fma.f64 (*.f64 p p) (/.f64 #s(literal -25/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 7/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (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))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/32 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 p p) (*.f64 p p)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (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)))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/32 binary64))) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 x (*.f64 x (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/32 binary64))))) #s(literal -1/4 binary64))) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (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))))))
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(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/.f64 (fma.f64 x x (*.f64 (*.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)

eval222.0ms (2%)

Memory
27.8MiB live, 182.9MiB allocated
Compiler

Compiled 21 711 to 2 242 computations (89.7% saved)

prune158.0ms (1.4%)

Memory
-6.6MiB live, 153.9MiB allocated
Pruning

12 alts after pruning (1 fresh and 11 done)

PrunedKeptTotal
New9360936
Fresh011
Picked055
Done066
Total93612948
Accuracy
100.0%
Counts
948 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓24.6%
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
22.2%
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p (*.f64 x x))) p) (neg.f64 x))
✓31.4%
(/.f64 (neg.f64 p) x)
✓5.4%
(/.f64 p x)
✓31.3%
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
✓70.9%
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓74.3%
(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)))
✓49.3%
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓26.4%
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
✓74.3%
(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)))))))))
✓52.8%
(sqrt.f64 #s(literal 1/2 binary64))
✓33.6%
#s(literal 1 binary64)
Compiler

Compiled 386 to 184 computations (52.3% saved)

regimes61.0ms (0.6%)

Memory
-15.5MiB live, 64.3MiB 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 (/.f64 #s(literal -1 binary64) x) p)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.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))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 p p))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (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 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p (*.f64 x x))) p) (neg.f64 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)))))))))
(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)))
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

7 calls:

15.0ms
p
15.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
7.0ms
x
6.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
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
79.4%2p
80.6%2x
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))))
79.4%2(*.f64 (*.f64 #s(literal 4 binary64) p) p)
Compiler

Compiled 80 to 56 computations (30% saved)

regimes18.0ms (0.2%)

Memory
25.8MiB live, 25.8MiB allocated
Counts
17 → 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 (/.f64 #s(literal -1 binary64) x) p)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.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))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 p p))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (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 p (*.f64 #s(literal 2 binary64) (/.f64 p x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
Calls

4 calls:

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

regimes20.0ms (0.2%)

Memory
-16.4MiB live, 23.0MiB allocated
Counts
14 → 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 (/.f64 #s(literal -1 binary64) x) p)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.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))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 p p))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #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)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #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))))
4.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
4.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
Results
AccuracySegmentsBranch
99.6%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)))))))
99.6%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))))))
99.6%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.6%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)

regimes23.0ms (0.2%)

Memory
-18.2MiB live, 21.1MiB allocated
Counts
13 → 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 (/.f64 #s(literal -1 binary64) x) p)
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (*.f64 p p) (*.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))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 p p))))
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 (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
Calls

4 calls:

4.0ms
(/.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)))))
4.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
3.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
Results
AccuracySegmentsBranch
99.5%3(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
99.5%3(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
99.5%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.5%3(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes10.0ms (0.1%)

Memory
14.6MiB live, 14.6MiB 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 (/.f64 #s(literal -1 binary64) x) p)
(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:

2.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
2.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
2.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
Results
AccuracySegmentsBranch
99.4%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)))))))
99.4%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))))))
99.4%3(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
99.4%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)

regimes9.0ms (0.1%)

Memory
13.5MiB live, 13.5MiB 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 (/.f64 #s(literal -1 binary64) x) p)
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)

regimes16.0ms (0.1%)

Memory
-18.0MiB live, 21.3MiB 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:

4.0ms
x
2.0ms
p
2.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
2.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
Results
AccuracySegmentsBranch
65.6%2p
65.6%2(*.f64 (*.f64 #s(literal 4 binary64) p) p)
59.6%2x
70.8%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
70.8%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
70.8%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
70.8%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)

regimes8.0ms (0.1%)

Memory
15.7MiB live, 15.7MiB 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:

1.0ms
p
1.0ms
x
1.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
1.0ms
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
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
33.6%1x
33.6%1p
33.6%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
33.6%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)))))))
33.6%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))))))
33.6%1(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
33.6%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)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-0.9999999999899051
-0.24508204340679324
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-0.9999999999899051
-0.24508204340679324
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
9.297617417110778e-8
0.9999999351396561
0.0ms
-0.9999999999899051
-0.24508204340679324
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
9.297617417110778e-8
0.9999999351396561
0.0ms
-0.9999999999899051
-0.24508204340679324
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
9.297617417110778e-8
0.9999999351396561
0.0ms
-0.9999999999899051
-0.24508204340679324
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
9.297617417110778e-8
0.9999999351396561
0.0ms
-0.9999999999899051
-0.24508204340679324
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
9.297617417110778e-8
0.9999999351396561
Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify17.0ms (0.2%)

Memory
-37.4MiB live, 13.5MiB allocated
Algorithm
1×egg-herbie
Rules
12×*-commutative_binary64
8×+-commutative_binary64
6×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
051270
162270
268270
373270
476270
577270
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 -1/2 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 p (*.f64 #s(literal 2 binary64) (/.f64 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 -1/2 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 944473296573929/9444732965739290427392 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -1/2 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 944473296573929/9444732965739290427392 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #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 -1/2 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 944473296573929/9444732965739290427392 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 -1/2 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 944473296573929/9444732965739290427392 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 944473296573929/9444732965739290427392 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 -1/2 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 -1/2 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 p (*.f64 #s(literal 2 binary64) (/.f64 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 p (*.f64 #s(literal 2 binary64) (/.f64 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 -1/2 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 944473296573929/9444732965739290427392 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #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)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 944473296573929/9444732965739290427392 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1/2 binary64))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -1/2 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 944473296573929/9444732965739290427392 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #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 -1/2 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 944473296573929/9444732965739290427392 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 (/.f64 (*.f64 p p) (*.f64 x x)) #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 -1/2 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 944473296573929/9444732965739290427392 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 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -1/2 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 944473296573929/9444732965739290427392 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 -1/2 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 944473296573929/9444732965739290427392 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 -1/2 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 944473296573929/9444732965739290427392 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 944473296573929/9444732965739290427392 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 944473296573929/9444732965739290427392 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.3s (11.5%)

Memory
39.0MiB live, 636.8MiB allocated
Rules
11 178×lower-fma.f64
11 178×lower-fma.f32
9 590×lower-fma.f64
9 590×lower-fma.f32
8 502×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025130
047130
1158109
2992105
08554105
04342482
113252377
246062304
080752141
032178
060174
1224174
21531174
08155170
09766799
130276597
086716211
01466
02366
17766
250166
3696766
0849259
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 567 to 267 computations (52.9% saved)

preprocess288.0ms (2.6%)

Memory
-11.3MiB live, 186.5MiB allocated
Compiler

Compiled 686 to 190 computations (72.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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