Examples.Basics.BasicTests:f2 from sbv-4.4

Time bar (total: 4.5s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample653.0ms (14.5%)

Memory
26.7MiB live, 1 019.0MiB allocated
Samples
425.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 227.0ms
ival-mult: 183.0ms (80.7% of total)
ival-sub: 35.0ms (15.4% of total)
ival-true: 6.0ms (2.6% of total)
ival-assert: 3.0ms (1.3% of total)
Bogosity

explain64.0ms (1.4%)

Memory
16.9MiB live, 91.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
200-0-(-.f64 (*.f64 x x) (*.f64 y y))
00-0-y
00-0-(*.f64 y y)
00-0-(*.f64 x x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (*.f64 x x) (*.f64 y y))nan-rescue200
(*.f64 x x)overflow67
(*.f64 y y)overflow68
Confusion
Predicted +Predicted -
+200
-0236
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+2000
-00236
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0236
120
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
25.0ms512×0valid
Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 7.0ms (72.2% of total)
ival-sub: 2.0ms (20.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess919.0ms (20.4%)

Memory
-39.4MiB live, 283.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01338
15135
214435
336635
489235
5122335
6175435
7234035
8415235
9472735
10484035
11495435
12503435
13503435
14641535
15739335
16787735
17789335
18789335
057
087
1167
2277
3537
41147
53157
65677
712387
824957
941247
1049977
1153667
1255967
1357107
1457107
1566707
1668307
1771507
1871507
1975507
2077107
2177907
2277907
2377907
0102687
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (*.f64 y y))
Outputs
(fma.f64 (neg.f64 y) y (*.f64 x x))
Symmetry

(abs y)

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
92.2%
(-.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify570.0ms (12.7%)

Memory
33.4MiB live, 184.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y y)
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) (*.f64 y y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0515
0815
11615
22715
35315
411415
531515
656715
7123815
8249515
9412415
10499715
11536615
12559615
13571015
14571015
15667015
16683015
17715015
18715015
19755015
20771015
21779015
22779015
23779015
01026815
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (*.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y
Outputs
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y

localize87.0ms (1.9%)

Memory
-2.9MiB live, 36.2MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 y y)
accuracy0
(*.f64 x x)
accuracy4.496073108302059
(-.f64 (*.f64 x x) (*.f64 y y))
Samples
82.0ms256×0valid
Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 3.0ms (64.4% of total)
ival-sub: 1.0ms (21.5% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
11.7MiB live, 11.7MiB allocated
Counts
3 → 48
Calls
Call 1
Inputs
#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())
Outputs
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (*.f64 x x) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify174.0ms (3.9%)

Memory
-18.2MiB live, 188.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017219
139219
2113219
3469219
41677219
52848219
65012219
08437219
Stop Event
iter limit
node limit
Counts
48 → 48
Calls
Call 1
Inputs
(pow x 2)
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 (pow y 2))
(- (pow x 2) (pow y 2))
(- (pow x 2) (pow y 2))
(- (pow x 2) (pow y 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (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 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(*.f64 x x)
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 y y)
(*.f64 y y)
(*.f64 y y)
(*.f64 y y)
(*.f64 (neg.f64 y) y)
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 y y)
(*.f64 y y)
(*.f64 y y)
(*.f64 y y)
(*.f64 (neg.f64 y) y)
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 y y)
(*.f64 y y)
(*.f64 y y)
(*.f64 y y)
(*.f64 (neg.f64 y) y)
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)

rewrite214.0ms (4.8%)

Memory
2.9MiB live, 234.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0513
0813
13213
221613
3196713
0877813
Stop Event
iter limit
node limit
iter limit
Counts
3 → 252
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (*.f64 y y))
(*.f64 x x)
(*.f64 y y)
Outputs
#<batchref>
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eval36.0ms (0.8%)

Memory
-6.7MiB live, 74.7MiB allocated
Compiler

Compiled 8 823 to 759 computations (91.4% saved)

prune5.0ms (0.1%)

Memory
19.2MiB live, 19.2MiB allocated
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2973300
Fresh000
Picked101
Done000
Total2983301
Accuracy
100.0%
Counts
301 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 (-.f64 x y) (+.f64 y x))
55.8%
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
53.6%
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify354.0ms (7.9%)

Memory
-27.5MiB live, 377.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 y x)
cost-diff0
(-.f64 x y)
cost-diff0
(*.f64 (-.f64 x y) (+.f64 y x))
cost-diff0
(neg.f64 y)
cost-diff0
(*.f64 (neg.f64 y) y)
cost-diff0
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01349
01949
13749
26449
314449
428549
559049
6149049
7288349
8399149
9455849
10479749
11492749
12494949
13494949
14494949
0868349
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
y
(*.f64 (-.f64 x y) (+.f64 y x))
(-.f64 x y)
x
y
(+.f64 y x)
Outputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
y
(*.f64 (+.f64 y x) (-.f64 x y))
(-.f64 x y)
x
y
(+.f64 y x)

localize33.0ms (0.7%)

Memory
-5.4MiB live, 74.1MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 x y)
accuracy0
(+.f64 y x)
accuracy0
(*.f64 (-.f64 x y) (+.f64 y x))
accuracy0
(*.f64 (neg.f64 y) y)
accuracy0
(neg.f64 y)
accuracy28.281272384916207
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
accuracy0
(*.f64 x x)
accuracy29.674714383152118
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Samples
19.0ms256×0valid
Compiler

Compiled 91 to 25 computations (72.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 6.0ms (55.6% of total)
ival-sub: 2.0ms (18.5% of total)
ival-add: 1.0ms (9.3% of total)
ival-neg: 1.0ms (9.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory
30.5MiB live, 30.5MiB allocated
Counts
8 → 156
Calls
Call 1
Inputs
#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())
Outputs
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (neg.f64 y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x y) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 y x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify193.0ms (4.3%)

Memory
12.1MiB live, 196.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
092651
1281651
2829651
33555651
08745651
Stop Event
iter limit
node limit
Counts
156 → 147
Calls
Call 1
Inputs
(pow x 2)
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
(pow x 2)
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(pow x 2)
(+ (* y (+ x (* -1 x))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
x
(+ x y)
(+ x y)
(+ x y)
(* -1 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* -1 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 (pow y 2))
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* -1 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* -1 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 (pow y 2))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (pow y 2))
(- (pow x 2) (pow y 2))
(- (pow x 2) (pow y 2))
(- (pow x 2) (pow y 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (pow y 2))
(- (pow x 2) (pow y 2))
(- (pow x 2) (pow y 2))
(- (pow x 2) (pow y 2))
(* -1 (pow y 2))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(* -1 y)
(- x y)
(- x y)
(- x y)
y
(+ x y)
(+ x y)
(+ x y)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (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 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (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 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
Outputs
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(neg.f64 y)
(neg.f64 y)
(neg.f64 y)
(neg.f64 y)
(*.f64 x x)
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
x
(-.f64 x y)
(-.f64 x y)
(-.f64 x y)
x
(+.f64 y x)
(+.f64 y x)
(+.f64 y x)
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(neg.f64 y)
(neg.f64 y)
(neg.f64 y)
(neg.f64 y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)
(-.f64 x y)
(-.f64 x y)
(-.f64 x y)
y
(+.f64 y x)
(+.f64 y x)
(+.f64 y x)
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(neg.f64 y)
(neg.f64 y)
(neg.f64 y)
(neg.f64 y)
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)
(-.f64 x y)
(-.f64 x y)
(-.f64 x y)
y
(+.f64 y x)
(+.f64 y x)
(+.f64 y x)
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 (neg.f64 y) y)
(*.f64 (neg.f64 y) y)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)
(-.f64 x y)
(-.f64 x y)
(-.f64 x y)
y
(+.f64 y x)
(+.f64 y x)
(+.f64 y x)
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 x x)
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
x
(-.f64 x y)
(-.f64 x y)
(-.f64 x y)
x
(+.f64 y x)
(+.f64 y x)
(+.f64 y x)
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(*.f64 x x)
(*.f64 x x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
x
(-.f64 x y)
(-.f64 x y)
(-.f64 x y)
x
(+.f64 y x)
(+.f64 y x)
(+.f64 y x)

rewrite468.0ms (10.4%)

Memory
-12.3MiB live, 152.2MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01345
01945
17045
251145
3676336
0929036
Stop Event
iter limit
node limit
iter limit
Counts
8 → 733
Calls
Call 1
Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
(*.f64 (-.f64 x y) (+.f64 y x))
(-.f64 x y)
(+.f64 y x)
Outputs
#<batchref>
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eval151.0ms (3.4%)

Memory
11.5MiB live, 210.1MiB allocated
Compiler

Compiled 19 178 to 1 569 computations (91.8% saved)

prune28.0ms (0.6%)

Memory
-30.0MiB live, 54.5MiB allocated
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New8800880
Fresh000
Picked033
Done000
Total8803883
Accuracy
100.0%
Counts
883 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 (-.f64 x y) (+.f64 y x))
55.8%
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
53.6%
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Compiler

Compiled 67 to 35 computations (47.8% saved)

regimes11.0ms (0.2%)

Memory
20.1MiB live, 20.1MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (-.f64 x y) (+.f64 y x))
(-.f64 (*.f64 x x) (*.f64 y y))
Outputs
(*.f64 (-.f64 x y) (+.f64 y x))
Calls

5 calls:

2.0ms
x
2.0ms
y
2.0ms
(*.f64 y y)
2.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
2.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(-.f64 (*.f64 x x) (*.f64 y y))
100.0%1(*.f64 x x)
100.0%1(*.f64 y y)
Compiler

Compiled 15 to 15 computations (0% saved)

regimes14.0ms (0.3%)

Memory
-11.1MiB live, 20.2MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
Outputs
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Calls

5 calls:

7.0ms
y
2.0ms
x
2.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
1.0ms
(*.f64 y y)
1.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
80.8%2x
79.0%2y
95.6%2(-.f64 (*.f64 x x) (*.f64 y y))
80.8%2(*.f64 x x)
79.0%2(*.f64 y y)
Compiler

Compiled 15 to 15 computations (0% saved)

regimes6.0ms (0.1%)

Memory
13.7MiB live, 13.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Outputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Calls

5 calls:

1.0ms
x
1.0ms
y
1.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
1.0ms
(*.f64 y y)
1.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
53.6%1y
53.6%1(*.f64 y y)
53.6%1x
53.6%1(*.f64 x x)
53.6%1(-.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 15 to 15 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-7.51306e-319
0.0
Compiler

Compiled 10 to 10 computations (0% saved)

simplify28.0ms (0.6%)

Memory
-7.3MiB live, 66.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01851
12951
23551
33851
43951
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (-.f64 x y) (+.f64 y x))
(if (<=.f64 (-.f64 (*.f64 x x) (*.f64 y y)) #s(literal -101201/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #s(approx (- (* x x) (* y y)) (*.f64 x x)))
#s(approx (- (* x x) (* y y)) (*.f64 x x))
Outputs
(*.f64 (+.f64 y x) (-.f64 x y))
(if (<=.f64 (-.f64 (*.f64 x x) (*.f64 y y)) #s(literal -101201/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #s(approx (- (* x x) (* y y)) (*.f64 x x)))
#s(approx (- (* x x) (* y y)) (*.f64 x x))

soundness428.0ms (9.5%)

Memory
16.9MiB live, 223.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017219
139219
2113219
3469219
41677219
52848219
65012219
08437219
0513
0813
13213
221613
3196713
0877813
Stop Event
done
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 75 to 36 computations (52% saved)

preprocess50.0ms (1.1%)

Memory
-17.6MiB live, 56.7MiB allocated
Remove

(abs x)

(abs y)

Compiler

Compiled 172 to 86 computations (50% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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