Data.Octree.Internal:octantDistance from Octree-0.5.4.2

Time bar (total: 28.3s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 10 to 5 computations (50% saved)

sample789.0ms (2.8%)

Memory
2.3MiB live, 890.8MiB allocated
Samples
602.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 287.0ms
ival-hypot: 277.0ms (96.6% of total)
ival-true: 6.0ms (2.1% of total)
ival-assert: 3.0ms (1% of total)
Bogosity

explain100.0ms (0.4%)

Memory
26.7MiB live, 103.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1350-2(1.807142125221636e-156 2.1702606633658027e-190)(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
00-0-(+.f64 (*.f64 x x) (*.f64 y y))
00-0-y
00-0-(*.f64 y y)
00-0-(*.f64 x x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))oflow-rescue1120
(*.f64 y y)overflow71
(*.f64 x x)overflow59
(+.f64 (*.f64 x x) (*.f64 y y))overflow112
sqrt.f64(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))uflow-rescue210
(*.f64 y y)underflow54
(*.f64 x x)underflow79
(+.f64 (*.f64 x x) (*.f64 y y))underflow21
Confusion
Predicted +Predicted -
+1332
-0121
Precision
1.0
Recall
0.9851851851851852
Confusion?
Predicted +Predicted MaybePredicted -
+13302
-00121
Precision?
1.0
Recall?
0.9851851851851852
Freqs
test
numberfreq
0123
1133
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
52.0ms512×0valid
Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
ival-mult: 29.0ms (72.9% of total)
ival-hypot: 8.0ms (20.1% of total)
ival-add: 2.0ms (5% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess30.0ms (0.1%)

Memory
1.6MiB live, 39.6MiB allocated
Algorithm
egg-herbie
Rules
32×sub-neg
30×distribute-lft-neg-in
30×neg-sub0
28×unsub-neg
24×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01642
13542
27742
314542
420442
521742
621942
068
0108
1118
0113
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
(hypot.f64 y x)
Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
51.5%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify7.0ms (0%)

Memory
-35.6MiB live, 8.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff-5120
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
cost-diff0
(*.f64 y y)
cost-diff0
(*.f64 x x)
cost-diff128
(+.f64 (*.f64 x x) (*.f64 y y))
Rules
lower-hypot.f32
lower-hypot.f64
lower-fma.f64
lift-*.f64
lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0623
01023
11123
01117
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
(+.f64 (*.f64 x x) (*.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
(hypot.f64 y x)
(+.f64 (*.f64 x x) (*.f64 y y))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y

localize22.0ms (0.1%)

Memory
12.2MiB live, 50.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 y y)
accuracy0
(*.f64 x x)
accuracy0.0078125
(+.f64 (*.f64 x x) (*.f64 y y))
accuracy31.04734792617676
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
Samples
15.0ms256×0valid
Compiler

Compiled 25 to 8 computations (68% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-hypot: 4.0ms (45.4% of total)
ival-mult: 3.0ms (34.1% of total)
ival-add: 1.0ms (11.4% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0%)

Memory
15.7MiB live, 15.7MiB allocated
Counts
4 → 72
Calls
Call 1
Inputs
#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())
Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ y (* 1/2 (/ (pow x 2) y))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x x) (*.f64 y y)) (patch (+.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y))) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
1.0ms
y
@0
((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms
y
@inf
((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms
x
@inf
((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms
y
@-inf
((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms
x
@0
((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))

simplify179.0ms (0.6%)

Memory
-10.6MiB live, 217.0MiB allocated
Algorithm
egg-herbie
Rules
18 004×lower-fma.f64
18 004×lower-fma.f32
5 072×lower-*.f64
5 072×lower-*.f32
2 260×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0104620
1296620
2953618
33667584
46426582
08051530
Stop Event
iter limit
node limit
Counts
72 → 68
Calls
Call 1
Inputs
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
Outputs
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) x (neg.f64 y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) y (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y)))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) x (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) y))
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.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)
y
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))) x) x (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x) y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.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)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) x (*.f64 (/.f64 (*.f64 y y) x) #s(literal 1/2 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.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)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x))

rewrite193.0ms (0.7%)

Memory
12.3MiB live, 170.7MiB allocated
Rules
5 720×lower-fma.f64
5 720×lower-fma.f32
4 038×lower-/.f64
4 038×lower-/.f32
3 184×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0621
01021
12921
219621
3178821
0862415
Stop Event
iter limit
node limit
iter limit
Counts
4 → 245
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (*.f64 y y))
(*.f64 x x)
(*.f64 y y)
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
Outputs
(*.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (*.f64 (-.f64 x y) (+.f64 y x))))))
(*.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (*.f64 x x)))
(*.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (+.f64 y x))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 1 binary64) (fma.f64 y y (*.f64 x x)))
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)))
(*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 y y (*.f64 x x)) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (fma.f64 y y (*.f64 x x)) (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x))))
(*.f64 (fma.f64 y y (*.f64 x x)) (*.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64))))
(pow.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64))
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(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 y x)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(hypot.f64 y x)
(hypot.f64 x y)
(exp.f64 (fma.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/2 binary64)))

eval191.0ms (0.7%)

Memory
3.9MiB live, 96.6MiB allocated
Compiler

Compiled 7 655 to 987 computations (87.1% saved)

prune135.0ms (0.5%)

Memory
-7.7MiB live, 109.0MiB allocated
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3067313
Fresh000
Picked101
Done000
Total3077314
Accuracy
100.0%
Counts
314 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 y x)
51.1%
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
51.5%
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
51.0%
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
4.5%
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
99.3%
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
1.8%
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
Compiler

Compiled 96 to 76 computations (20.8% saved)

simplify6.0ms (0%)

Memory
13.0MiB live, 13.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff-5120
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 y y (*.f64 x x))
cost-diff0
(*.f64 y y)
cost-diff0
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff0
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (+ (* x x) (* y y)) (*.f64 x x))
cost-diff0
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
cost-diff0
(neg.f64 x)
cost-diff0
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
cost-diff0
(hypot.f64 y x)
Rules
24×lower-+.f64
24×lower-+.f32
12×lower-fma.f32
10×lower-fma.f64
lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01787
02478
12978
23178
33378
43578
53978
64878
75478
85878
05878
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(hypot.f64 y x)
y
x
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
x
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
#s(approx (+ (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
x
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 y y)
y
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
y
(*.f64 x x)
x
Outputs
(hypot.f64 y x)
(hypot.f64 x y)
y
x
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
x
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
#s(approx (+ (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
x
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 y y)
y
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(hypot.f64 x y)
(fma.f64 y y (*.f64 x x))
(fma.f64 x x (*.f64 y y))
y
(*.f64 x x)
x

localize35.0ms (0.1%)

Memory
-28.1MiB live, 88.9MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 y y (*.f64 x x))
accuracy0
(*.f64 x x)
accuracy31.04734792617676
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy0
(*.f64 y y)
accuracy0.3299593409751988
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy31.04734792617676
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy0
(*.f64 x x)
accuracy31.04734792617676
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
accuracy51.99797853203401
#s(approx (+ (* x x) (* y y)) (*.f64 x x))
accuracy0
(neg.f64 x)
accuracy62.82336435384393
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy0
(hypot.f64 y x)
Samples
25.0ms256×0valid
Compiler

Compiled 81 to 11 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-hypot: 9.0ms (61% of total)
ival-mult: 3.0ms (20.3% of total)
ival-add: 2.0ms (13.6% of total)
ival-neg: 1.0ms (6.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series9.0ms (0%)

Memory
23.5MiB live, 23.5MiB allocated
Counts
11 → 228
Calls
Call 1
Inputs
#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (hypot.f64 y x) (patch (hypot.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 x x)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (*.f64 y y)) (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (*.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x))))
1.0ms
x
@-inf
((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x))))
1.0ms
y
@inf
((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x))))
1.0ms
y
@-inf
((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x))))
0.0ms
y
@0
((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (sqrt (+ (* y y) (* x x))))

simplify172.0ms (0.6%)

Memory
-17.3MiB live, 218.3MiB allocated
Algorithm
egg-herbie
Rules
18 004×lower-fma.f64
18 004×lower-fma.f32
5 072×lower-*.f64
5 072×lower-*.f32
2 260×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01042548
12962548
29532538
336712368
464332358
080582134
Stop Event
iter limit
node limit
Counts
228 → 208
Calls
Call 1
Inputs
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
Outputs
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
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(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) 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 (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.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)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 y y) x)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) y (*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x))

rewrite208.0ms (0.7%)

Memory
18.4MiB live, 263.6MiB allocated
Rules
3 958×lower-fma.f32
3 956×lower-fma.f64
3 618×lower-*.f32
3 614×lower-*.f64
2 154×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01777
02468
15868
233868
3336868
0858768
Stop Event
iter limit
node limit
iter limit
Counts
11 → 421
Calls
Call 1
Inputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
#s(approx (+ (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 y y)
(fma.f64 y y (*.f64 x x))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
Outputs
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (hypot.f64 x y))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))) (sqrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (hypot.f64 x y))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x y)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 x y))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 x y))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 x y))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (pow.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(*.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 x y))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)))
(*.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (pow.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (pow.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (pow.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 x y) (sqrt.f64 (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(*.f64 (hypot.f64 x y) (sqrt.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (*.f64 (-.f64 x y) (+.f64 x y)))))
(*.f64 (hypot.f64 x y) (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1 binary64)))))
(*.f64 (hypot.f64 x y) (sqrt.f64 (*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1 binary64)))))
(*.f64 (hypot.f64 x y) (pow.f64 (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 x y) (pow.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 x y) (pow.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
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(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 3 binary64))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 x y) (+.f64 x y)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) (*.f64 (-.f64 x y) (+.f64 x y)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64))) (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 x y))) (*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 x y)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 x y)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) (sqrt.f64 (*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (+.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64)))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (sqrt.f64 (*.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 x y) #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64)))) (sqrt.f64 (*.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 x y)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 x y))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))
(sqrt.f64 (fma.f64 x x (*.f64 y y)))
(hypot.f64 x y)
(hypot.f64 y x)
(exp.f64 (fma.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x (*.f64 y y))) #s(literal 1/2 binary64)))

eval95.0ms (0.3%)

Memory
-0.9MiB live, 118.3MiB allocated
Compiler

Compiled 12 517 to 1 138 computations (90.9% saved)

prune94.0ms (0.3%)

Memory
-4.9MiB live, 76.6MiB allocated
Pruning

7 alts after pruning (2 fresh and 5 done)

PrunedKeptTotal
New6531654
Fresh112
Picked055
Done000
Total6547661
Accuracy
100.0%
Counts
661 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 y x)
51.1%
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
51.5%
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
51.0%
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
4.5%
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
99.3%
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
1.8%
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
Compiler

Compiled 48 to 38 computations (20.8% saved)

simplify6.0ms (0%)

Memory
3.3MiB live, 3.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 y y (*.f64 x x))
cost-diff0
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
cost-diff0
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
cost-diff0
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
cost-diff0
(/.f64 x y)
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
cost-diff0
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
Rules
48×lower-*.f32
42×lower-*.f64
20×lower-fma.f32
16×lower-fma.f64
14×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01888
02988
13988
24988
35388
45688
55988
05984
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(/.f64 x y)
y
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
(fma.f64 y y (*.f64 x x))
y
(*.f64 x x)
x
(+.f64 y x)
(sqrt.f64 (+.f64 y x))
Outputs
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(/.f64 x y)
y
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))))
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
(sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
(/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))
(fma.f64 y y (*.f64 x x))
(fma.f64 x x (*.f64 y y))
y
(*.f64 x x)
x
(+.f64 y x)
(+.f64 x y)
(sqrt.f64 (+.f64 y x))
(sqrt.f64 (+.f64 x y))

localize107.0ms (0.4%)

Memory
-21.8MiB live, 52.7MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(sqrt.f64 (+.f64 y x))
accuracy0.0078125
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
accuracy0.4921875
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
accuracy31.109746689736067
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
accuracy0
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
accuracy0
(/.f64 x y)
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0.4620211082109554
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
Samples
80.0ms256×0valid
Compiler

Compiled 87 to 18 computations (79.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 71.0ms
ival-add: 52.0ms (73.5% of total)
ival-mult: 7.0ms (9.9% of total)
ival-hypot: 5.0ms (7.1% of total)
ival-sqrt: 4.0ms (5.7% of total)
ival-div: 3.0ms (4.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series21.0ms (0.1%)

Memory
27.7MiB live, 27.7MiB allocated
Counts
9 → 204
Calls
Call 1
Inputs
#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())
#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2)))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (* y (- (pow y 2) (* -1 (pow y 2))))))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (- (* -1 (pow y 2)) (pow y 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (- (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1 (* y (- (* -1 (pow y 2)) (pow y 2)))) (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (patch (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x x)) (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
4.0ms
y
@-inf
((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
3.0ms
x
@-inf
((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
3.0ms
x
@inf
((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
2.0ms
y
@inf
((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
2.0ms
y
@0
((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))

simplify346.0ms (1.2%)

Memory
-6.9MiB live, 144.1MiB allocated
Algorithm
egg-herbie
Rules
11 852×lower-fma.f64
11 852×lower-fma.f32
5 482×lower-*.f64
5 482×lower-*.f32
4 202×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04582943
114512807
248732721
081292532
Stop Event
iter limit
node limit
Counts
204 → 187
Calls
Call 1
Inputs
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* 1/2 (/ (pow x 2) y))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt x)
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y)))))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3)))))))))
x
(+ x (* -1 y))
(+ x (* y (- (* 2 (/ y x)) 1)))
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(/ x y)
(/ x y)
(/ x y)
(/ x y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (* x (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2)))))))))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (- (+ 1 (/ (pow x 2) (pow y 2))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))))
(* y (- (+ 1 (+ (* -1 (/ (* x (- (pow x 2) (* -1 (pow x 2)))) (pow y 3))) (/ (pow x 2) (pow y 2)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
y
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (- (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1 (/ (+ (* 1/2 (* (sqrt y) (- (* -1 (pow x 2)) (pow x 2)))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1 (* x (- (* -1 (pow x 2)) (pow x 2)))) (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow x 2)) (pow x 2)) y)) x) y)) 1)))
(* -1 (* y (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (- (* -1 (pow x 2)) (pow x 2))) y)) (* -1 (pow x 2))) (pow x 2)) y)) x) y)) 1)))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* 1/2 (/ (pow x 2) y)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* 7/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -9/16 (* x (sqrt (/ 1 (pow y 5))))) (* 7/8 (sqrt (/ 1 (pow y 3)))))))))
y
(+ y (* -1 x))
(+ y (* x (- (* 2 (/ x y)) 1)))
(+ y (* x (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1)))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (* y (- (pow y 2) (* -1 (pow y 2))))))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2)))))))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))
(* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (- (* -1 (pow y 2)) (pow y 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (- (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1 (* y (- (* -1 (pow y 2)) (pow y 2)))) (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
Outputs
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
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(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
(* 1/2 (/ (pow x 2) y))
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 y y)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 y y)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 y y)) y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 7/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -9/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 7/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 2 (/ y x)) 1)))
(fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64))))) y y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64))))) y y)
(sqrt y)
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(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (* x (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2)))))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) y) #s(literal 1/4 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) x)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
y
(* y (+ 1 (* -1 (/ x y))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
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(*.f64 (fma.f64 (/.f64 #s(literal -1 binary64) y) (fma.f64 (/.f64 (*.f64 x x) y) #s(literal -2 binary64) x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))))) y)
(pow y 2)
(*.f64 y y)
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(*.f64 (*.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y) y)
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(*.f64 (*.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y) y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(*.f64 (*.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y) y)
(sqrt y)
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(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(*.f64 (fma.f64 y (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(*.f64 (fma.f64 (*.f64 y y) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64)))) x x))
(* 1/2 (/ (pow x 2) y))
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 y (/.f64 (/.f64 y x) x)) #s(literal 1/2 binary64)))) x x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (- (* -1 (pow y 2)) (pow y 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (neg.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (- (* -1 (pow y 2)) (pow y 2)))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1 (* y (- (* -1 (pow y 2)) (pow y 2)))) (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (neg.f64 x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 (*.f64 y y) x) #s(literal -1 binary64)) #s(literal -1/4 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 y y)) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(*.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 (*.f64 y y) x) #s(literal -2 binary64) y) #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
(*.f64 (+.f64 (/.f64 (-.f64 (/.f64 (*.f64 y (+.f64 (fma.f64 (/.f64 (*.f64 y y) x) #s(literal -2 binary64) y) y)) x) y) x) #s(literal 1 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))

rewrite599.0ms (2.1%)

Memory
-16.6MiB live, 267.8MiB allocated
Rules
7 168×lower-fma.f32
7 164×lower-fma.f64
5 646×lower-*.f32
5 640×lower-*.f64
4 016×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01877
02976
19568
267968
3799368
0916657
Stop Event
iter limit
node limit
iter limit
Counts
9 → 620
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 x y)
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
(fma.f64 y y (*.f64 x x))
(sqrt.f64 (+.f64 y x))
Outputs
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y)) (-.f64 (*.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 y (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) (-.f64 (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y) (*.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y)) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))
(*.f64 (fma.f64 y y (*.f64 #s(literal -1/4 binary64) (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x)))))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y)))
(*.f64 (pow.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y)) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))))
(*.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))
(*.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y)))))
(*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))
(*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))
(*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y)) (/.f64 (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y))))
(*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y)) (*.f64 (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y) (pow.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y)) #s(literal -1 binary64))))
(*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 y (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x))) y)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y) (/.f64 (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y))))
(*.f64 (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y))) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 y y)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y))) (fma.f64 (*.f64 y y) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 y y)) (pow.f64 (*.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64))))
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(fma.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)) y) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y)))
(fma.f64 x (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y)))
(fma.f64 x x (*.f64 y y))
(fma.f64 (*.f64 y y) (/.f64 (*.f64 y y) (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(fma.f64 y (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(fma.f64 y (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y)))
(fma.f64 y y (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) y))))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x x (*.f64 y y))))
(+.f64 (neg.f64 (*.f64 (neg.f64 y) y)) (neg.f64 (*.f64 (neg.f64 x) x)))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 (*.f64 (neg.f64 y) y)))
(+.f64 (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y)) (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y)))
(+.f64 (/.f64 (*.f64 y (fma.f64 x x (*.f64 y y))) (+.f64 x y)) (/.f64 (*.f64 x (fma.f64 x x (*.f64 y y))) (+.f64 x y)))
(+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(+.f64 (*.f64 x x) (*.f64 y y))
(+.f64 (*.f64 y y) (*.f64 x x))
(*.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 y x))))
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) #s(literal -1 binary64))))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (+.f64 x y))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 x y) (+.f64 x y)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (+.f64 x y) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) (neg.f64 (sqrt.f64 (-.f64 y x))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))) (sqrt.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (-.f64 (neg.f64 y) x))) (sqrt.f64 (fma.f64 #s(literal -1 binary64) y x)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (-.f64 y x)))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x y) #s(literal -1/2 binary64)))
(sqrt.f64 (+.f64 x y))
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x y)) #s(literal 1/2 binary64)))

eval211.0ms (0.7%)

Memory
37.6MiB live, 149.8MiB allocated
Compiler

Compiled 21 427 to 2 909 computations (86.4% saved)

prune22.6s (79.9%)

Memory
-5.7MiB live, 195.3MiB allocated
Pruning

9 alts after pruning (2 fresh and 7 done)

PrunedKeptTotal
New8052807
Fresh000
Picked022
Done055
Total8059814
Accuracy
100.0%
Counts
814 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 y x)
51.1%
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
47.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
51.5%
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
51.0%
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
4.5%
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
99.3%
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
51.8%
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
1.8%
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
Compiler

Compiled 87 to 63 computations (27.6% saved)

simplify269.0ms (0.9%)

Memory
0.0MiB live, 73.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y)))
cost-diff0
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)))
cost-diff0
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
cost-diff1152
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))
cost-diff0
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
cost-diff384
(/.f64 (/.f64 y x) x)
cost-diff448
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x)
cost-diff704
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
Rules
7 108×lower-fma.f32
7 104×lower-fma.f64
2 388×lower-*.f32
2 376×lower-*.f64
2 220×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031211
049210
175210
2119210
3251210
4641192
51384172
63569172
08673162
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
#s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x)
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x))
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(/.f64 (/.f64 y x) x)
(/.f64 y x)
x
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)))
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y)))
(fma.f64 x x (*.f64 y y))
x
(*.f64 y y)
y
(fma.f64 x x (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
(-.f64 x y)
(sqrt.f64 (+.f64 y x))
(+.f64 y x)
Outputs
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)))
#s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))
#s(approx (+ (* (* 1/2 x) (/ x y)) y) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (/.f64 y x))
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x))
(+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(/.f64 (/.f64 y x) x)
(/.f64 y (*.f64 x x))
(/.f64 y x)
x
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))))
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)))
(sqrt.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))
(/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y)))
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x)))
(fma.f64 x x (*.f64 y y))
x
(*.f64 y y)
y
(fma.f64 x x (*.f64 (neg.f64 y) y))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
(-.f64 x y)
(sqrt.f64 (+.f64 y x))
(sqrt.f64 (+.f64 x y))
(+.f64 y x)
(+.f64 x y)

localize261.0ms (0.9%)

Memory
-30.1MiB live, 150.3MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))
accuracy0.0078125
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)))
accuracy0.4921875
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
accuracy33.08807501240855
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y)))
accuracy0.14453125
(/.f64 (/.f64 y x) x)
accuracy0.4620211082109554
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
accuracy14.87336629075456
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
accuracy15.074564329206149
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x)
Samples
110.0ms256×0valid
Compiler

Compiled 185 to 29 computations (84.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 79.0ms
ival-div: 32.0ms (40.6% of total)
ival-hypot: 23.0ms (29.2% of total)
ival-mult: 12.0ms (15.2% of total)
ival-add: 5.0ms (6.3% of total)
ival-sqrt: 3.0ms (3.8% of total)
ival-sub: 1.0ms (1.3% of total)
ival-neg: 1.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series32.0ms (0.1%)

Memory
25.8MiB live, 66.1MiB allocated
Counts
8 → 192
Calls
Call 1
Inputs
#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())
#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) (patch (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor 0 y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 x) (/ (pow y 2) x)) y) (taylor 0 y) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) (patch (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) (patch #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (- (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (/ (pow y 3) x)) (* -1 (/ (pow y 3) x))) x))) x)) 1))) (taylor -inf x) (#s(alt (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) (patch (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) (patch (*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (- (pow y 3) (+ (* -1 (pow y 3)) (* -1/4 (* x (pow y 2)))))))) (* 1/2 (* (sqrt x) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2))))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (patch (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (patch (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
8.0ms
x
@0
((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))))
5.0ms
y
@0
((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))))
3.0ms
x
@-inf
((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))))
3.0ms
y
@inf
((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))))
3.0ms
x
@inf
((* (* (+ (/ 1/2 y) (/ (/ y x) x)) x) x) (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (/ (/ y x) x) (sqrt (+ (* y y) (* x x))) (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y)) (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))))

simplify184.0ms (0.7%)

Memory
10.5MiB live, 240.4MiB allocated
Algorithm
egg-herbie
Rules
9 790×lower-fma.f64
9 790×lower-fma.f32
5 040×lower-*.f64
5 040×lower-*.f32
3 196×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06353343
120502746
276682678
080922505
Stop Event
iter limit
node limit
Counts
192 → 175
Calls
Call 1
Inputs
(* 1/2 (/ (pow x 2) y))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(* 1/2 (/ x y))
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y)
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y)
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y)
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
x
(+ x (* -1 y))
(+ x (* y (- (* 2 (/ y x)) 1)))
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
x
(+ x (* 1/2 (/ (* y (+ x (* -1 x))) x)))
(+ x (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)) (* 1/2 (/ (+ x (* -1 x)) x)))))
(+ x (* y (+ (* 1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1 (/ (+ x (* -1 x)) (pow x 2))) (* 1/2 (/ (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2))))) x)) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))) x)))))))
(sqrt x)
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y)))))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3)))))))))
1
(+ 1 (* 2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(/ y x)
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x)))
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x)))
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x)))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (- (+ 1 (+ (* -1 (/ x y)) (/ (pow x 2) (pow y 2)))) (* -1 (/ (pow x 2) (pow y 2)))))
(* y (- (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 2) (pow y 2))))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (pow x 3) (pow y 3)))))
y
(* y (+ 1 (* -1/2 (/ (+ x (* -1 x)) y))))
(* y (+ 1 (+ (* -1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 2))))))
(* y (+ 1 (+ (* -1/2 (/ (+ x (* -1 x)) y)) (+ (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 2))) (* 1/2 (/ (- (* -1 (+ (* -1 (pow x 3)) (pow x 3))) (+ (* -1/2 (* (+ x (* -1 x)) (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (* (pow x 2) (+ x (* -1 x))))) (pow y 3)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (pow x 2))))) (* 1/2 (* (sqrt (/ 1 (pow y 7))) (- (* -1 (pow x 3)) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))))))))
-1
(- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ (pow x 2) (pow y 2))))
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (+ 1 (/ (pow x 2) (pow y 2))))
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) (pow y 6))) (+ 1 (+ (* -1 (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (/ (pow x 2) (pow y 2)))))
y
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(/ y x)
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x))))
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x))))
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x))))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (pow x 2)) (pow x 2)) y))) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ (* -1 x) (* -1 (/ (- (+ (* -1 (/ (- (* -1 (pow x 3)) (pow x 3)) y)) (* -1 (pow x 2))) (pow x 2)) y))) y)) 1)))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1/2 (+ x (* -1 x))) (* -1/2 (/ (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) y))) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (+ (* -1 (pow x 3)) (pow x 3))) (+ (* -1/2 (* (+ x (* -1 x)) (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (* (pow x 2) (+ x (* -1 x))))) y)) (* 1/2 (- (* -1 (+ (* -1 (pow x 2)) (pow x 2))) (+ (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) y)) (* -1/2 (+ x (* -1 x)))) y)))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (- (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 y)) (- (* -1 (pow x 3)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (* 1/2 (* (sqrt y) (- (* -1 (pow x 2)) (pow x 2))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
-1
(- (* -1 (/ (pow x 2) (pow y 2))) (+ 1 (/ (pow x 2) (pow y 2))))
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (+ 1 (/ (pow x 2) (pow y 2))))
(- (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) (pow y 6))) (+ 1 (+ (* -1 (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) (pow y 4))) (/ (pow x 2) (pow y 2)))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* 1/2 (/ (pow x 2) y)))
(/ y x)
(/ (+ y (* 1/2 (/ (pow x 2) y))) x)
(/ (+ y (* 1/2 (/ (pow x 2) y))) x)
(/ (+ y (* 1/2 (/ (pow x 2) y))) x)
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
y
(+ y (* -1 x))
(+ y (* x (- (* 2 (/ x y)) 1)))
(+ y (* x (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1)))
y
(+ y (* -1/2 (/ (* x (+ (* -1 (pow y 3)) (pow y 3))) (pow y 3))))
(+ y (* x (+ (* -1/2 (/ (+ (* -1 (pow y 3)) (pow y 3)) (pow y 3))) (* 1/2 (/ (* x (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow y 2)))) (* 1/4 (/ (pow (+ (* -1 (pow y 3)) (pow y 3)) 2) (pow y 6))))) y)))))
(+ y (* x (+ (* -1/2 (/ (+ (* -1 (pow y 3)) (pow y 3)) (pow y 3))) (* x (+ (* 1/2 (/ (* x (- (* -1 (/ (+ y (* -1 y)) (pow y 2))) (* -1/2 (/ (* (+ (* -1 (pow y 3)) (pow y 3)) (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow y 2)))) (* 1/4 (/ (pow (+ (* -1 (pow y 3)) (pow y 3)) 2) (pow y 6))))) (pow y 4))))) y)) (* 1/2 (/ (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow y 2)))) (* 1/4 (/ (pow (+ (* -1 (pow y 3)) (pow y 3)) 2) (pow y 6)))) y)))))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* 7/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -9/16 (* x (sqrt (/ 1 (pow y 5))))) (* 7/8 (sqrt (/ 1 (pow y 3)))))))))
-1
(- (* -2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (- (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* 1/2 (/ x y))
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (- (+ 1 (+ (* -1 (/ y x)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2)))))
(* x (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 3) (pow x 3))) (/ (pow y 2) (pow x 2))))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ (pow y 3) (pow x 3)))))
x
(* x (+ 1 (* 1/2 (/ (+ y (* -1 y)) x))))
(* x (+ 1 (+ (* 1/2 (/ (+ y (* -1 y)) x)) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))) (pow x 2))))))
(* x (+ 1 (+ (* 1/2 (/ (+ y (* -1 y)) x)) (+ (* 1/2 (/ (- (+ (* -1 (pow y 3)) (pow y 3)) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* 1/2 (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))))))) (pow x 3))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))) (pow x 2)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))) (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))))))))
1
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* 1/2 (/ x y))
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y)))))
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y)))))
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y)))))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 y) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (- (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (/ (pow y 3) x)) (* -1 (/ (pow y 3) x))) x))) x)) 1)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (+ y (* -1 y)) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (+ (* -1 (pow y 3)) (pow y 3)) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* 1/2 (/ (* (+ y (* -1 y)) (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))))) x)) (* 1/2 (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (- (pow y 3) (+ (* -1 (pow y 3)) (* -1/4 (* x (pow y 2)))))))) (* 1/2 (* (sqrt x) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2))))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
1
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2)))))
Outputs
(* 1/2 (/ (pow x 2) y))
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 y y (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 y y (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 y y (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) y)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 y y) x)) y)
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 y y) x)) y)
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 (*.f64 y y) x)) y)
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 2 (/ y x)) 1)))
(fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) (/.f64 y (*.f64 x x)) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
x
(+ x (* 1/2 (/ (* y (+ x (* -1 x))) x)))
(+.f64 (/.f64 #s(literal 0 binary64) x) x)
(+ x (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)) (* 1/2 (/ (+ x (* -1 x)) x)))))
(fma.f64 (fma.f64 (/.f64 (+.f64 y (/.f64 (/.f64 #s(literal 0 binary64) x) x)) x) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) x)) y x)
(+ x (* y (+ (* 1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1 (/ (+ x (* -1 x)) (pow x 2))) (* 1/2 (/ (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2))))) x)) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))) x)))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) x) (/.f64 (/.f64 #s(literal 0 binary64) x) x)) x) #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 0 binary64) x) x)) x)) y (/.f64 #s(literal 0 binary64) x)) y x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* 7/8 (* (sqrt (/ 1 (pow x 3))) y)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 7/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -9/16 (* (sqrt (/ 1 (pow x 5))) y)) (* 7/8 (sqrt (/ 1 (pow x 3)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -9/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 7/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (sqrt.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
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(fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal -2 binary64) #s(literal -1 binary64))
(- (* (pow x 2) (- (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (*.f64 x (/.f64 x (pow.f64 y #s(literal 4 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (fma.f64 (*.f64 x (/.f64 x (pow.f64 y #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) (pow.f64 y #s(literal 4 binary64)))) (*.f64 x x) (/.f64 #s(literal -2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(* 1/2 (/ (pow x 2) y))
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x)
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x)
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x)
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64)))) x x)
x
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* x (- (+ 1 (+ (* -1 (/ y x)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2)))))
(*.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1 binary64) y (/.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) x)) x) #s(literal 1 binary64)) x)
(* x (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 3) (pow x 3))) (/ (pow y 2) (pow x 2))))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ (pow y 3) (pow x 3)))))
(*.f64 (-.f64 (+.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal -1 binary64) (/.f64 (fma.f64 y (/.f64 y x) (neg.f64 y)) x)) (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64))) (pow.f64 (/.f64 y x) #s(literal 3 binary64))) x)
x
(* x (+ 1 (* 1/2 (/ (+ y (* -1 y)) x))))
(+.f64 (/.f64 #s(literal 0 binary64) x) x)
(* x (+ 1 (+ (* 1/2 (/ (+ y (* -1 y)) x)) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))) (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 y (/.f64 y (*.f64 x x)) (/.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* 1/2 (/ (+ y (* -1 y)) x)) (+ (* 1/2 (/ (- (+ (* -1 (pow y 3)) (pow y 3)) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* 1/2 (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))))))) (pow x 3))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow (+ y (* -1 y)) 2))) (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 y (/.f64 y (*.f64 x x)) (/.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))) x x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 y y) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- (pow y 2) (* -1 (pow y 2))))) (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- (* -1 (pow y 3)) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))))))))
(*.f64 (fma.f64 (fma.f64 (-.f64 (neg.f64 (pow.f64 y #s(literal 3 binary64))) (*.f64 (*.f64 y y) (fma.f64 #s(literal 1/4 binary64) x y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) #s(literal 1/2 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
1
#s(literal 1 binary64)
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) (*.f64 y y) #s(literal 1 binary64))
(- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64))
(- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) (*.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64)))) (*.f64 y (/.f64 y (*.f64 x x)))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64))))
(* 1/2 (/ (pow x 2) y))
(*.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y)))))
(*.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x)))) (neg.f64 x))
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y)))))
(*.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x)))) (neg.f64 x))
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y)))))
(*.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x)))) (neg.f64 x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(*.f64 (fma.f64 (*.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64)))) x x))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (- (+ (* -1 y) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)) 1)))
(fma.f64 (/.f64 (fma.f64 #s(literal -1 binary64) y (/.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) x)) (neg.f64 x)) (neg.f64 x) x)
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (- (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (/ (pow y 3) x)) (* -1 (/ (pow y 3) x))) x))) x)) 1)))
(fma.f64 (/.f64 (-.f64 (/.f64 (+.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (*.f64 (*.f64 y y) #s(literal 2 binary64))) (/.f64 (pow.f64 y #s(literal 3 binary64)) x)) (neg.f64 x)) y) (neg.f64 x)) (neg.f64 x) x)
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (+ y (* -1 y)) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) x)
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 (*.f64 (neg.f64 y) y) x) #s(literal -1/2 binary64) #s(literal 0 binary64)) x)) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (+ (* -1 (pow y 3)) (pow y 3)) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* 1/2 (/ (* (+ y (* -1 y)) (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))))) x)) (* 1/2 (- (* -1 (pow y 2)) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) x)) (neg.f64 x)) x)) (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (neg.f64 x))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (- (pow y 3) (+ (* -1 (pow y 3)) (* -1/4 (* x (pow y 2)))))))) (* 1/2 (* (sqrt x) (* (pow (sqrt -1) 2) (- (pow y 2) (* -1 (pow y 2))))))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (-.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)))) (sqrt.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 (*.f64 (*.f64 y y) (fma.f64 #s(literal 1/4 binary64) x y)))) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 x))
1
#s(literal 1 binary64)
(- (+ 1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) (*.f64 y y) #s(literal 1 binary64))
(- (+ 1 (+ (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4)) (/ (pow y 2) (pow x 2)))) (* -1 (/ (pow y 2) (pow x 2))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 y y) #s(literal 1 binary64))
(- (+ 1 (+ (/ (* (pow y 4) (- (pow y 2) (* -1 (pow y 2)))) (pow x 6)) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (* (pow y 2) (- (pow y 2) (* -1 (pow y 2)))) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) (*.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64)))) (*.f64 y (/.f64 y (*.f64 x x)))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (*.f64 (*.f64 y y) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64))))

rewrite214.0ms (0.8%)

Memory
-2.6MiB live, 322.9MiB allocated
Rules
5 612×lower-/.f32
5 604×lower-/.f64
4 854×lower-fma.f32
4 850×lower-fma.f64
3 604×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031136
049134
1187134
21758116
08445103
Stop Event
iter limit
node limit
iter limit
Counts
8 → 370
Calls
Call 1
Inputs
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x)
(/.f64 (/.f64 y x) x)
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
(*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y)))
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y)))
Outputs
(*.f64 (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) x) (*.f64 (/.f64 x y) x))
(*.f64 (/.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) y) (/.f64 (*.f64 x x) x))
(*.f64 (*.f64 x x) (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)))
(*.f64 (*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(*.f64 x (*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) x))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) (*.f64 x x))) (neg.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) (*.f64 x x))) (neg.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (/.f64 y x) y (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))) (neg.f64 (*.f64 x y)))
(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)))
(/.f64 (*.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) (*.f64 x x)) (fma.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 y x) x) (-.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (+.f64 x y) (-.f64 y x)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (fma.f64 x x (*.f64 y y))) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))
(/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x (*.f64 y y))) (fma.f64 (neg.f64 y) y (*.f64 x x))))
(neg.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (*.f64 (+.f64 x y) (-.f64 y x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))) (/.f64 (fma.f64 x x (*.f64 y y)) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (+.f64 x y) (-.f64 y x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (+.f64 x y) (-.f64 y x))) (fma.f64 (neg.f64 y) y (*.f64 x x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x))))
(-.f64 (/.f64 (*.f64 x x) (fma.f64 (neg.f64 y) y (*.f64 x x))) (/.f64 (*.f64 (neg.f64 y) y) (fma.f64 (neg.f64 y) y (*.f64 x x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 x x (*.f64 y y)))) #s(literal -1 binary64)))

eval128.0ms (0.5%)

Memory
-2.7MiB live, 155.8MiB allocated
Compiler

Compiled 15 429 to 2 438 computations (84.2% saved)

prune160.0ms (0.6%)

Memory
-22.1MiB live, 172.8MiB allocated
Pruning

9 alts after pruning (3 fresh and 6 done)

PrunedKeptTotal
New5423545
Fresh000
Picked022
Done347
Total5459554
Accuracy
100.0%
Counts
554 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 y x)
51.1%
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
47.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
51.5%
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
98.8%
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y))
4.9%
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)
99.3%
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
51.8%
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
75.9%
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 #s(approx (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y)) x)))
Compiler

Compiled 228 to 128 computations (43.9% saved)

regimes32.0ms (0.1%)

Memory
1.2MiB live, 81.9MiB allocated
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 #s(approx (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y)) x)))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
(hypot.f64 y x)
Outputs
(hypot.f64 y x)
Calls

6 calls:

8.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
6.0ms
x
5.0ms
y
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
4.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
100.0%1(+.f64 (*.f64 x x) (*.f64 y y))
100.0%1(*.f64 x x)
100.0%1(*.f64 y y)
Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes27.0ms (0.1%)

Memory
33.1MiB live, 70.8MiB allocated
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) x) x)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (* 1/2 x) (/ x y)) y) (*.f64 #s(approx (* (+ (/ 1/2 y) (/ (/ y x) x)) x) (*.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) y)) x)))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 (neg.f64 y) y))) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
Outputs
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
Calls

6 calls:

5.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
4.0ms
y
4.0ms
x
4.0ms
(*.f64 y y)
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
Results
AccuracySegmentsBranch
99.3%1x
99.3%1y
99.3%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
99.3%1(+.f64 (*.f64 x x) (*.f64 y y))
99.3%1(*.f64 x x)
99.3%1(*.f64 y y)
Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes39.0ms (0.1%)

Memory
-25.8MiB live, 64.7MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
Outputs
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y))
Calls

6 calls:

25.0ms
x
3.0ms
y
2.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
2.0ms
(*.f64 y y)
2.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
Results
AccuracySegmentsBranch
98.8%1x
98.8%1y
98.8%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
98.8%1(+.f64 (*.f64 x x) (*.f64 y y))
98.8%1(*.f64 x x)
98.8%1(*.f64 y y)
Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes14.0ms (0%)

Memory
-17.7MiB live, 21.9MiB allocated
Accuracy

Total -2.0b remaining (-3.2%)

Threshold costs -2b (-3.2%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
Outputs
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)
Calls

6 calls:

5.0ms
y
2.0ms
x
1.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
1.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
1.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
4.9%1x
4.9%1y
4.9%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))
4.9%1(+.f64 (*.f64 x x) (*.f64 y y))
4.9%1(*.f64 x x)
4.9%1(*.f64 y y)
Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify30.0ms (0.1%)

Memory
15.4MiB live, 53.9MiB allocated
Algorithm
egg-herbie
Rules
*-commutative-binary64-*.f64
+-commutative-binary64-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02780
12980
Stop Event
saturated
Calls
Call 1
Inputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y))
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)
Outputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) (+.f64 (/.f64 #s(literal 0 binary64) y) y))
#s(approx (* (sqrt (* (/ (+ (* x x) (* y y)) (+ (* x x) (* (neg y) y))) (- x y))) (sqrt (+ y x))) x)

soundness684.0ms (2.4%)

Memory
-8.6MiB live, 630.8MiB allocated
Rules
18 004×lower-fma.f64
18 004×lower-fma.f32
9 790×lower-fma.f64
9 790×lower-fma.f32
7 168×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06353343
120502746
276682678
080922505
01877
02976
19568
267968
3799368
0916657
0104620
1296620
2953618
33667584
46426582
08051530
0621
01021
12921
219621
3178821
0862415
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 141 to 83 computations (41.1% saved)

preprocess45.0ms (0.2%)

Memory
10.3MiB live, 128.4MiB allocated
Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 112 to 82 computations (26.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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