Numeric.Integration.TanhSinh:everywhere from integration-0.2.1

Time bar (total: 5.9s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze3.0ms (0%)

Memory
-36.3MiB live, 0.6MiB 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 8 computations (11.1% saved)

sample828.0ms (13.9%)

Memory
37.1MiB live, 864.1MiB allocated
Samples
519.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 257.0ms
ival-mult: 204.0ms (79.5% of total)
ival-add: 38.0ms (14.8% of total)
ival-true: 6.0ms (2.3% of total)
exact: 5.0ms (1.9% of total)
ival-assert: 3.0ms (1.2% of total)
Bogosity

explain100.0ms (1.7%)

Memory
-5.9MiB live, 168.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
170-0-(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
00-0-y
00-0-#s(literal 1 binary64)
00-0-(*.f64 y y)
00-0-(+.f64 #s(literal 1 binary64) (*.f64 y y))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
*.f64(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))n*o170
Confusion
Predicted +Predicted -
+170
-0239
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+1700
-00239
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0239
117
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
24.0ms512×0valid
Compiler

Compiled 101 to 46 computations (54.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 7.0ms (65.8% of total)
ival-add: 2.0ms (18.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess32.0ms (0.5%)

Memory
-22.5MiB live, 16.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01637
16537
219435
346335
463935
576235
678935
067
097
1197
2277
3497
4497
0496
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Outputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
Symmetry

(abs y)

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
93.8%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory
1.7MiB live, 1.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y y)
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
cost-diff128
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
0918
11918
22718
34918
44918
04916
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
x
(+.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(*.f64 y y)
y
Outputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
x
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(fma.f64 y y #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 y y)
y

localize16.0ms (0.3%)

Memory
12.0MiB live, 12.0MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 y y)
accuracy0.00390625
(+.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy3.991998467683647
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Samples
11.0ms256×0valid
Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 3.0ms (60.7% of total)
ival-add: 1.0ms (20.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
3.8MiB live, 3.8MiB allocated
Counts
3 → 48
Calls
Call 1
Inputs
#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor -inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms
y
@inf
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms
x
@0
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms
y
@0
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms
x
@-inf
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))

simplify472.0ms (7.9%)

Memory
13.8MiB live, 165.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015246
142246
274246
3214246
4721246
51940246
62658246
73752246
85094246
95986246
106927246
117270246
127376246
137453246
147522246
157669246
08207216
Stop Event
iter limit
node limit
Counts
48 → 47
Calls
Call 1
Inputs
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
Outputs
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
x
(+ x (* x (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(+ x (* x (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(+ x (* x (pow y 2)))
(*.f64 x (fma.f64 y 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)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y 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)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y 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)
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))

rewrite151.0ms (2.5%)

Memory
14.0MiB live, 248.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
0915
13415
220915
3140415
0826913
Stop Event
iter limit
node limit
iter limit
Counts
3 → 368
Calls
Call 1
Inputs
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(*.f64 y y)
Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval50.0ms (0.8%)

Memory
-39.6MiB live, 121.5MiB allocated
Compiler

Compiled 9 642 to 1 119 computations (88.4% saved)

prune10.0ms (0.2%)

Memory
36.9MiB live, 36.9MiB allocated
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New4096415
Fresh000
Picked101
Done000
Total4106416
Accuracy
99.9%
Counts
416 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.9%
(fma.f64 (*.f64 x y) y x)
65.2%
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
93.7%
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
93.6%
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) x))
45.5%
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
52.2%
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Compiler

Compiled 92 to 78 computations (15.2% saved)

simplify189.0ms (3.2%)

Memory
-30.6MiB live, 209.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(pow.f64 y #s(literal 4 binary64))
cost-diff0
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
cost-diff0
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
cost-diff0
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
cost-diff0
(fma.f64 y y #s(literal 1 binary64))
cost-diff0
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
cost-diff6848
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
cost-diff0
(*.f64 y y)
cost-diff0
#s(approx (+ 1 (* y y)) (*.f64 y y))
cost-diff0
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
cost-diff0
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
cost-diff0
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
cost-diff0
(*.f64 x y)
cost-diff0
(fma.f64 (*.f64 x y) y x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022112
036106
156106
281106
3144106
4238106
5519106
61105106
71949106
83939106
95645106
106965106
117649106
08022106
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
x
y
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
x
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
x
#s(approx (+ 1 (* y y)) (*.f64 y y))
(*.f64 y y)
y
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
x
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 y y #s(literal 1 binary64))
y
#s(literal 1 binary64)
#s(literal -1 binary64)
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
#s(literal 1 binary64)
x
(fma.f64 y y #s(literal -1 binary64))
#s(literal -1 binary64)
Outputs
(fma.f64 (*.f64 x y) y x)
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(*.f64 x y)
(*.f64 y x)
x
y
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
(*.f64 #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) x)
x
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
(*.f64 #s(approx (+ 1 (* y y)) (*.f64 y y)) x)
x
#s(approx (+ 1 (* y y)) (*.f64 y y))
(*.f64 y y)
y
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
x
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 y y #s(literal 1 binary64))
y
#s(literal 1 binary64)
#s(literal -1 binary64)
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
#s(literal 1 binary64)
x
(fma.f64 y y #s(literal -1 binary64))
#s(literal -1 binary64)

localize53.0ms (0.9%)

Memory
13.2MiB live, 50.2MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(pow.f64 y #s(literal 4 binary64))
accuracy0.00390625
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
accuracy1.9000214078049262
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
accuracy17.428525536749724
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
accuracy0
(fma.f64 y y #s(literal 1 binary64))
accuracy0.32838080731346087
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy3.8024152763568213
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy0
(*.f64 y y)
accuracy3.991998467683647
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
accuracy31.192085795561734
#s(approx (+ 1 (* y y)) (*.f64 y y))
accuracy3.991998467683647
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
accuracy30.85116426341651
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
accuracy0
(*.f64 x y)
accuracy0.07421875
(fma.f64 (*.f64 x y) y x)
Samples
35.0ms256×0valid
Compiler

Compiled 200 to 41 computations (79.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-mult: 8.0ms (36.5% of total)
ival-pow: 5.0ms (22.8% of total)
ival-add: 4.0ms (18.2% of total)
ival-div: 3.0ms (13.7% of total)
ival-sub: 1.0ms (4.6% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series35.0ms (0.6%)

Memory
-5.6MiB live, 31.6MiB allocated
Counts
14 → 252
Calls
Call 1
Inputs
#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())
#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())
#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #s(approx (+ 1 (* y y)) (*.f64 y y)) (patch #s(approx (+ 1 (* y y)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (patch (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 y #s(literal 4 binary64)) (patch (pow.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (*.f64 y y)) (patch #s(approx (+ 1 (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (*.f64 y y)) (patch #s(approx (+ 1 (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (*.f64 y y)) (patch #s(approx (+ 1 (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (*.f64 y y)) (patch #s(approx (+ 1 (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (patch (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) (patch (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor -inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor -inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor -inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* x (- (pow y 4) 1)) (- (pow y 2) 1)) (taylor -inf x) (#s(alt (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) (patch (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor -inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor -inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor -inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow y 4) 1)) (taylor -inf x) (#s(alt (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (patch (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify140.0ms (2.3%)

Memory
9.2MiB live, 163.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0551542
11421519
23301515
39541511
438171511
578511511
082551378
Stop Event
iter limit
node limit
Counts
252 → 247
Calls
Call 1
Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* -1 x)
(+ (* -1 x) (* x (pow y 4)))
(+ (* -1 x) (* x (pow y 4)))
(+ (* -1 x) (* x (pow y 4)))
-1
(- (pow y 4) 1)
(- (pow y 4) 1)
(- (pow y 4) 1)
(pow y 4)
(pow y 4)
(pow y 4)
(pow y 4)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 4))
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(pow y 4)
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(pow y 4)
(pow y 4)
(pow y 4)
(pow y 4)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 4))
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(pow y 4)
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(pow y 4)
(pow y 4)
(pow y 4)
(pow y 4)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
(* x (- (pow y 4) 1))
Outputs
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y 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)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(-.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y #s(literal -1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y)))
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* x (pow y 4)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(+ (* -1 x) (* x (pow y 4)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(+ (* -1 x) (* x (pow y 4)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
-1
#s(literal -1 binary64)
(- (pow y 4) 1)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(- (pow y 4) 1)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(- (pow y 4) 1)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y 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)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 y y)) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)) y) y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (pow y 4))
(*.f64 (pow.f64 y #s(literal 4 binary64)) x)
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y 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)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 y y)) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)) y) y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (pow y 4))
(*.f64 (pow.f64 y #s(literal 4 binary64)) x)
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* (pow y 4) (+ x (* -1 (/ x (pow y 4)))))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(* (pow y 4) (- 1 (/ 1 (pow y 4))))
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
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(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
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(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
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(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
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(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
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(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
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(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
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(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
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(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(/ (* x (- (pow y 4) 1)) (- (pow y 2) 1))
(*.f64 (/.f64 x (fma.f64 y y #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(* x (- (pow y 4) 1))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)

rewrite209.0ms (3.5%)

Memory
-4.0MiB live, 256.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02293
03681
114181
285781
0842381
Stop Event
iter limit
node limit
iter limit
Counts
14 → 1 645
Calls
Call 1
Inputs
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
#s(approx (+ 1 (* y y)) (*.f64 y y))
(*.f64 y y)
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 y y #s(literal 1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow.f64 y #s(literal 4 binary64))
Outputs
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eval407.0ms (6.8%)

Memory
28.3MiB live, 288.4MiB allocated
Compiler

Compiled 38 486 to 3 221 computations (91.6% saved)

prune425.0ms (7.2%)

Memory
-20.5MiB live, 95.4MiB allocated
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1 88751 892
Fresh101
Picked235
Done000
Total1 89081 898
Accuracy
100.0%
Counts
1 898 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.9%
(fma.f64 (*.f64 x y) y x)
88.6%
(/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y))
45.4%
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
99.8%
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)))
93.6%
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x))
99.4%
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
45.5%
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
52.2%
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Compiler

Compiled 142 to 94 computations (33.8% saved)

simplify244.0ms (4.1%)

Memory
9.7MiB live, 130.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (*.f64 y x) y x)
cost-diff0
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
cost-diff0
(pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
cost-diff26880
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
cost-diff0
(fma.f64 y y #s(literal 1 binary64))
cost-diff0
(/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64)))
cost-diff0
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
cost-diff1792
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x))
cost-diff0
(fma.f64 y y #s(literal 1 binary64))
cost-diff0
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))
cost-diff128
(*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)))
cost-diff1280
(/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y))
cost-diff0
(*.f64 y y)
cost-diff0
(/.f64 #s(literal 1 binary64) (*.f64 y y))
cost-diff0
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
cost-diff0
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
cost-diff0
(*.f64 y x)
cost-diff0
(fma.f64 (*.f64 y x) y x)
cost-diff0
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
cost-diff7168
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026194
044163
174163
2157163
3380163
41425163
56126163
08366162
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
(fma.f64 (*.f64 y x) y x)
(*.f64 y x)
y
x
#s(literal -1 binary64)
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
x
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(*.f64 y y)
y
(/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y))
(*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)))
x
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))
(fma.f64 y y #s(literal 1 binary64))
y
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) y)
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x))
#s(literal -1 binary64)
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
(/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64)))
(fma.f64 y y #s(literal 1 binary64))
y
#s(literal 1 binary64)
x
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
(fma.f64 (*.f64 y x) y x)
(*.f64 y x)
y
x
#s(literal -1 binary64)
#s(literal -1/2 binary64)
Outputs
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
#s(literal 1 binary64)
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
(pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal -1 binary64))
(fma.f64 (*.f64 y x) y x)
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(*.f64 y x)
(*.f64 x y)
y
x
#s(literal -1 binary64)
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
x
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(*.f64 y y)
y
(/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)))
(*.f64 (fma.f64 x y x) (fma.f64 y y #s(literal 1 binary64)))
x
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))
(*.f64 (+.f64 y #s(literal 1 binary64)) (fma.f64 y y #s(literal 1 binary64)))
(fma.f64 y y #s(literal 1 binary64))
y
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) y)
(+.f64 y #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
#s(literal -1 binary64)
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
(/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64)))
(fma.f64 y y #s(literal 1 binary64))
y
#s(literal 1 binary64)
x
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
(pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal -1 binary64))
(fma.f64 (*.f64 y x) y x)
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(*.f64 y x)
(*.f64 x y)
y
x
#s(literal -1 binary64)
#s(literal -1/2 binary64)

localize97.0ms (1.6%)

Memory
-21.5MiB live, 144.4MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.07421875
(fma.f64 (*.f64 y x) y x)
accuracy0.3193550293053261
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
accuracy0.4022883639669849
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
accuracy10.836195455012422
(pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
accuracy0
(fma.f64 y y #s(literal 1 binary64))
accuracy0.125
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x))
accuracy0.32838080731346087
(/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64)))
accuracy3.8777021319347877
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
accuracy0
(+.f64 #s(literal 1 binary64) y)
accuracy0.046875
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))
accuracy1.8880851388814603
(*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)))
accuracy5.347588148115212
(/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y))
accuracy0
(*.f64 y y)
accuracy0.38306830731346087
(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy3.8024152763568213
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
accuracy31.182233672581788
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
accuracy0
(*.f64 y x)
accuracy0.07421875
(fma.f64 (*.f64 y x) y x)
accuracy0.125
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)))
accuracy0.4022883639669849
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
Samples
75.0ms256×0valid
Compiler

Compiled 384 to 49 computations (87.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 37.0ms
ival-div: 11.0ms (29.7% of total)
ival-mult: 11.0ms (29.7% of total)
ival-pow: 10.0ms (27% of total)
ival-add: 5.0ms (13.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series28.0ms (0.5%)

Memory
17.9MiB live, 55.7MiB allocated
Counts
18 → 348
Calls
Call 1
Inputs
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 y x) y x) (patch (fma.f64 (*.f64 y x) y x) #<representation binary64>) () ())
#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())
#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) (patch (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())
#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) (patch (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())
#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) y) (patch (+.f64 #s(literal 1 binary64) y) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (pow y 2) x)) (/ 1 x)) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x)) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x)) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) y x) (patch (fma.f64 (*.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) y x) (patch (fma.f64 (*.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) y x) (patch (fma.f64 (*.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 y x) y x) (patch (fma.f64 (*.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow y 2))) (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (pow y 2) 1))) (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1))) (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) (patch (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) (patch (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) (patch (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) (patch (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x y)) (taylor 0 y) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ x (* x y)))) (taylor 0 y) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ x (* y (+ x (* x y)))))) (taylor 0 y) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) (patch (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 y) (taylor 0 y) (#s(alt (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) (patch (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (+ 1 y))) (taylor 0 y) (#s(alt (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) (patch (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (+ 1 (* y (+ 1 y))))) (taylor 0 y) (#s(alt (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) (patch (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 y) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (- (/ (pow y 2) x) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) (patch (/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (* (+ 1 y) (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (* (+ 1 y) (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (* (+ 1 y) (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (* (+ 1 y) (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (patch (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) (patch (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify167.0ms (2.8%)

Memory
5.6MiB live, 245.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01992862
16152824
220102719
363632715
085942479
Stop Event
iter limit
node limit
Counts
348 → 339
Calls
Call 1
Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(/ 1 x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
x
(+ x (* x y))
(+ x (* y (+ x (* x y))))
(+ x (* y (+ x (* y (+ x (* x y))))))
1
(+ 1 y)
(+ 1 (* y (+ 1 y)))
(+ 1 (* y (+ 1 (* y (+ 1 y)))))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(/ -1 x)
(- (/ (pow y 2) x) (/ 1 x))
(- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))
(- (* (pow y 2) (+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))) (/ 1 x))
-1
(- (pow y 2) 1)
(- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)
(- (* (pow y 2) (+ 1 (* (pow y 2) (- (pow y 2) 1)))) 1)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt x) (pow y 2))))
(+ (sqrt x) (* (pow y 2) (+ (* -1/8 (* (sqrt x) (pow y 2))) (* 1/2 (sqrt x)))))
(+ (sqrt x) (* (pow y 2) (+ (* 1/2 (sqrt x)) (* (pow y 2) (+ (* -1/8 (sqrt x)) (* 1/16 (* (sqrt x) (pow y 2))))))))
1
(+ 1 y)
(+ 1 y)
(+ 1 y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 3))
(* (pow y 3) (+ x (/ x y)))
(* (pow y 3) (+ x (+ (/ x y) (/ x (pow y 2)))))
(* (pow y 3) (+ x (+ (/ x y) (+ (/ x (pow y 2)) (/ x (pow y 3))))))
(pow y 3)
(* (pow y 3) (+ 1 (/ 1 y)))
(* (pow y 3) (+ 1 (+ (/ 1 y) (/ 1 (pow y 2)))))
(* (pow y 3) (+ 1 (+ (/ 1 y) (+ (/ 1 (pow y 2)) (/ 1 (pow y 3))))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ -1 (* x (pow y 2)))
(/ (- (/ 1 (* x (pow y 2))) (/ 1 x)) (pow y 2))
(/ (- (/ 1 (* x (pow y 2))) (+ (/ 1 x) (/ 1 (* x (pow y 4))))) (pow y 2))
(/ (- (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6)))) (+ (/ 1 x) (/ 1 (* x (pow y 4))))) (pow y 2))
(/ -1 (pow y 2))
(/ (- (/ 1 (pow y 2)) 1) (pow y 2))
(/ (- (/ 1 (pow y 2)) (+ 1 (/ 1 (pow y 4)))) (pow y 2))
(/ (- (+ (/ 1 (pow y 2)) (/ 1 (pow y 6))) (+ 1 (/ 1 (pow y 4)))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (sqrt x) y)
(* y (+ (sqrt x) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))
(* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2)))))))
(* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (+ (* 1/16 (* (sqrt x) (/ 1 (pow y 6)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))))
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 3))
(* -1 (* (pow y 3) (+ (* -1 x) (* -1 (/ x y)))))
(* -1 (* (pow y 3) (+ (* -1 x) (* -1 (/ (+ x (/ x y)) y)))))
(* -1 (* (pow y 3) (+ (* -1 x) (* -1 (/ (+ x (* -1 (/ (+ (* -1 x) (* -1 (/ x y))) y))) y)))))
(pow y 3)
(* (pow y 3) (+ 1 (/ 1 y)))
(* -1 (* (pow y 3) (- (* -1 (/ (+ 1 (/ 1 y)) y)) 1)))
(* -1 (* (pow y 3) (- (* -1 (/ (+ 1 (+ (/ 1 y) (/ 1 (pow y 2)))) y)) 1)))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ -1 (* x (pow y 2)))
(/ (- (/ 1 (* x (pow y 2))) (/ 1 x)) (pow y 2))
(/ (- (/ 1 (* x (pow y 2))) (+ (/ 1 x) (/ 1 (* x (pow y 4))))) (pow y 2))
(/ (- (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6)))) (+ (/ 1 x) (/ 1 (* x (pow y 4))))) (pow y 2))
(/ -1 (pow y 2))
(/ (- (/ 1 (pow y 2)) 1) (pow y 2))
(/ (- (/ 1 (pow y 2)) (+ 1 (/ 1 (pow y 4)))) (pow y 2))
(/ (- (+ (/ 1 (pow y 2)) (/ 1 (pow y 6))) (+ 1 (/ 1 (pow y 4)))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* -1 (* (sqrt x) y))
(* -1 (* y (+ (sqrt x) (* 1/2 (* (sqrt x) (/ 1 (pow y 2)))))))
(* -1 (* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))))
(* -1 (* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (+ (* 1/16 (* (sqrt x) (/ 1 (pow y 6)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2)))))))))
y
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* y (+ 1 (/ 1 y)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(/ -1 (* x (+ 1 (pow y 2))))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
Outputs
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(fma.f64 (/.f64 (neg.f64 y) x) y (/.f64 #s(literal 1 binary64) x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(fma.f64 (/.f64 (*.f64 y y) x) (fma.f64 y y #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
(fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (/.f64 (*.f64 y y) x) (/.f64 #s(literal -1 binary64) x)) (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(fma.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(fma.f64 (fma.f64 (-.f64 y (pow.f64 y #s(literal 3 binary64))) y #s(literal -1 binary64)) (*.f64 y y) #s(literal 1 binary64))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
x
(+ x (* x y))
(fma.f64 y x x)
(+ x (* y (+ x (* x y))))
(fma.f64 (fma.f64 y x x) y x)
(+ x (* y (+ x (* y (+ x (* x y))))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (fma.f64 y x x))
1
#s(literal 1 binary64)
(+ 1 y)
(+.f64 #s(literal 1 binary64) y)
(+ 1 (* y (+ 1 y)))
(fma.f64 (+.f64 #s(literal 1 binary64) y) y #s(literal 1 binary64))
(+ 1 (* y (+ 1 (* y (+ 1 y)))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(- (/ (pow y 2) x) (/ 1 x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 y y #s(literal -1 binary64)))
(- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (/.f64 (*.f64 y y) x) (/.f64 #s(literal -1 binary64) x))
(- (* (pow y 2) (+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))) (/ 1 x))
(*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 y y #s(literal -1 binary64))))
-1
#s(literal -1 binary64)
(- (pow y 2) 1)
(fma.f64 y y #s(literal -1 binary64))
(- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)
(fma.f64 (-.f64 y (pow.f64 y #s(literal 3 binary64))) y #s(literal -1 binary64))
(- (* (pow y 2) (+ 1 (* (pow y 2) (- (pow y 2) 1)))) 1)
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y #s(literal -1 binary64)) (fma.f64 y y #s(literal -1 binary64)))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt x) (pow y 2))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) #s(literal 1 binary64)) (sqrt.f64 x))
(+ (sqrt x) (* (pow y 2) (+ (* -1/8 (* (sqrt x) (pow y 2))) (* 1/2 (sqrt x)))))
(fma.f64 (*.f64 (sqrt.f64 x) (fma.f64 #s(literal -1/8 binary64) (*.f64 y y) #s(literal 1/2 binary64))) (*.f64 y y) (sqrt.f64 x))
(+ (sqrt x) (* (pow y 2) (+ (* 1/2 (sqrt x)) (* (pow y 2) (+ (* -1/8 (sqrt x)) (* 1/16 (* (sqrt x) (pow y 2))))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y y) #s(literal 1 binary64)) (sqrt.f64 x) (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (sqrt.f64 x) (fma.f64 #s(literal 1/16 binary64) (*.f64 y y) #s(literal -1/8 binary64)))))
1
#s(literal 1 binary64)
(+ 1 y)
(+.f64 #s(literal 1 binary64) y)
(+ 1 y)
(+.f64 #s(literal 1 binary64) y)
(+ 1 y)
(+.f64 #s(literal 1 binary64) y)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (* x (pow y 2)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x)
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x)) (*.f64 y y))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/.f64 (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x)) (*.f64 y y))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(/.f64 (-.f64 (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 6 binary64)) x))) (*.f64 y y))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal 1 binary64))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (pow y 3))
(*.f64 (pow.f64 y #s(literal 3 binary64)) x)
(* (pow y 3) (+ x (/ x y)))
(*.f64 (*.f64 (fma.f64 y x x) y) y)
(* (pow y 3) (+ x (+ (/ x y) (/ x (pow y 2)))))
(*.f64 (fma.f64 (+.f64 #s(literal 1 binary64) y) x (/.f64 x y)) (*.f64 y y))
(* (pow y 3) (+ x (+ (/ x y) (+ (/ x (pow y 2)) (/ x (pow y 3))))))
(fma.f64 (fma.f64 (+.f64 #s(literal 1 binary64) y) x (/.f64 x y)) (*.f64 y y) x)
(pow y 3)
(pow.f64 y #s(literal 3 binary64))
(* (pow y 3) (+ 1 (/ 1 y)))
(*.f64 (fma.f64 y y y) y)
(* (pow y 3) (+ 1 (+ (/ 1 y) (/ 1 (pow y 2)))))
(fma.f64 (fma.f64 y y y) y y)
(* (pow y 3) (+ 1 (+ (/ 1 y) (+ (/ 1 (pow y 2)) (/ 1 (pow y 3))))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ -1 (* x (pow y 2)))
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 y y) x))
(/ (- (/ 1 (* x (pow y 2))) (/ 1 x)) (pow y 2))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 y y))
(/ (- (/ 1 (* x (pow y 2))) (+ (/ 1 x) (/ 1 (* x (pow y 4))))) (pow y 2))
(/.f64 (-.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6)))) (+ (/ 1 x) (/ 1 (* x (pow y 4))))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 y #s(literal 6 binary64)) x)) (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x))) (*.f64 y y))
(/ -1 (pow y 2))
(/.f64 #s(literal -1 binary64) (*.f64 y y))
(/ (- (/ 1 (pow y 2)) 1) (pow y 2))
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal 1 binary64)) y) y)
(/ (- (/ 1 (pow y 2)) (+ 1 (/ 1 (pow y 4)))) (pow y 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ (/ 1 (pow y 2)) (/ 1 (pow y 6))) (+ 1 (/ 1 (pow y 4)))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal 1 binary64)))) (*.f64 y y))
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (sqrt x) y)
(*.f64 (sqrt.f64 x) y)
(* y (+ (sqrt x) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))
(fma.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) y))
(* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2)))))))
(*.f64 (fma.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) (sqrt.f64 x)) y)
(* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (+ (* 1/16 (* (sqrt x) (/ 1 (pow y 6)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))))
(*.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 y y))))) y)
y
(* y (+ 1 (/ 1 y)))
(+.f64 #s(literal 1 binary64) y)
(* y (+ 1 (/ 1 y)))
(+.f64 #s(literal 1 binary64) y)
(* y (+ 1 (/ 1 y)))
(+.f64 #s(literal 1 binary64) y)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
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(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
(/ -1 (* x (+ 1 (pow y 2))))
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
(/ -1 (* x (+ 1 (pow y 2))))
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
(/ -1 (* x (+ 1 (pow y 2))))
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) x)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) x)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) x)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) x)))

rewrite203.0ms (3.4%)

Memory
7.9MiB live, 287.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026155
044122
1179115
21106115
08746114
Stop Event
iter limit
node limit
iter limit
Counts
18 → 2 134
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)))
(pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64))
(fma.f64 (*.f64 y x) y x)
(*.f64 y x)
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(*.f64 y y)
(/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y))
(*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))
(fma.f64 y y #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x))
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x)
(/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal 1 binary64) y)
Outputs
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval460.0ms (7.7%)

Memory
39.3MiB live, 756.1MiB allocated
Compiler

Compiled 85 370 to 6 282 computations (92.6% saved)

prune82.0ms (1.4%)

Memory
-1.4MiB live, 197.2MiB allocated
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New3 57273 579
Fresh000
Picked415
Done033
Total3 576113 587
Accuracy
100.0%
Counts
3 587 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.9%
(fma.f64 (*.f64 x y) y x)
93.6%
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
41.2%
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
45.4%
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
99.7%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 y #s(literal 1 binary64)) (fma.f64 (*.f64 x y) y x)) (+.f64 y #s(literal 1 binary64))))
99.8%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
99.9%
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))))
52.0%
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(approx (pow (pow (+ (* (* y x) y) x) -1) -1/2) (*.f64 (sqrt.f64 x) y)))
99.5%
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x)))
45.5%
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
52.2%
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Compiler

Compiled 216 to 139 computations (35.6% saved)

simplify137.0ms (2.3%)

Memory
11.8MiB live, 166.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x y)
cost-diff0
(fma.f64 (*.f64 x y) y x)
cost-diff0
(sqrt.f64 (fma.f64 (*.f64 x y) y x))
cost-diff2304
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x)))
cost-diff0
(*.f64 x y)
cost-diff0
(fma.f64 (*.f64 x y) y x)
cost-diff0
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x))
cost-diff1408
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
cost-diff0
(fma.f64 (fma.f64 y y y) y y)
cost-diff0
#s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))
cost-diff0
(*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)))
cost-diff0
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
cost-diff0
(/.f64 #s(literal -1 binary64) x)
cost-diff0
(*.f64 y y)
cost-diff0
(-.f64 #s(literal -1 binary64) (*.f64 y y))
cost-diff1216
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
cost-diff0
(*.f64 x y)
cost-diff0
(fma.f64 (*.f64 x y) y x)
cost-diff320
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))))
cost-diff7168
(*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028207
049197
192173
2205173
3523173
42650173
56403173
08242170
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))))
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
x
y
(*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(-.f64 #s(literal -1 binary64) y)
#s(literal -1 binary64)
(pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal -1 binary64) (*.f64 y y))
#s(literal -1 binary64)
(*.f64 y y)
y
(/.f64 #s(literal -1 binary64) x)
x
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
(*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)))
x
#s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))
(fma.f64 (fma.f64 y y y) y y)
(fma.f64 y y y)
y
(+.f64 #s(literal 1 binary64) y)
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x))
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
x
y
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x)))
(sqrt.f64 (fma.f64 (*.f64 x y) y x))
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
x
y
Outputs
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))))
(fma.f64 (*.f64 y x) y x)
(fma.f64 (*.f64 x y) y x)
(fma.f64 (*.f64 y x) y x)
(*.f64 x y)
(*.f64 y x)
x
y
(*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
#s(literal 1 binary64)
(-.f64 #s(literal -1 binary64) y)
#s(literal -1 binary64)
(pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
(fma.f64 (*.f64 y x) y x)
(-.f64 #s(literal -1 binary64) (*.f64 y y))
#s(literal -1 binary64)
(*.f64 y y)
y
(/.f64 #s(literal -1 binary64) x)
x
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
(*.f64 (/.f64 x (-.f64 y #s(literal -1 binary64))) #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)))
(*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)))
(*.f64 #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)) x)
x
#s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))
(fma.f64 (fma.f64 y y y) y y)
(fma.f64 y y y)
y
(+.f64 #s(literal 1 binary64) y)
(-.f64 y #s(literal -1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
(fma.f64 (*.f64 y x) y x)
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x))
(fma.f64 (*.f64 x y) y x)
(fma.f64 (*.f64 y x) y x)
(*.f64 x y)
(*.f64 y x)
x
y
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x)))
(fma.f64 (*.f64 y x) y x)
(sqrt.f64 (fma.f64 (*.f64 x y) y x))
(sqrt.f64 (fma.f64 (*.f64 y x) y x))
(fma.f64 (*.f64 x y) y x)
(fma.f64 (*.f64 y x) y x)
(*.f64 x y)
(*.f64 y x)
x
y

localize79.0ms (1.3%)

Memory
-7.1MiB live, 107.8MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x y)
accuracy0.07421875
(fma.f64 (*.f64 x y) y x)
accuracy0.3193550293053261
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x)))
accuracy11.26062781597605
(sqrt.f64 (fma.f64 (*.f64 x y) y x))
accuracy0
(*.f64 x y)
accuracy0.07421875
(fma.f64 (*.f64 x y) y x)
accuracy0.125
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
accuracy0.4022883639669849
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x))
accuracy0.05078125
(fma.f64 (fma.f64 y y y) y y)
accuracy1.8880851388814603
(*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)))
accuracy5.347588148115212
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
accuracy30.5714409978717
#s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))
accuracy0
(/.f64 #s(literal -1 binary64) x)
accuracy0
(*.f64 y y)
accuracy0.00390625
(-.f64 #s(literal -1 binary64) (*.f64 y y))
accuracy4.081842217683647
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
accuracy0
(*.f64 x y)
accuracy0.00390625
(pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))
accuracy0.0625
(*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
accuracy0.07421875
(fma.f64 (*.f64 x y) y x)
Samples
60.0ms256×0valid
Compiler

Compiled 377 to 53 computations (85.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 45.0ms
ival-mult: 14.0ms (31.4% of total)
ival-add: 12.0ms (26.9% of total)
ival-div: 8.0ms (17.9% of total)
ival-pow: 6.0ms (13.5% of total)
ival-sub: 2.0ms (4.5% of total)
ival-sqrt: 2.0ms (4.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series53.0ms (0.9%)

Memory
-50.1MiB live, 71.7MiB allocated
Counts
17 → 324
Calls
Call 1
Inputs
#s(alt (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) (patch (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) (patch (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())
#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1 binary64) (*.f64 y y)) (patch (-.f64 #s(literal -1 binary64) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y)) (patch (/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())
#s(alt (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (patch (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)) (patch #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 y y y) y y) (patch (fma.f64 (fma.f64 y y y) y y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) (patch (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (patch (sqrt.f64 (fma.f64 (*.f64 x y) y x)) #<representation binary64>) () ())
#s(alt (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (patch (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) #<representation binary64>) () ())
Outputs
#s(alt 1 (taylor 0 y) (#s(alt (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) (patch (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) (patch (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) (patch (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) (patch (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) (patch (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) (patch (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) (patch (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) (patch (*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (*.f64 x y) y x) (patch (fma.f64 (*.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 x y) (patch (*.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) (patch (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) (patch (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) (patch (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) (patch (*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (patch (sqrt.f64 (fma.f64 (*.f64 x y) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (patch (sqrt.f64 (fma.f64 (*.f64 x y) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (patch (sqrt.f64 (fma.f64 (*.f64 x y) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (patch (sqrt.f64 (fma.f64 (*.f64 x y) y x)) #<representation binary64>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
18.0ms
x
@inf
((* (- -1 y) (pow (- -1 y) -1)) (* (+ (* (* x y) y) x) (* (- -1 y) (pow (- -1 y) -1))) (+ (* (* x y) y) x) (* x y) (/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ (* x (* (+ (* y y) 1) (+ 1 y))) (+ 1 y)) (* x (* (+ (* y y) 1) (+ 1 y))) (* (+ (* y y) 1) (+ 1 y)) (+ (* (+ (* y y) y) y) y) (/ 1 (/ 1 (+ (* (* x y) y) x))) (/ 1 (+ (* (* x y) y) x)) (* (sqrt (+ (* (* x y) y) x)) (sqrt (+ (* (* x y) y) x))) (sqrt (+ (* (* x y) y) x)) (pow (- -1 y) -1))
15.0ms
x
@-inf
((* (- -1 y) (pow (- -1 y) -1)) (* (+ (* (* x y) y) x) (* (- -1 y) (pow (- -1 y) -1))) (+ (* (* x y) y) x) (* x y) (/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ (* x (* (+ (* y y) 1) (+ 1 y))) (+ 1 y)) (* x (* (+ (* y y) 1) (+ 1 y))) (* (+ (* y y) 1) (+ 1 y)) (+ (* (+ (* y y) y) y) y) (/ 1 (/ 1 (+ (* (* x y) y) x))) (/ 1 (+ (* (* x y) y) x)) (* (sqrt (+ (* (* x y) y) x)) (sqrt (+ (* (* x y) y) x))) (sqrt (+ (* (* x y) y) x)) (pow (- -1 y) -1))
4.0ms
y
@0
((* (- -1 y) (pow (- -1 y) -1)) (* (+ (* (* x y) y) x) (* (- -1 y) (pow (- -1 y) -1))) (+ (* (* x y) y) x) (* x y) (/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ (* x (* (+ (* y y) 1) (+ 1 y))) (+ 1 y)) (* x (* (+ (* y y) 1) (+ 1 y))) (* (+ (* y y) 1) (+ 1 y)) (+ (* (+ (* y y) y) y) y) (/ 1 (/ 1 (+ (* (* x y) y) x))) (/ 1 (+ (* (* x y) y) x)) (* (sqrt (+ (* (* x y) y) x)) (sqrt (+ (* (* x y) y) x))) (sqrt (+ (* (* x y) y) x)) (pow (- -1 y) -1))
1.0ms
x
@0
((* (- -1 y) (pow (- -1 y) -1)) (* (+ (* (* x y) y) x) (* (- -1 y) (pow (- -1 y) -1))) (+ (* (* x y) y) x) (* x y) (/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ (* x (* (+ (* y y) 1) (+ 1 y))) (+ 1 y)) (* x (* (+ (* y y) 1) (+ 1 y))) (* (+ (* y y) 1) (+ 1 y)) (+ (* (+ (* y y) y) y) y) (/ 1 (/ 1 (+ (* (* x y) y) x))) (/ 1 (+ (* (* x y) y) x)) (* (sqrt (+ (* (* x y) y) x)) (sqrt (+ (* (* x y) y) x))) (sqrt (+ (* (* x y) y) x)) (pow (- -1 y) -1))
1.0ms
y
@inf
((* (- -1 y) (pow (- -1 y) -1)) (* (+ (* (* x y) y) x) (* (- -1 y) (pow (- -1 y) -1))) (+ (* (* x y) y) x) (* x y) (/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ (* x (* (+ (* y y) 1) (+ 1 y))) (+ 1 y)) (* x (* (+ (* y y) 1) (+ 1 y))) (* (+ (* y y) 1) (+ 1 y)) (+ (* (+ (* y y) y) y) y) (/ 1 (/ 1 (+ (* (* x y) y) x))) (/ 1 (+ (* (* x y) y) x)) (* (sqrt (+ (* (* x y) y) x)) (sqrt (+ (* (* x y) y) x))) (sqrt (+ (* (* x y) y) x)) (pow (- -1 y) -1))

simplify153.0ms (2.6%)

Memory
33.4MiB live, 186.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01902418
15852376
218822283
351862264
082642035
Stop Event
iter limit
node limit
Counts
324 → 316
Calls
Call 1
Inputs
1
1
1
1
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
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x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
-1
(- (* -1 (pow y 2)) 1)
(- (* -1 (pow y 2)) 1)
(- (* -1 (pow y 2)) 1)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
x
(+ x (* x y))
(+ x (* y (+ x (* x y))))
(+ x (* y (+ x (* y (+ x (* x y))))))
1
(+ 1 y)
(+ 1 (* y (+ 1 y)))
(+ 1 (* y (+ 1 (* y (+ 1 y)))))
y
(* y (+ 1 y))
(* y (+ 1 (* y (+ 1 y))))
(* y (+ 1 (* y (+ 1 y))))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(/ 1 x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt x) (pow y 2))))
(+ (sqrt x) (* (pow y 2) (+ (* -1/8 (* (sqrt x) (pow y 2))) (* 1/2 (sqrt x)))))
(+ (sqrt x) (* (pow y 2) (+ (* 1/2 (sqrt x)) (* (pow y 2) (+ (* -1/8 (sqrt x)) (* 1/16 (* (sqrt x) (pow y 2))))))))
-1
(- y 1)
(- (* y (+ 1 (* -1 y))) 1)
(- (* y (+ 1 (* y (- y 1)))) 1)
1
1
1
1
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* -1 (pow y 2))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 3))
(* (pow y 3) (+ x (/ x y)))
(* (pow y 3) (+ x (+ (/ x y) (/ x (pow y 2)))))
(* (pow y 3) (+ x (+ (/ x y) (+ (/ x (pow y 2)) (/ x (pow y 3))))))
(pow y 3)
(* (pow y 3) (+ 1 (/ 1 y)))
(* (pow y 3) (+ 1 (+ (/ 1 y) (/ 1 (pow y 2)))))
(* (pow y 3) (+ 1 (+ (/ 1 y) (+ (/ 1 (pow y 2)) (/ 1 (pow y 3))))))
(pow y 3)
(* (pow y 3) (+ 1 (/ 1 y)))
(* (pow y 3) (+ 1 (+ (/ 1 y) (/ 1 (pow y 2)))))
(* (pow y 3) (+ 1 (+ (/ 1 y) (/ 1 (pow y 2)))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (sqrt x) y)
(* y (+ (sqrt x) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))
(* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2)))))))
(* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (+ (* 1/16 (* (sqrt x) (/ 1 (pow y 6)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))))
(/ -1 y)
(/ (- (/ 1 y) 1) y)
(/ (- (/ 1 y) (+ 1 (/ 1 (pow y 2)))) y)
(/ (- (+ (/ 1 y) (/ 1 (pow y 3))) (+ 1 (/ 1 (pow y 2)))) y)
1
1
1
1
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* -1 (pow y 2))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 3))
(* -1 (* (pow y 3) (+ (* -1 x) (* -1 (/ x y)))))
(* -1 (* (pow y 3) (+ (* -1 x) (* -1 (/ (+ x (/ x y)) y)))))
(* -1 (* (pow y 3) (+ (* -1 x) (* -1 (/ (+ x (* -1 (/ (+ (* -1 x) (* -1 (/ x y))) y))) y)))))
(pow y 3)
(* (pow y 3) (+ 1 (/ 1 y)))
(* -1 (* (pow y 3) (- (* -1 (/ (+ 1 (/ 1 y)) y)) 1)))
(* -1 (* (pow y 3) (- (* -1 (/ (+ 1 (+ (/ 1 y) (/ 1 (pow y 2)))) y)) 1)))
(pow y 3)
(* (pow y 3) (+ 1 (/ 1 y)))
(* -1 (* (pow y 3) (- (* -1 (/ (+ 1 (/ 1 y)) y)) 1)))
(* -1 (* (pow y 3) (- (* -1 (/ (+ 1 (/ 1 y)) y)) 1)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* -1 (* (sqrt x) y))
(* -1 (* y (+ (sqrt x) (* 1/2 (* (sqrt x) (/ 1 (pow y 2)))))))
(* -1 (* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2))))))))
(* -1 (* y (+ (sqrt x) (+ (* -1/8 (* (sqrt x) (/ 1 (pow y 4)))) (+ (* 1/16 (* (sqrt x) (/ 1 (pow y 6)))) (* 1/2 (* (sqrt x) (/ 1 (pow y 2)))))))))
(/ -1 y)
(* -1 (/ (- 1 (/ 1 y)) y))
(* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 y)) y))) y))
(* -1 (/ (+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 y)) y))) y))) y))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(sqrt (* x (+ 1 (pow y 2))))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* x (* (+ 1 y) (+ 1 (pow y 2))))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
(* -1 (* (sqrt (* x (- (* -1 (pow y 2)) 1))) (sqrt -1)))
Outputs
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
-1
#s(literal -1 binary64)
(- (* -1 (pow y 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(- (* -1 (pow y 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(- (* -1 (pow y 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
x
(+ x (* x y))
(fma.f64 y x x)
(+ x (* y (+ x (* x y))))
(fma.f64 (fma.f64 y x x) y x)
(+ x (* y (+ x (* y (+ x (* x y))))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (fma.f64 y x x))
1
#s(literal 1 binary64)
(+ 1 y)
(+.f64 y #s(literal 1 binary64))
(+ 1 (* y (+ 1 y)))
(fma.f64 (+.f64 y #s(literal 1 binary64)) y #s(literal 1 binary64))
(+ 1 (* y (+ 1 (* y (+ 1 y)))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 y #s(literal 1 binary64)))
y
(* y (+ 1 y))
(fma.f64 y y y)
(* y (+ 1 (* y (+ 1 y))))
(fma.f64 (fma.f64 y y y) y y)
(* y (+ 1 (* y (+ 1 y))))
(fma.f64 (fma.f64 y y y) y y)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
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rewrite152.0ms (2.6%)

Memory
-30.7MiB live, 203.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028165
049142
1209133
21625132
08637128
Stop Event
iter limit
node limit
iter limit
Counts
17 → 961
Calls
Call 1
Inputs
(*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))))
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(*.f64 y y)
(/.f64 #s(literal -1 binary64) x)
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
(*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y)))
#s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))
(fma.f64 (fma.f64 y y y) y y)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x)))
(sqrt.f64 (fma.f64 (*.f64 x y) y x))
(pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))
Outputs
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eval308.0ms (5.2%)

Memory
38.6MiB live, 381.3MiB allocated
Compiler

Compiled 41 859 to 2 780 computations (93.4% saved)

prune42.0ms (0.7%)

Memory
16.6MiB live, 130.8MiB allocated
Pruning

12 alts after pruning (6 fresh and 6 done)

PrunedKeptTotal
New1 94951 954
Fresh112
Picked325
Done044
Total1 953121 965
Accuracy
100.0%
Counts
1 965 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.9%
(fma.f64 (*.f64 x y) y x)
99.8%
(/.f64 (/.f64 (fma.f64 (*.f64 x y) y x) (-.f64 #s(literal -1 binary64) y)) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
41.2%
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
45.4%
(/.f64 #s(approx (- -1 (* y y)) (*.f64 (neg.f64 y) y)) (/.f64 #s(literal -1 binary64) x))
45.4%
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
99.7%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 y #s(literal 1 binary64)) (fma.f64 (*.f64 x y) y x)) (+.f64 y #s(literal 1 binary64))))
99.8%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x)) y x)))
99.8%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
51.3%
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) #s(approx (pow (- -1 y) -1) (/.f64 #s(literal -1 binary64) y))))
52.1%
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) #s(approx (sqrt (+ (* (* x y) y) x)) (*.f64 (sqrt.f64 x) y)))
45.5%
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
52.2%
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Compiler

Compiled 408 to 173 computations (57.6% saved)

regimes37.0ms (0.6%)

Memory
-23.9MiB live, 61.4MiB allocated
Counts
24 → 1
Calls
Call 1
Inputs
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
(fma.f64 (*.f64 x y) y x)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 #s(approx (- -1 (* y y)) (*.f64 (neg.f64 y) y)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 x #s(approx (* (+ (* y y) 1) (+ 1 y)) (fma.f64 (fma.f64 y y y) y y))) (+.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) y x)))
(/.f64 (*.f64 x (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) y))) (+.f64 #s(literal 1 binary64) y))
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) #s(approx (pow (- -1 y) -1) (/.f64 #s(literal -1 binary64) y))))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal 1 binary64))) x))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) #s(approx (sqrt (+ (* (* x y) y) x)) (*.f64 (sqrt.f64 x) y)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x y) y x)) (sqrt.f64 (fma.f64 (*.f64 x y) y x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 y #s(literal 1 binary64)) (fma.f64 (*.f64 x y) y x)) (+.f64 y #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x)) y x)))
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
(*.f64 (fma.f64 (*.f64 x y) y x) (*.f64 (-.f64 #s(literal -1 binary64) y) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) x))
(/.f64 (/.f64 (fma.f64 (*.f64 x y) y x) (-.f64 #s(literal -1 binary64) y)) (pow.f64 (-.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(approx (pow (pow (+ (* (* y x) y) x) -1) -1/2) (*.f64 (sqrt.f64 x) y)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
Outputs
(fma.f64 (*.f64 x y) y x)
Calls

5 calls:

9.0ms
y
8.0ms
(*.f64 y y)
7.0ms
x
6.0ms
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
6.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1y
99.9%1(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
99.9%1(+.f64 #s(literal 1 binary64) (*.f64 y y))
99.9%1(*.f64 y y)
Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes8.0ms (0.1%)

Memory
17.7MiB live, 17.7MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
Outputs
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
Calls

5 calls:

2.0ms
x
2.0ms
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
1.0ms
y
1.0ms
(*.f64 y y)
1.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Results
AccuracySegmentsBranch
62.6%5x
92.7%2y
77.7%2(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
92.7%2(+.f64 #s(literal 1 binary64) (*.f64 y y))
92.7%2(*.f64 y y)
Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes9.0ms (0.2%)

Memory
-16.4MiB live, 20.9MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Outputs
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Calls

5 calls:

3.0ms
(*.f64 y y)
1.0ms
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
1.0ms
x
1.0ms
y
1.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Results
AccuracySegmentsBranch
52.2%1x
52.2%1(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
52.2%1(+.f64 #s(literal 1 binary64) (*.f64 y y))
52.2%1(*.f64 y y)
52.2%1y
Compiler

Compiled 17 to 18 computations (-5.9% saved)

bsearch10.0ms (0.2%)

Memory
-12.2MiB live, 27.0MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
8.0ms
0.6054304413452645
19.284957673673215
Samples
4.0ms112×0valid
Compiler

Compiled 80 to 95 computations (-18.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-add: 1.0ms (45.2% of total)
ival-mult: 1.0ms (45.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify22.0ms (0.4%)

Memory
39.1MiB live, 39.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01439
12039
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 (*.f64 x y) y x)
(if (<=.f64 y #s(literal 1 binary64)) (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))))
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Outputs
(fma.f64 (*.f64 x y) y x)
(fma.f64 (*.f64 y x) y x)
(if (<=.f64 y #s(literal 1 binary64)) (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))))
(if (<=.f64 y #s(literal 1 binary64)) (*.f64 #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) x) (*.f64 #s(approx (+ 1 (* y y)) (*.f64 y y)) x))
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
(*.f64 #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) x)

soundness471.0ms (7.9%)

Memory
-42.7MiB live, 177.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015246
142246
274246
3214246
4721246
51940246
62658246
73752246
85094246
95986246
106927246
117270246
127376246
137453246
147522246
157669246
08207216
0615
0915
13415
220915
3140415
0826913
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 48 to 32 computations (33.3% saved)

preprocess56.0ms (0.9%)

Memory
16.8MiB live, 94.8MiB allocated
Remove

(negabs x)

(abs y)

Compiler

Compiled 148 to 94 computations (36.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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