Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3

Time bar (total: 7.5s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory
3.2MiB live, 3.2MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
75%74.9%25%0.1%0%0%0%3
87.5%87.4%12.5%0.1%0%0%0%4
93.8%93.7%6.2%0.1%0%0%0%5
96.9%96.8%3.1%0.1%0%0%0%6
98.4%98.3%1.6%0.1%0%0%0%7
99.2%99.1%0.8%0.1%0%0%0%8
99.6%99.5%0.4%0.1%0%0%0%9
99.8%99.7%0.2%0.1%0%0%0%10
99.9%99.8%0.1%0.1%0%0%0%11
100%99.9%0%0.1%0%0%0%12
Compiler

Compiled 21 to 11 computations (47.6% saved)

sample987.0ms (13.1%)

Memory
17.5MiB live, 1 146.2MiB allocated
Samples
682.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 389.0ms
ival-mult: 198.0ms (50.9% of total)
ival-add: 90.0ms (23.1% of total)
ival-div: 50.0ms (12.8% of total)
ival-sub: 37.0ms (9.5% of total)
ival-true: 7.0ms (1.8% of total)
exact: 6.0ms (1.5% of total)
ival-assert: 3.0ms (0.8% of total)
Bogosity

explain154.0ms (2%)

Memory
-35.9MiB live, 301.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1390-1(8.814645392452577e-161 -3.7036896187164463e-160)(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
170-0-(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
00-0-(*.f64 (*.f64 y #s(literal 4 binary64)) y)
00-0-(*.f64 y #s(literal 4 binary64))
00-0-#s(literal 4 binary64)
00-0-(*.f64 x x)
00-0-(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
00-0-y
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
/.f64(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))o/o1170
↳(*.f64 (*.f64 y #s(literal 4 binary64)) y)overflow73
↳(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))overflow117
↳(*.f64 y #s(literal 4 binary64))overflow1
↳(*.f64 x x)overflow61
↳(*.f64 (*.f64 y #s(literal 4 binary64)) y)overflow73
↳(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))overflow117
↳(*.f64 y #s(literal 4 binary64))overflow1
↳(*.f64 x x)overflow61
/.f64(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))u/u210
↳(*.f64 (*.f64 y #s(literal 4 binary64)) y)underflow61
↳(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))underflow21
↳(*.f64 x x)underflow69
↳(*.f64 (*.f64 y #s(literal 4 binary64)) y)underflow61
↳(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))underflow21
↳(*.f64 x x)underflow69
-.f64(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))nan-rescue170
↳(*.f64 x x)overflow61
↳(*.f64 (*.f64 y #s(literal 4 binary64)) y)overflow73
↳(*.f64 y #s(literal 4 binary64))overflow1
Confusion
Predicted +Predicted -
+1381
-0117
Precision
1.0
Recall
0.9928057553956835
Confusion?
Predicted +Predicted MaybePredicted -
+13801
-00117
Precision?
1.0
Recall?
0.9928057553956835
Freqs
test
numberfreq
0118
1121
217
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
38.0ms512×0valid
Compiler

Compiled 125 to 31 computations (75.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-mult: 10.0ms (53.5% of total)
ival-div: 3.0ms (16.1% of total)
ival-sub: 2.0ms (10.7% of total)
ival-add: 2.0ms (10.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess200.0ms (2.7%)

Memory
19.8MiB live, 135.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02597
18997
224095
362095
4174395
5272195
6296295
7298195
8299695
9300195
10300195
11330195
12343795
13343795
14358195
15441795
16441795
0919
01519
12719
25619
311219
421519
534419
651119
772419
8119119
9221119
10226019
11229819
12232619
13232619
0232617
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
Outputs
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
(/.f64 (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (fma.f64 y (*.f64 y #s(literal 4 binary64)) (*.f64 x x)))
Symmetry

(abs y)

(abs x)

Compiler

Compiled 19 to 9 computations (52.6% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶45.9%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
Compiler

Compiled 19 to 9 computations (52.6% saved)

simplify56.0ms (0.7%)

Memory
4.9MiB live, 41.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
cost-diff128
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
cost-diff128
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0951
01551
12751
25651
311251
421551
534451
651151
772451
8119151
9221151
10226051
11229851
12232651
13232651
0232647
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(*.f64 x x)
x
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
Outputs
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
(/.f64 (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (fma.f64 y (*.f64 y #s(literal 4 binary64)) (*.f64 x x)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(*.f64 x x)
x
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
(*.f64 y (*.f64 y #s(literal 4 binary64)))
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(fma.f64 y (*.f64 y #s(literal 4 binary64)) (*.f64 x x))

localize37.0ms (0.5%)

Memory
20.8MiB live, 57.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0.00390625
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
accuracy3.953102294132264
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
accuracy34.04440820466611
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
Samples
31.0ms256×0valid
Compiler

Compiled 53 to 11 computations (79.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-mult: 19.0ms (82% of total)
ival-div: 2.0ms (8.6% of total)
ival-sub: 1.0ms (4.3% of total)
ival-add: 1.0ms (4.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series24.0ms (0.3%)

Memory
-0.2MiB live, 36.1MiB allocated
Counts
4 → 84
Calls
Call 1
Inputs
#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())
#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -4 (pow y 2)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow y 2)) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -4 (pow y 2)) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow y 2)) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
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#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
16.0ms
y
@inf
((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x))
1.0ms
x
@inf
((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x))
1.0ms
x
@-inf
((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x))
1.0ms
x
@0
((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x))
1.0ms
y
@0
((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x))

simplify205.0ms (2.7%)

Memory
-0.4MiB live, 355.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115954
1319954
2956808
34078800
08264730
Stop Event
1×iter limit
1×node limit
Counts
84 → 84
Calls
Call 1
Inputs
(pow x 2)
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(pow x 2)
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* -4 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* 4 (pow y 2))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -4 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* 4 (pow y 2))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -4 (pow y 2))
(- (pow x 2) (* 4 (pow y 2)))
(- (pow x 2) (* 4 (pow y 2)))
(- (pow x 2) (* 4 (pow y 2)))
(* 4 (pow y 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(pow x 2)
(*.f64 x x)
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(* -4 (pow y 2))
(*.f64 (*.f64 y y) #s(literal -4 binary64))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* 4 (pow y 2))
(*.f64 #s(literal 4 binary64) (*.f64 y y))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
(* -4 (pow y 2))
(*.f64 (*.f64 y y) #s(literal -4 binary64))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* 4 (pow y 2))
(*.f64 #s(literal 4 binary64) (*.f64 y y))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
(* -4 (pow y 2))
(*.f64 (*.f64 y y) #s(literal -4 binary64))
(- (pow x 2) (* 4 (pow y 2)))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(- (pow x 2) (* 4 (pow y 2)))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(- (pow x 2) (* 4 (pow y 2)))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* 4 (pow y 2))
(*.f64 #s(literal 4 binary64) (*.f64 y y))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/32 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal -8 binary64) (*.f64 y y)) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 16 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal -8 binary64) (*.f64 y y)) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 16 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite194.0ms (2.6%)

Memory
2.9MiB live, 284.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0940
01540
15440
239740
3632340
0848836
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 602
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
(*.f64 x x)
Outputs
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eval127.0ms (1.7%)

Memory
-26.2MiB live, 217.0MiB allocated
Compiler

Compiled 25 742 to 1 555 computations (94% saved)

prune36.0ms (0.5%)

Memory
17.4MiB live, 56.2MiB allocated
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New7016707
Fresh000
Picked101
Done000
Total7026708
Accuracy
99.3%
Counts
708 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶45.9%
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
45.9%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
▶52.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
▶46.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
▶44.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
▶55.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Compiler

Compiled 122 to 90 computations (26.2% saved)

simplify289.0ms (3.8%)

Memory
-4.9MiB live, 77.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 y y)
cost-diff0
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
cost-diff0
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (*.f64 x x) y)
cost-diff0
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
cost-diff0
(/.f64 y x)
cost-diff0
(*.f64 #s(literal -8 binary64) (/.f64 y x))
cost-diff0
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
030197
047193
185189
2144189
3234189
4369189
5523189
6704189
71059189
82406189
94157189
104737189
114886189
124930189
134946189
144950189
155216189
165332189
175332189
185502189
195664189
205800189
215807189
225963189
236192189
246224189
256224189
06224189
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal -8 binary64) (/.f64 y x))
#s(literal -8 binary64)
(/.f64 y x)
y
x
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(/.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
#s(literal -4 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(*.f64 #s(literal 4 binary64) y)
#s(literal 4 binary64)
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal -8 binary64) (/.f64 y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
#s(literal -8 binary64)
(/.f64 y x)
y
x
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x))
#s(literal -4 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(*.f64 #s(literal 4 binary64) y)
#s(literal 4 binary64)

localize90.0ms (1.2%)

Memory
-2.9MiB live, 154.0MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 #s(literal 4 binary64) y)
accuracy0.00390625
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
accuracy3.957008544132264
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
accuracy34.04440820466611
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
accuracy0
(*.f64 x x)
accuracy1.470677805796728
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
accuracy8.242708092462165
(/.f64 (*.f64 x x) y)
accuracy27.33577412700474
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
accuracy0
(/.f64 y x)
accuracy0.014003759768442016
(*.f64 #s(literal -8 binary64) (/.f64 y x))
accuracy0.109375
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
accuracy34.21724571510739
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
accuracy35.350500494424814
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
accuracy28.30196474226929
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Samples
66.0ms256×0valid
Compiler

Compiled 179 to 31 computations (82.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-add: 23.0ms (45.3% of total)
ival-mult: 18.0ms (35.5% of total)
ival-div: 8.0ms (15.8% of total)
ival-sub: 1.0ms (2% of total)
exact: 1.0ms (2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series29.0ms (0.4%)

Memory
15.9MiB live, 53.2MiB allocated
Counts
15 → 324
Calls
Call 1
Inputs
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (*.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())
#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 x x) y) (patch (/.f64 (*.f64 x x) y) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (patch (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (patch (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 4 binary64) y) (patch (*.f64 #s(literal 4 binary64) y) #<representation binary64>) () ())
Outputs
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#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@0
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (+ (* (* 4 y) y) (* x x)) (* 4 y))
4.0ms
y
@-inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (+ (* (* 4 y) y) (* x x)) (* 4 y))
3.0ms
y
@0
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (+ (* (* 4 y) y) (* x x)) (* 4 y))
3.0ms
y
@inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (+ (* (* 4 y) y) (* x x)) (* 4 y))
2.0ms
x
@inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* x x) y) (/ 1/2 y)) -1) (/ (* x x) y) (* x x) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (+ (* (* 4 y) y) (* x x)) (* 4 y))

simplify212.0ms (2.8%)

Memory
-0.9MiB live, 319.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01293727
13503444
210453274
343623188
085432946
Stop Event
1×iter limit
1×node limit
Counts
324 → 324
Calls
Call 1
Inputs
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(pow x 2)
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow x 2)
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -4 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* 4 (pow y 2))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -4 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* 4 (pow y 2))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(* -8 (/ (pow y 2) (pow x 2)))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(* -4 (pow y 2))
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(* 4 (pow y 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (/.f64 x y))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.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)
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
(* -8 (/ (pow y 2) (pow x 2)))
(*.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y)
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (*.f64 x x) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
(* -4 (pow y 2))
(*.f64 #s(literal -4 binary64) (*.f64 y y))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
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1
#s(literal 1 binary64)
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(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
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1
#s(literal 1 binary64)
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(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
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(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
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(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
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(* -8 (/ y x))
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(/ y x)
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(/ y x)
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1
#s(literal 1 binary64)
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(pow x 2)
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(pow x 2)
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(pow x 2)
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1
#s(literal 1 binary64)
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(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
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(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(pow x 2)
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(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
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1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
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(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (/.f64 x y))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(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
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))

rewrite174.0ms (2.3%)

Memory
-1.2MiB live, 187.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030177
047173
1191167
21422165
08451163
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
15 → 629
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal -8 binary64) (/.f64 y x))
(/.f64 y x)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(/.f64 (*.f64 x x) y)
(*.f64 x x)
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(*.f64 y y)
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(*.f64 #s(literal 4 binary64) y)
Outputs
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eval142.0ms (1.9%)

Memory
15.6MiB live, 252.1MiB allocated
Compiler

Compiled 26 237 to 2 115 computations (91.9% saved)

prune33.0ms (0.4%)

Memory
12.0MiB live, 89.4MiB allocated
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1 03371 040
Fresh011
Picked235
Done000
Total1 035111 046
Accuracy
99.6%
Counts
1 046 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
45.9%
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
33.0%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))))
▶45.9%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
▶42.6%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
▶57.3%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
✓46.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
▶56.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))))
▶56.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))))
56.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
✓44.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓55.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Compiler

Compiled 375 to 212 computations (43.5% saved)

simplify211.0ms (2.8%)

Memory
-44.5MiB live, 109.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))))
cost-diff1408
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))))
cost-diff6464
(pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))
cost-diff8064
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))
cost-diff0
(-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))))
cost-diff6464
(pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))
cost-diff8768
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64)))
cost-diff0
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
cost-diff128
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
cost-diff0
(*.f64 #s(literal -8 binary64) y)
cost-diff0
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff320
(*.f64 y #s(literal 1 binary64))
cost-diff0
(/.f64 (*.f64 x #s(literal 1/2 binary64)) y)
cost-diff0
(/.f64 x y)
cost-diff0
(fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044422
074408
1137408
2304408
3624408
41157350
52342342
64900342
08266336
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))
(/.f64 x y)
x
y
(/.f64 (*.f64 x #s(literal 1/2 binary64)) y)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x))
(*.f64 #s(literal -8 binary64) y)
#s(literal -8 binary64)
y
(*.f64 x x)
x
(*.f64 y #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(*.f64 x x)
x
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))
(*.f64 y y)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64)))
(-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))
#s(literal 1/2 binary64)
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
(/.f64 x y)
x
y
#s(literal -2 binary64)
#s(literal 2 binary64)
#s(literal 1 binary64)
(-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))))
#s(literal 1 binary64)
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))
#s(literal -1 binary64)
(/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))
#s(literal 1/2 binary64)
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
(/.f64 x y)
x
y
#s(literal -2 binary64)
(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))
(fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(/.f64 x y)
x
y
(/.f64 (*.f64 x #s(literal 1/2 binary64)) y)
(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) (*.f64 y y) #s(literal 1 binary64)))
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) (*.f64 y y) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x))
(*.f64 (/.f64 (/.f64 #s(literal -8 binary64) x) x) y)
(*.f64 #s(literal -8 binary64) y)
#s(literal -8 binary64)
y
(*.f64 x x)
x
(*.f64 y #s(literal 1 binary64))
y
#s(literal 1 binary64)
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(*.f64 x x)
x
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
(*.f64 (*.f64 #s(literal 4 binary64) y) y)
(*.f64 y #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) y)
y
#s(literal 4 binary64)
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))
(*.f64 y y)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 1 binary64))
(-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 x y) #s(literal -4 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))
(/.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 x y) #s(literal -4 binary64)))
(/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))
#s(literal 1/2 binary64)
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
(/.f64 x y)
x
y
#s(literal -2 binary64)
#s(literal 2 binary64)
#s(literal 1 binary64)
(-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))
#s(literal -1 binary64)
(/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))
#s(literal 1/2 binary64)
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
(/.f64 x y)
x
y
#s(literal -2 binary64)
(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 x y) #s(literal -4 binary64))))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))
(/.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 x y) #s(literal -4 binary64)))
#s(literal 2 binary64)

localize173.0ms (2.3%)

Memory
9.3MiB live, 122.9MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.23798754884221007
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
accuracy0.25258520658031014
(/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))
accuracy19.980606069599833
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))
accuracy27.33577412700474
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))))
accuracy0.23798754884221007
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
accuracy0.25258520658031014
(/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))
accuracy17.110191872621467
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64)))
accuracy27.33577412700474
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))))
accuracy0
(*.f64 y #s(literal 4 binary64))
accuracy0
(*.f64 x x)
accuracy3.953102294132264
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
accuracy34.04440820466611
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
accuracy0
(*.f64 #s(literal -8 binary64) y)
accuracy2.618231939656097
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy8.282004345165946
(/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x))
accuracy34.21724571510739
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy0
(/.f64 x y)
accuracy0
(*.f64 x #s(literal 1/2 binary64))
accuracy0.09765625
(fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))
accuracy27.33577412700474
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
Samples
72.0ms256×0valid
Compiler

Compiled 358 to 41 computations (88.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-mult: 15.0ms (29.7% of total)
ival-div: 13.0ms (25.7% of total)
ival-add: 11.0ms (21.8% of total)
ival-sub: 5.0ms (9.9% of total)
ival-pow2: 3.0ms (5.9% of total)
ival-pow: 3.0ms (5.9% of total)
exact: 1.0ms (2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series132.0ms (1.8%)

Memory
-25.3MiB live, 100.2MiB allocated
Counts
24 → 504
Calls
Call 1
Inputs
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) (patch (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #<representation binary64>) () ())
#s(alt (*.f64 y #s(literal 1 binary64)) (patch (*.f64 y #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -8 binary64) y) (patch (*.f64 #s(literal -8 binary64) y) #<representation binary64>) () ())
#s(alt (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (patch (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) y) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) y) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))) (patch (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64)))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))) (patch (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 1/2 binary64)) (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (patch (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) (patch (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 x y) #s(literal -2 binary64)) (patch (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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Calls

6 calls:

TimeVariablePointExpression
37.0ms
y
@0
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ x y) (/ (* x 1/2) y)) -1) (/ x y) (/ (* x 1/2) y) (* y 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) (* x x)) (* y 1)) 1) (* -8 y) (- (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (* x x) (* (* y 4) y) (/ (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (- (/ 1/2 (pow (/ x y) -2)) -1)) (pow (/ 1/2 (pow (/ x y) -2)) 2) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x 1/2) (/ (* -8 y) (* x x)) (* y 4) (/ 1/2 (pow (/ x y) -2)) (pow (/ x y) -2))
30.0ms
x
@0
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ x y) (/ (* x 1/2) y)) -1) (/ x y) (/ (* x 1/2) y) (* y 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) (* x x)) (* y 1)) 1) (* -8 y) (- (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (* x x) (* (* y 4) y) (/ (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (- (/ 1/2 (pow (/ x y) -2)) -1)) (pow (/ 1/2 (pow (/ x y) -2)) 2) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x 1/2) (/ (* -8 y) (* x x)) (* y 4) (/ 1/2 (pow (/ x y) -2)) (pow (/ x y) -2))
6.0ms
x
@inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ x y) (/ (* x 1/2) y)) -1) (/ x y) (/ (* x 1/2) y) (* y 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) (* x x)) (* y 1)) 1) (* -8 y) (- (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (* x x) (* (* y 4) y) (/ (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (- (/ 1/2 (pow (/ x y) -2)) -1)) (pow (/ 1/2 (pow (/ x y) -2)) 2) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x 1/2) (/ (* -8 y) (* x x)) (* y 4) (/ 1/2 (pow (/ x y) -2)) (pow (/ x y) -2))
6.0ms
y
@inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ x y) (/ (* x 1/2) y)) -1) (/ x y) (/ (* x 1/2) y) (* y 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) (* x x)) (* y 1)) 1) (* -8 y) (- (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (* x x) (* (* y 4) y) (/ (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (- (/ 1/2 (pow (/ x y) -2)) -1)) (pow (/ 1/2 (pow (/ x y) -2)) 2) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x 1/2) (/ (* -8 y) (* x x)) (* y 4) (/ 1/2 (pow (/ x y) -2)) (pow (/ x y) -2))
5.0ms
y
@-inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ x y) (/ (* x 1/2) y)) -1) (/ x y) (/ (* x 1/2) y) (* y 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ (* -8 y) (* x x)) (* y 1)) 1) (* -8 y) (- (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (* x x) (* (* y 4) y) (/ (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (- (/ 1/2 (pow (/ x y) -2)) -1)) (pow (/ 1/2 (pow (/ x y) -2)) 2) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (pow (/ 1/2 (pow (/ x y) -2)) 2) 1) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x 1/2) (/ (* -8 y) (* x x)) (* y 4) (/ 1/2 (pow (/ x y) -2)) (pow (/ x y) -2))

simplify312.0ms (4.1%)

Memory
11.8MiB live, 243.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01985847
15425510
215855180
357874966
081524662
Stop Event
1×iter limit
1×node limit
Counts
504 → 492
Calls
Call 1
Inputs
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
y
y
y
y
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 y)
(* -8 y)
(* -8 y)
(* -8 y)
(pow x 2)
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 4 (pow y 2))
(* 4 (pow y 2))
(* 4 (pow y 2))
(* 4 (pow y 2))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(* 1/4 (/ (pow x 4) (pow y 4)))
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(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/4 (/ (pow x 4) (pow y 4)))
(/ (+ (* -1 (pow y 4)) (* 1/4 (pow x 4))) (pow y 4))
(/ (+ (* -1 (pow y 4)) (* 1/4 (pow x 4))) (pow y 4))
(/ (+ (* -1 (pow y 4)) (* 1/4 (pow x 4))) (pow y 4))
(* 2 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (+ (* 4 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow y 2) (+ (* (pow y 2) (+ (* 8 (/ (pow y 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow y 2) (+ (* (pow y 2) (+ (* (pow y 2) (+ (* 16 (/ (pow y 2) (pow x 8))) (* 8 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 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))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
y
y
y
y
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
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(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
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(* -8 y)
(* -8 y)
(* -8 y)
(* -8 y)
(* -4 (pow y 2))
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(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* 4 (pow y 2))
(* 4 (pow y 2))
(* 4 (pow y 2))
(* 4 (pow y 2))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
-1
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(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
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(- (* 1/4 (/ (pow x 4) (pow y 4))) 1)
(- (* 1/4 (/ (pow x 4) (pow y 4))) 1)
-1
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(- (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/4 (/ (pow x 4) (pow y 4)))) 1)
(- (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* -1/8 (/ (pow x 6) (pow y 6))))) 1)
-1
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(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
-1
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(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
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(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
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-1
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(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
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(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
y
y
y
y
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
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(* -8 y)
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(* -8 y)
(* -4 (pow y 2))
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-1
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(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* 4 (pow y 2))
(* 4 (pow y 2))
(* 4 (pow y 2))
(* 4 (pow y 2))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
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(- (* 1/4 (/ (pow x 4) (pow y 4))) 1)
(- (* 1/4 (/ (pow x 4) (pow y 4))) 1)
-1
(- (* -1/2 (/ (pow x 2) (pow y 2))) 1)
(- (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/4 (/ (pow x 4) (pow y 4)))) 1)
(- (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* -1/8 (/ (pow x 6) (pow y 6))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
-1
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(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 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))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(* -8 (/ (pow y 2) (pow x 2)))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(* -4 (pow y 2))
(- (pow x 2) (* 4 (pow y 2)))
(- (pow x 2) (* 4 (pow y 2)))
(- (pow x 2) (* 4 (pow y 2)))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/4 (/ (pow x 4) (pow y 4))) 1)
(- (* 1/4 (/ (pow x 4) (pow y 4))) 1)
(- (* 1/4 (/ (pow x 4) (pow y 4))) 1)
-1
(- (* -1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (- (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 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))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(* 2 (/ (pow y 2) (pow x 2)))
(/ (+ (* 2 (pow y 2)) (* 4 (/ (pow y 4) (pow x 2)))) (pow x 2))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (* 8 (/ (pow y 6) (pow x 4))))) (pow x 2))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (+ (* 8 (/ (pow y 6) (pow x 4))) (* 16 (/ (pow y 8) (pow x 6)))))) (pow x 2))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 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))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* 1/4 (/ (pow x 4) (pow y 4)))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/4 (/ (pow x 4) (pow y 4)))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(* 2 (/ (pow y 2) (pow x 2)))
(/ (+ (* 2 (pow y 2)) (* 4 (/ (pow y 4) (pow x 2)))) (pow x 2))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (* 8 (/ (pow y 6) (pow x 4))))) (pow x 2))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (+ (* 8 (/ (pow y 6) (pow x 4))) (* 16 (/ (pow y 8) (pow x 6)))))) (pow x 2))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* 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))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(* 1/2 (/ x y))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(* 1/2 (/ x y))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(* 1/2 (/ x y))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(* 1/2 (/ x y))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
y
y
y
y
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(* -8 y)
(*.f64 y #s(literal -8 binary64))
(* -8 y)
(*.f64 y #s(literal -8 binary64))
(* -8 y)
(*.f64 y #s(literal -8 binary64))
(* -8 y)
(*.f64 y #s(literal -8 binary64))
(pow x 2)
(*.f64 x x)
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
(* 4 (pow y 2))
(*.f64 #s(literal 4 binary64) (*.f64 y y))
(* 4 (pow y 2))
(*.f64 #s(literal 4 binary64) (*.f64 y y))
(* 4 (pow y 2))
(*.f64 #s(literal 4 binary64) (*.f64 y y))
(* 4 (pow y 2))
(*.f64 #s(literal 4 binary64) (*.f64 y y))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* -1 (pow y 4)) (* 1/4 (pow x 4))) (pow y 4))
(fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))
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(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -128 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -128 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -128 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))))
(* 1/4 (/ (pow x 4) (pow y 4)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))
(* (pow x 4) (- (* 1/4 (/ 1 (pow y 4))) (/ 1 (pow x 4))))
(fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))
(* 2 (/ (pow y 2) (pow x 2)))
(*.f64 (*.f64 #s(literal 2 binary64) (/.f64 y x)) (/.f64 y x))
(/ (+ (* 2 (pow y 2)) (* 4 (/ (pow y 4) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (/.f64 #s(literal 4 binary64) x) x) (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 y y) #s(literal 2 binary64))) (*.f64 x x))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (* 8 (/ (pow y 6) (pow x 4))))) (pow x 2))
(/.f64 (fma.f64 (*.f64 #s(literal 2 binary64) y) y (fma.f64 (/.f64 (/.f64 #s(literal 4 binary64) x) x) (pow.f64 y #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))))) (*.f64 x x))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (+ (* 8 (/ (pow y 6) (pow x 4))) (* 16 (/ (pow y 8) (pow x 6)))))) (pow x 2))
(/.f64 (fma.f64 (*.f64 #s(literal 2 binary64) y) y (fma.f64 (/.f64 (/.f64 #s(literal 4 binary64) x) x) (pow.f64 y #s(literal 4 binary64)) (fma.f64 (pow.f64 y #s(literal 8 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64))))))) (*.f64 x x))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
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(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 y (/.f64 #s(literal -8 binary64) x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -128 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))))
(* 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)
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 y x) (/.f64 y x))
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 y x) (/.f64 y x))
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 y x) (/.f64 y x))
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 y x) (/.f64 y x))

rewrite499.0ms (6.6%)

Memory
-7.4MiB live, 272.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044327
072269
1299253
22282249
08336235
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
24 → 1 067
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))
(/.f64 x y)
(/.f64 (*.f64 x #s(literal 1/2 binary64)) y)
(*.f64 y #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
(fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -8 binary64) y)
(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
(*.f64 x x)
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))))
(-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))))
(*.f64 x #s(literal 1/2 binary64))
(/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x))
(*.f64 y #s(literal 4 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
Outputs
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eval392.0ms (5.2%)

Memory
62.5MiB live, 877.0MiB allocated
Compiler

Compiled 61 105 to 5 815 computations (90.5% saved)

prune90.0ms (1.2%)

Memory
-14.4MiB live, 185.2MiB allocated
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New2 46352 468
Fresh213
Picked415
Done033
Total2 469102 479
Accuracy
99.6%
Counts
2 479 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶45.9%
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
▶33.0%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))))
▶42.6%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
✓57.3%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
✓46.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
▶52.4%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
56.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal -2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 (/.f64 x y) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)))))
▶56.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
✓44.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓55.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Compiler

Compiled 274 to 161 computations (41.2% saved)

simplify150.0ms (2%)

Memory
-7.8MiB live, 212.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
cost-diff0
(*.f64 x x)
cost-diff1152
(-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
cost-diff5888
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 #s(literal -4 binary64) y)
cost-diff0
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x))
cost-diff0
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
cost-diff0
(/.f64 y (*.f64 x x))
cost-diff0
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
cost-diff0
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
cost-diff0
(*.f64 y y)
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
cost-diff0
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
cost-diff0
#s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))
cost-diff0
(/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))
cost-diff0
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056459
087423
1177420
2433419
31464413
47419413
08118412
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))
#s(literal 1 binary64)
#s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 x y))
#s(literal -1/2 binary64)
(/.f64 x y)
x
y
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))
x
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(*.f64 y y)
y
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
(/.f64 y (*.f64 x x))
y
(*.f64 x x)
x
#s(literal -8 binary64)
#s(literal 1 binary64)
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x))
(*.f64 #s(literal -4 binary64) y)
#s(literal -4 binary64)
y
(*.f64 x x)
x
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))
(*.f64 y y)
#s(literal 4 binary64)
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))))
(-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)))
(*.f64 x x)
x
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(*.f64 #s(literal 4 binary64) y)
#s(literal 4 binary64)
y
(*.f64 (*.f64 #s(literal 4 binary64) y) y)
(*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 x y) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 x y) #s(literal -1 binary64))))
#s(literal 1 binary64)
#s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))
#s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 x y) #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(fma.f64 (*.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 x y) #s(literal -1 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 x y))
(*.f64 (/.f64 x y) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 x y)
x
y
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64)))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
x
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y))
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) x)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(*.f64 y y)
y
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y (*.f64 x x))) y #s(literal 1 binary64)))
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y (*.f64 x x))) y #s(literal 1 binary64))
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
(*.f64 #s(literal -8 binary64) (/.f64 y (*.f64 x x)))
(/.f64 y (*.f64 x x))
y
(*.f64 x x)
x
#s(literal -8 binary64)
#s(literal 1 binary64)
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x))
(*.f64 #s(literal -4 binary64) y)
#s(literal -4 binary64)
y
(*.f64 x x)
x
(fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(*.f64 y y)
#s(literal 4 binary64)
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))))
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (fma.f64 (/.f64 (/.f64 x #s(literal 4 binary64)) y) (/.f64 x y) #s(literal -1 binary64)))
(*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)))
(*.f64 (/.f64 (/.f64 x #s(literal 4 binary64)) y) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) y) x))
(*.f64 x x)
x
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))
(/.f64 (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) y) (*.f64 #s(literal 4 binary64) y))
(fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))
(*.f64 #s(literal 4 binary64) y)
#s(literal 4 binary64)
y
(*.f64 (*.f64 #s(literal 4 binary64) y) y)
(*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)))
(*.f64 (/.f64 (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) y) (*.f64 #s(literal 4 binary64) y)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))

localize154.0ms (2%)

Memory
-1.6MiB live, 238.0MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy2.190667816823596
(*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)))
accuracy12.710914794132272
(-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
accuracy25.01825975632623
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))
accuracy38.40704376163917
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))))
accuracy0
(*.f64 x x)
accuracy0
(*.f64 #s(literal -4 binary64) y)
accuracy2.753876661885808
(fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x))
accuracy34.04440820466611
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
accuracy0.017910009768442016
(*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64))
accuracy2.618231939656097
(fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))
accuracy8.250850473045569
(/.f64 y (*.f64 x x))
accuracy34.21724571510739
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy1.7070530638597212
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))
accuracy8.176426086763996
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y))
accuracy27.33577412700474
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
accuracy0.078125
(/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))
accuracy0.09765625
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
accuracy27.33577412700474
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
accuracy28.126898415073022
#s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))
Samples
92.0ms256×0valid
Compiler

Compiled 401 to 53 computations (86.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 72.0ms
ival-mult: 30.0ms (41.8% of total)
ival-div: 21.0ms (29.3% of total)
ival-add: 8.0ms (11.2% of total)
ival-sub: 5.0ms (7% of total)
ival-pow: 5.0ms (7% of total)
ival-pow2: 3.0ms (4.2% of total)
exact: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series116.0ms (1.5%)

Memory
-24.1MiB live, 95.1MiB allocated
Counts
22 → 480
Calls
Call 1
Inputs
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) (patch #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) (patch (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)) (patch (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) (patch (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 y (*.f64 x x)) (patch (/.f64 y (*.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -4 binary64) y) (patch (*.f64 #s(literal -4 binary64) y) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)))) (patch (/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)))) #<representation binary64>) () ())
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#s(alt (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (patch (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) (patch (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)) (patch (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y)) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (patch (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow y 2) (pow x 2))) (taylor 0 y) (#s(alt #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) (patch #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ (* 4 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))) (taylor 0 y) (#s(alt #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) (patch #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ (* (pow y 2) (+ (* 8 (/ (pow y 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))) (taylor 0 y) (#s(alt #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) (patch #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ (* (pow y 2) (+ (* (pow y 2) (+ (* 16 (/ (pow y 2) (pow x 8))) (* 8 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))) (taylor 0 y) (#s(alt #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) (patch #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) (patch (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) (patch (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) (patch (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#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 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)) (patch (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -8 (/ y (pow x 2))) (taylor 0 y) (#s(alt (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) (patch (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 4) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2))))) (taylor -inf x) (#s(alt (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (patch (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
38.0ms
y
@0
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (+ (* (* -1/2 (/ x y)) (/ x y)) -1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* x (/ (* 1/2 x) (* y y))) -1) (* 1/2 x) (* y y) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (+ (* (* (/ y (* x x)) -8) y) 1) (* (/ y (* x x)) -8) (/ y (* x x)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (* x x) (/ (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (* (+ (* (* 4 y) y) (* x x)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)))) (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (/ (* 1/2 x) (* y y)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)) (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))))
19.0ms
x
@inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (+ (* (* -1/2 (/ x y)) (/ x y)) -1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* x (/ (* 1/2 x) (* y y))) -1) (* 1/2 x) (* y y) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (+ (* (* (/ y (* x x)) -8) y) 1) (* (/ y (* x x)) -8) (/ y (* x x)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (* x x) (/ (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (* (+ (* (* 4 y) y) (* x x)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)))) (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (/ (* 1/2 x) (* y y)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)) (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))))
11.0ms
x
@0
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (+ (* (* -1/2 (/ x y)) (/ x y)) -1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* x (/ (* 1/2 x) (* y y))) -1) (* 1/2 x) (* y y) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (+ (* (* (/ y (* x x)) -8) y) 1) (* (/ y (* x x)) -8) (/ y (* x x)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (* x x) (/ (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (* (+ (* (* 4 y) y) (* x x)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)))) (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (/ (* 1/2 x) (* y y)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)) (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))))
5.0ms
y
@inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (+ (* (* -1/2 (/ x y)) (/ x y)) -1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* x (/ (* 1/2 x) (* y y))) -1) (* 1/2 x) (* y y) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (+ (* (* (/ y (* x x)) -8) y) 1) (* (/ y (* x x)) -8) (/ y (* x x)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (* x x) (/ (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (* (+ (* (* 4 y) y) (* x x)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)))) (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (/ (* 1/2 x) (* y y)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)) (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))))
4.0ms
x
@-inf
((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2)))) (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (+ (* (* -1/2 (/ x y)) (/ x y)) -1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* x (/ (* 1/2 x) (* y y))) -1) (* 1/2 x) (* y y) (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (+ (* (* (/ y (* x x)) -8) y) 1) (* (/ y (* x x)) -8) (/ y (* x x)) (/ (+ (* (* -4 y) y) (* x x)) (+ (* (* y y) 4) (* x x))) (+ (* (* -4 y) y) (* x x)) (* -4 y) (* x x) (/ (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (* (+ (* (* 4 y) y) (* x x)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)))) (- (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))) (+ (* (* 4 y) y) (* x x))) (+ (* (* 4 y) y) (* x x)) (/ (* 1/2 x) (* y y)) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)) (* (* x x) (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y))))

simplify264.0ms (3.5%)

Memory
12.3MiB live, 211.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02636102
17325730
221755530
357125318
081514942
Stop Event
1×iter limit
1×node limit
Counts
480 → 480
Calls
Call 1
Inputs
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(* 2 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (+ (* 4 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow y 2) (+ (* (pow y 2) (+ (* 8 (/ (pow y 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow y 2) (+ (* (pow y 2) (+ (* (pow y 2) (+ (* 16 (/ (pow y 2) (pow x 8))) (* 8 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
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(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (+ (* -8 (/ (pow y 2) (pow x 2))) (* 4 (/ (- (* -4 (pow y 4)) (+ (* -16 (pow y 4)) (* 4 (pow y 4)))) (pow x 4)))))
(+ 1 (+ (* -8 (/ (pow y 2) (pow x 2))) (+ (* -4 (/ (+ (* -32 (pow y 6)) (* 8 (* (pow y 2) (- (* -4 (pow y 4)) (+ (* -16 (pow y 4)) (* 4 (pow y 4))))))) (pow x 6))) (* 4 (/ (- (* -4 (pow y 4)) (+ (* -16 (pow y 4)) (* 4 (pow y 4)))) (pow x 4))))))
(* 1/4 (/ (pow x 4) (pow y 2)))
(* (pow x 4) (+ (* -4 (/ (pow y 2) (pow x 4))) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (* -4 (/ (pow y 2) (pow x 4))) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (* -4 (/ (pow y 2) (pow x 4))) (* 1/4 (/ 1 (pow y 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ x (pow y 2)))
(* 1/2 (/ x (pow y 2)))
(* 1/2 (/ x (pow y 2)))
(* 1/2 (/ x (pow y 2)))
(* 1/4 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 2) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 2) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* 1/4 (/ (pow x 4) (pow y 2)))
(* (pow x 4) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 2 (/ (pow y 2) (pow x 2)))
(/ (+ (* 2 (pow y 2)) (* 4 (/ (pow y 4) (pow x 2)))) (pow x 2))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (* 8 (/ (pow y 6) (pow x 4))))) (pow x 2))
(/ (+ (* 2 (pow y 2)) (+ (* 4 (/ (pow y 4) (pow x 2))) (+ (* 8 (/ (pow y 6) (pow x 4))) (* 16 (/ (pow y 8) (pow x 6)))))) (pow x 2))
(* -1/2 (/ (pow x 2) (pow y 2)))
(* -1 (* (pow x 2) (+ (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))))
(* -1 (* (pow x 2) (+ (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))))
(* -1 (* (pow x 2) (+ (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (+ (* -8 (/ (pow y 2) (pow x 2))) (* 4 (/ (- (* -4 (pow y 4)) (+ (* -16 (pow y 4)) (* 4 (pow y 4)))) (pow x 4)))))
(+ 1 (+ (* -8 (/ (pow y 2) (pow x 2))) (+ (* -4 (/ (+ (* -32 (pow y 6)) (* 8 (* (pow y 2) (- (* -4 (pow y 4)) (+ (* -16 (pow y 4)) (* 4 (pow y 4))))))) (pow x 6))) (* 4 (/ (- (* -4 (pow y 4)) (+ (* -16 (pow y 4)) (* 4 (pow y 4)))) (pow x 4))))))
(* 1/4 (/ (pow x 4) (pow y 2)))
(* (pow x 4) (+ (* -4 (/ (pow y 2) (pow x 4))) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (* -4 (/ (pow y 2) (pow x 4))) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (* -4 (/ (pow y 2) (pow x 4))) (* 1/4 (/ 1 (pow y 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ x (pow y 2)))
(* 1/2 (/ x (pow y 2)))
(* 1/2 (/ x (pow y 2)))
(* 1/2 (/ x (pow y 2)))
(* 1/4 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 2) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 2) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* 1/4 (/ (pow x 4) (pow y 2)))
(* (pow x 4) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
(* (pow x 4) (+ (/ 1 (pow x 2)) (* 1/4 (/ 1 (pow y 2)))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(* 2 (/ (pow y 2) (pow x 2)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) (/.f64 y x))
(* (pow y 2) (+ (* 4 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal 2 binary64) (*.f64 x x))) (*.f64 y y))
(* (pow y 2) (+ (* (pow y 2) (+ (* 8 (/ (pow y 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) y) y (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (*.f64 y y))
(* (pow y 2) (+ (* (pow y 2) (+ (* (pow y 2) (+ (* 16 (/ (pow y 2) (pow x 8))) (* 8 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 16 binary64) y) (/.f64 y (pow.f64 x #s(literal 8 binary64))) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 y y) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (*.f64 y y))
(* -1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 y y)) x) x)
(/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 y y)) x) x #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 y y)) x) x #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* -1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 y y)) x) x #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(* 1/2 (/ (pow x 2) (pow y 2)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
(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
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y)
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y)
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y)
(* -8 (/ y (pow x 2)))
(*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x 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))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x))
(* -4 y)
(*.f64 #s(literal -4 binary64) y)
(* -4 y)
(*.f64 #s(literal -4 binary64) y)
(* -4 y)
(*.f64 #s(literal -4 binary64) y)
(* -4 y)
(*.f64 #s(literal -4 binary64) y)
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 32 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(* 1/4 (/ (pow x 4) (pow y 2)))
(*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (/.f64 #s(literal 1/4 binary64) y))
(/ (+ (* -4 (pow y 4)) (* 1/4 (pow x 4))) (pow y 2))
(/.f64 (/.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) y) y)
(/ (+ (* -4 (pow y 4)) (* 1/4 (pow x 4))) (pow y 2))
(/.f64 (/.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) y) y)
(/ (+ (* -4 (pow y 4)) (* 1/4 (pow x 4))) (pow y 2))
(/.f64 (/.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -4 binary64) (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) y) y)
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (*.f64 y y) (*.f64 x x))
(* 1/2 (/ x (pow y 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x)
(* 1/2 (/ x (pow y 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x)
(* 1/2 (/ x (pow y 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x)
(* 1/2 (/ x (pow y 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x)
(* 1/4 (/ (pow x 2) (pow y 2)))
(*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) y) (/.f64 x y))
(/ (+ (* 1/4 (pow x 2)) (pow y 2)) (pow y 2))
(fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) y) (/.f64 x y) #s(literal 1 binary64))
(/ (+ (* 1/4 (pow x 2)) (pow y 2)) (pow y 2))
(fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) y) (/.f64 x y) #s(literal 1 binary64))
(/ (+ (* 1/4 (pow x 2)) (pow y 2)) (pow y 2))
(fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) y) (/.f64 x y) #s(literal 1 binary64))
(* 1/4 (/ (pow x 4) (pow y 2)))
(*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (/.f64 #s(literal 1/4 binary64) y))
(/ (+ (* 1/4 (pow x 4)) (* (pow x 2) (pow y 2))) (pow y 2))
(/.f64 (fma.f64 (*.f64 x (*.f64 y y)) x (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y))
(/ (+ (* 1/4 (pow x 4)) (* (pow x 2) (pow y 2))) (pow y 2))
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1
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1
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1
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rewrite282.0ms (3.7%)

Memory
-0.9MiB live, 194.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056383
087381
1385331
23104329
08691322
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
22 → 703
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
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#s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 y y)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
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Outputs
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eval683.0ms (9.1%)

Memory
-82.3MiB live, 350.0MiB allocated
Compiler

Compiled 62 262 to 3 515 computations (94.4% saved)

prune45.0ms (0.6%)

Memory
11.5MiB live, 169.5MiB allocated
Pruning

10 alts after pruning (2 fresh and 8 done)

PrunedKeptTotal
New1 63521 637
Fresh101
Picked145
Done044
Total1 637101 647
Accuracy
99.6%
Counts
1 647 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓45.9%
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
33.0%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(approx (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)) (fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) y) (/.f64 x y) #s(literal 1 binary64)))))
✓42.6%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
✓57.3%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
✓46.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
✓52.4%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
✓56.5%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
55.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (/.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
✓44.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓55.8%
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Compiler

Compiled 532 to 202 computations (62% saved)

regimes34.0ms (0.5%)

Memory
5.7MiB live, 81.3MiB allocated
Counts
21 → 3
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) (/.f64 x y) #s(literal -1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (fma.f64 (*.f64 y y) #s(literal 4 binary64) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(approx (/ (+ (* (* 4 y) y) (* x x)) (* (* 4 y) y)) (fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) y) (/.f64 x y) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)) (*.f64 (*.f64 #s(literal 4 binary64) y) y))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- -1 (/ 1/2 (pow (/ x y) -2))) (- 1 (pow (/ 1/2 (pow (/ x y) -2)) 2))) (/.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal -2 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal -2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 (/.f64 x y) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal -1 binary64))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))))))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
(/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
Calls

5 calls:

8.0ms
x
7.0ms
(*.f64 x x)
6.0ms
y
6.0ms
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
5.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
Results
AccuracySegmentsBranch
82.4%4x
82.5%3y
77.4%2(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
82.4%4(*.f64 x x)
82.5%3(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Compiler

Compiled 29 to 21 computations (27.6% saved)

regimes7.0ms (0.1%)

Memory
15.8MiB live, 15.8MiB allocated
Counts
9 → 3
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
Calls

2 calls:

3.0ms
y
3.0ms
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Results
AccuracySegmentsBranch
82.5%3y
82.5%3(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes38.0ms (0.5%)

Memory
-17.2MiB live, 22.0MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))
Calls

4 calls:

29.0ms
y
3.0ms
x
3.0ms
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
3.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
76.3%2x
76.3%2(*.f64 x x)
78.5%2y
78.5%2(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Compiler

Compiled 10 to 12 computations (-20% saved)

regimes6.0ms (0.1%)

Memory
10.1MiB live, 10.1MiB allocated
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
Calls

2 calls:

3.0ms
y
2.0ms
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Results
AccuracySegmentsBranch
78.2%2y
78.2%2(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes7.0ms (0.1%)

Memory
12.7MiB live, 12.7MiB allocated
Counts
5 → 2
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* (* y y) 4) (* x x))) (fma.f64 (*.f64 (/.f64 y (*.f64 x x)) #s(literal -8 binary64)) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 #s(literal -8 binary64) y) (*.f64 x x)) (*.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64)))
Calls

3 calls:

2.0ms
y
2.0ms
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
2.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
Results
AccuracySegmentsBranch
76.6%3(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
77.4%2y
77.4%2(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Compiler

Compiled 25 to 16 computations (36% saved)

regimes35.0ms (0.5%)

Memory
-34.6MiB live, 6.8MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Calls

2 calls:

33.0ms
y
1.0ms
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Results
AccuracySegmentsBranch
77.2%2y
77.2%2(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes6.0ms (0.1%)

Memory
16.6MiB live, 16.6MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Calls

5 calls:

1.0ms
x
1.0ms
y
1.0ms
(*.f64 (*.f64 y #s(literal 4 binary64)) y)
1.0ms
(*.f64 x x)
1.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
Results
AccuracySegmentsBranch
55.8%1(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))
55.8%1x
55.8%1(*.f64 x x)
55.8%1y
55.8%1(*.f64 (*.f64 y #s(literal 4 binary64)) y)
Compiler

Compiled 29 to 21 computations (27.6% saved)

bsearch1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
3.3737329169350587e+171
5.519214387177829e+172
0.0ms
8.217521758494927e-288
8.49267758183492e-277
Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
3.3737329169350587e+171
5.519214387177829e+172
0.0ms
8.217521758494927e-288
8.49267758183492e-277
Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.281671776349187e+72
3.164545100145419e+73
Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.281671776349187e+72
3.164545100145419e+73
Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.281671776349187e+72
3.164545100145419e+73
Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch13.0ms (0.2%)

Memory
-17.0MiB live, 20.4MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
12.0ms
1.281671776349187e+72
3.164545100145419e+73
Samples
8.0ms112×0valid
Compiler

Compiled 46 to 84 computations (-82.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-div: 3.0ms (57.5% of total)
ival-sub: 1.0ms (19.2% of total)
ival-add: 1.0ms (19.2% of total)
ival-mult: 1.0ms (19.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify27.0ms (0.4%)

Memory
27.2MiB live, 64.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056452
164452
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/685765508599211085406992031398401158759299079491541508764000248557024672719959118395646962442045349201660590667234013968119772982843080987903012964780708787451812337588750783066948774723991753080189067657794974398949244241113521123786594812548932026532556574571938698730267509225767960757581162756440064 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 5000000000000000413435814285529011838218138482576117668163267154416335697155678364686365832061086948358596321261632844174465033417199886349737788590053275114539444839907328 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/685765508599211085406992031398401158759299079491541508764000248557024672719959118395646962442045349201660590667234013968119772982843080987903012964780708787451812337588750783066948774723991753080189067657794974398949244241113521123786594812548932026532556574571938698730267509225767960757581162756440064 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 5000000000000000413435814285529011838218138482576117668163267154416335697155678364686365832061086948358596321261632844174465033417199886349737788590053275114539444839907328 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1299999999999999907326411310349564944287549420202758140687500295723286528 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
Outputs
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/685765508599211085406992031398401158759299079491541508764000248557024672719959118395646962442045349201660590667234013968119772982843080987903012964780708787451812337588750783066948774723991753080189067657794974398949244241113521123786594812548932026532556574571938698730267509225767960757581162756440064 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 5000000000000000413435814285529011838218138482576117668163267154416335697155678364686365832061086948358596321261632844174465033417199886349737788590053275114539444839907328 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))))
(if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 6857655085992111/685765508599211085406992031398401158759299079491541508764000248557024672719959118395646962442045349201660590667234013968119772982843080987903012964780708787451812337588750783066948774723991753080189067657794974398949244241113521123786594812548932026532556574571938698730267509225767960757581162756440064 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 5000000000000000413435814285529011838218138482576117668163267154416335697155678364686365832061086948358596321261632844174465033417199886349737788590053275114539444839907328 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -4 binary64) y) y (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal -1 binary64)))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/685765508599211085406992031398401158759299079491541508764000248557024672719959118395646962442045349201660590667234013968119772982843080987903012964780708787451812337588750783066948774723991753080189067657794974398949244241113521123786594812548932026532556574571938698730267509225767960757581162756440064 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 5000000000000000413435814285529011838218138482576117668163267154416335697155678364686365832061086948358596321261632844174465033417199886349737788590053275114539444839907328 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64)))))
(if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 6857655085992111/685765508599211085406992031398401158759299079491541508764000248557024672719959118395646962442045349201660590667234013968119772982843080987903012964780708787451812337588750783066948774723991753080189067657794974398949244241113521123786594812548932026532556574571938698730267509225767960757581162756440064 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 5000000000000000413435814285529011838218138482576117668163267154416335697155678364686365832061086948358596321261632844174465033417199886349737788590053275114539444839907328 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (*.f64 y y) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 x x))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal -1 binary64)))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 x y) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 y y)) #s(literal -1 binary64))))
(if (<=.f64 (*.f64 (*.f64 y #s(literal 4 binary64)) y) #s(literal 1299999999999999907326411310349564944287549420202758140687500295723286528 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
(if (<=.f64 (*.f64 (*.f64 #s(literal 4 binary64) y) y) #s(literal 1299999999999999907326411310349564944287549420202758140687500295723286528 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

soundness786.0ms (10.4%)

Memory
13.1MiB live, 607.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115954
1319954
2956808
34078800
08264730
044327
072269
1299253
22282249
08336235
0940
01540
15440
239740
3632340
0848836
030177
047173
1191167
21422165
08451163
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 552 to 240 computations (56.5% saved)

preprocess74.0ms (1%)

Memory
6.5MiB live, 200.1MiB allocated
Remove

(abs x)

(abs y)

Compiler

Compiled 830 to 280 computations (66.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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