Numeric.Integration.TanhSinh:everywhere from integration-0.2.1

Time bar (total: 5.8s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×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)

sample995.0ms (17.2%)

Memory
-49.0MiB live, 894.9MiB allocated
Samples
561.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 169.0ms
ival-mult: 119.0ms (70.3% of total)
ival-add: 37.0ms (21.9% of total)
ival-true: 6.0ms (3.5% of total)
exact: 5.0ms (3% of total)
ival-assert: 3.0ms (1.8% of total)
Bogosity

explain230.0ms (4%)

Memory
-8.0MiB live, 69.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
180-0-(*.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*o180
Confusion
Predicted +Predicted -
+180
-0238
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+1800
-00238
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0238
118
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
21.0ms512×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 7.0ms (70.6% of total)
ival-add: 2.0ms (20.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess34.0ms (0.6%)

Memory
12.0MiB live, 49.6MiB allocated
Algorithm
1×egg-herbie
Rules
158×associate-*r*
124×distribute-lft-in
112×unsub-neg
92×associate-*l*
82×distribute-lft-neg-out
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01637
16537
219435
346335
463935
576235
678935
067
097
1197
2277
3497
4497
0496
Stop Event
1×iter limit
1×saturated
1×iter limit
1×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
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶93.3%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Memory
6.7MiB live, 6.8MiB allocated
Algorithm
1×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))
Rules
46×lower-*.f32
42×lower-*.f64
22×lower-fma.f64
22×lower-fma.f32
14×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
0918
11918
22718
34918
44918
04916
Stop Event
1×iter limit
1×saturated
1×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

localize19.0ms (0.3%)

Memory
-16.6MiB live, 26.6MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy0
(*.f64 y y)
accuracy4.289266333061458
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Samples
14.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-mult: 7.0ms (85.4% of total)
ival-add: 1.0ms (12.2% 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
11.7MiB live, 11.7MiB 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
@0
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
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
@-inf
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms
y
@0
((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))

simplify794.0ms (13.7%)

Memory
21.2MiB live, 178.6MiB allocated
Algorithm
1×egg-herbie
Rules
9 064×lower-fma.f64
9 064×lower-fma.f32
6 574×lower-*.f64
6 574×lower-*.f32
2 432×cube-prod
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
1×iter limit
1×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)))

rewrite425.0ms (7.3%)

Memory
-11.4MiB live, 222.4MiB allocated
Rules
5 176×lower-fma.f64
5 176×lower-fma.f32
4 882×lower-/.f64
4 882×lower-/.f32
4 246×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
0915
13415
220915
3140415
0826913
Stop Event
1×iter limit
1×node limit
1×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
(*.f64 (/.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 y #s(literal 1 binary64))) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (-.f64 y #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (fma.f64 (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y))) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))))) (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))))) (pow.f64 (neg.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) (+.f64 (pow.f64 y #s(literal 18 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y))) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y))))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) #s(literal 1 binary64)) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))) (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -3 binary64)) (*.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))))
(*.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y y #s(literal -1 binary64)))))
(*.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64)))) (pow.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)))))
(*.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (pow.f64 y #s(literal 6 binary64))) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)))))
(*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)) (neg.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)))))
(*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (+.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)) (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 x (*.f64 y y)) #s(literal 2 binary64))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (*.f64 x x) (pow.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 x x) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (hypot.f64 x (*.f64 x (*.f64 y y))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (*.f64 x (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))) (*.f64 x (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x (*.f64 y y)) x) (-.f64 (pow.f64 (*.f64 x (*.f64 y y)) #s(literal 2 binary64)) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) (pow.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 x x) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))) #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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
(fma.f64 (/.f64 (*.f64 x x) x) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64)) (neg.f64 (*.f64 (/.f64 (*.f64 x x) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(fma.f64 (/.f64 x x) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (neg.f64 (*.f64 (/.f64 (*.f64 x x) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (neg.f64 (*.f64 (/.f64 (*.f64 x x) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(fma.f64 (*.f64 x y) y x)
(fma.f64 (*.f64 x x) (pow.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) #s(literal -1 binary64)) (neg.f64 (*.f64 (/.f64 (*.f64 x x) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(fma.f64 (*.f64 x (*.f64 y y)) #s(literal 1 binary64) x)
(fma.f64 x (*.f64 y y) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 y y)))
(fma.f64 (*.f64 y y) x x)
(fma.f64 y (*.f64 x y) x)
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y y)) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 x (*.f64 y y)))
(-.f64 (/.f64 (pow.f64 (*.f64 x (*.f64 y y)) #s(literal 2 binary64)) (-.f64 (*.f64 x (*.f64 y y)) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 y y)) x)))
(-.f64 (*.f64 (/.f64 x x) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (*.f64 (/.f64 (*.f64 x x) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(+.f64 (*.f64 (/.f64 x x) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (neg.f64 (*.f64 (/.f64 (*.f64 x x) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(+.f64 (*.f64 x (*.f64 y y)) x)
(+.f64 x (*.f64 x (*.f64 y y)))
(*.f64 (*.f64 y y) #s(literal 1 binary64))
(*.f64 y y)
(*.f64 #s(literal 1 binary64) (*.f64 y y))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval51.0ms (0.9%)

Memory
-0.6MiB live, 118.5MiB allocated
Compiler

Compiled 9 613 to 1 120 computations (88.3% saved)

prune10.0ms (0.2%)

Memory
4.7MiB live, 43.7MiB allocated
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New4105415
Fresh000
Picked101
Done000
Total4115416
Accuracy
100.0%
Counts
416 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.9%
(fma.f64 (*.f64 x y) y x)
▶93.3%
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
▶68.7%
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
▶42.6%
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
▶54.7%
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Compiler

Compiled 74 to 62 computations (16.2% saved)

simplify185.0ms (3.2%)

Memory
15.1MiB live, 177.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y y)
cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 y y))
cost-diff0
(/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))
cost-diff128
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 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)
Rules
5 576×lower-fma.f32
5 572×lower-fma.f64
1 944×lower-*.f32
1 934×lower-*.f64
1 404×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022116
036110
157110
285110
3128110
4286110
5463110
61262110
73737110
84712110
95337110
106213110
117164110
127712110
137927110
147977110
157980110
167980110
08154109
Stop Event
1×iter limit
1×node limit
1×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 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/.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
(-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))
(pow.f64 y #s(literal 4 binary64))
#s(literal 4 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 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 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 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
(-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))
(pow.f64 y #s(literal 4 binary64))
#s(literal 4 binary64)

localize65.0ms (1.1%)

Memory
-6.2MiB live, 148.2MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy0
(*.f64 y y)
accuracy3.387195650520581
(/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))
accuracy14.353552279669636
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
accuracy0
(fma.f64 y y #s(literal 1 binary64))
accuracy0.1797371328237418
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy4.293172583061458
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy0
(*.f64 y y)
accuracy4.289266333061458
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
accuracy32.641011549718066
#s(approx (+ 1 (* y y)) (*.f64 y y))
accuracy4.289266333061458
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
accuracy29.131489409815067
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
accuracy0
(*.f64 x y)
accuracy0.0625
(fma.f64 (*.f64 x y) y x)
Samples
51.0ms256×0valid
Compiler

Compiled 110 to 21 computations (80.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 31.0ms
ival-pow: 12.0ms (39.2% of total)
ival-mult: 8.0ms (26.1% of total)
ival-add: 5.0ms (16.3% of total)
ival-div: 3.0ms (9.8% of total)
ival-sub: 2.0ms (6.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series55.0ms (0.9%)

Memory
-20.9MiB live, 99.3MiB allocated
Counts
13 → 240
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 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<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 #s(literal 1 binary64) (*.f64 y y)) (patch (-.f64 #s(literal 1 binary64) (*.f64 y y)) #<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>) () ())) ())
#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 4))) (- 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<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 (* -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 (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<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
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) (* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)))
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) (* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)))
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) (* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)))
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) (* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)))
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) (* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)))

simplify211.0ms (3.6%)

Memory
5.9MiB live, 241.5MiB allocated
Algorithm
1×egg-herbie
Rules
10 932×lower-fma.f64
10 932×lower-fma.f32
3 030×lower-*.f64
3 030×lower-*.f32
2 590×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711579
11931570
24761566
318501554
468501554
080961428
Stop Event
1×iter limit
1×node limit
Counts
240 → 234
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)))
x
(+ x (* x (pow y 2)))
(+ x (* (pow y 2) (- (* x (pow y 2)) (* -1 x))))
(+ x (* (pow y 2) (- (* (pow y 2) (- (* x (pow y 2)) (* -1 x))) (* -1 x))))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* -1 (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 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))))
(* -1 (/ x (pow y 2)))
(/ (+ (* -1 x) (* -1 (/ x (pow y 2)))) (pow y 2))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 4)))) (/ x (pow y 2))) (pow y 2))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 6)))) (+ (/ x (pow y 2)) (/ x (pow y 4)))) (pow y 2))
(* -1 (pow y 2))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 1 (pow y 2)) 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 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))))
(* -1 (/ x (pow y 2)))
(/ (+ (* -1 x) (* -1 (/ x (pow y 2)))) (pow y 2))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 4)))) (/ x (pow y 2))) (pow y 2))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 6)))) (+ (/ x (pow y 2)) (/ x (pow y 4)))) (pow y 2))
(* -1 (pow y 2))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 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 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 (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 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)))
(* 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 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 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)))
(* -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 (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 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
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)))
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rewrite291.0ms (5%)

Memory
42.7MiB live, 353.9MiB allocated
Rules
9 206×lower-fma.f32
9 202×lower-fma.f64
5 178×lower-*.f32
5 168×lower-*.f64
4 310×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02291
03678
113778
285878
0861778
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
13 → 1 894
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 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
Outputs
(*.f64 (/.f64 (*.f64 x (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) x)) (-.f64 (pow.f64 (*.f64 (*.f64 y y) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) x (hypot.f64 x (*.f64 y x))))
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 y y) x) #s(literal 4 binary64)) (pow.f64 (*.f64 x (-.f64 x (*.f64 (*.f64 y y) x))) #s(literal 2 binary64)))) (fma.f64 x (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) x) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64)) (pow.f64 (*.f64 x (-.f64 x (*.f64 (*.f64 y y) x))) #s(literal 3 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64)) (*.f64 (*.f64 x (-.f64 x (*.f64 (*.f64 y y) x))) (-.f64 (*.f64 x (-.f64 x (*.f64 (*.f64 y y) x))) (pow.f64 (*.f64 (*.f64 y y) x) #s(literal 2 binary64))))))
(*.f64 (/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (fma.f64 y y #s(literal -1 binary64)) x)) (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (fma.f64 y y #s(literal -1 binary64)) x)) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y)) #s(literal 2 binary64)))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (+.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y)) #s(literal 3 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y)) #s(literal 2 binary64))) (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y))))
(*.f64 (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (neg.f64 y) y #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))))) (neg.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 y) y #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (/.f64 (*.f64 x (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) x)) (*.f64 x (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) x))) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(*.f64 (/.f64 (neg.f64 x) #s(literal 1 binary64)) (fma.f64 (neg.f64 y) y #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64)))) (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64)))) (*.f64 (fma.f64 y y #s(literal 1 binary64)) (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(*.f64 (/.f64 x #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 (*.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))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))))) (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)))
(*.f64 (*.f64 (/.f64 (*.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))) (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 (*.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))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 (*.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))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))))) (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))) (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x)) (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (*.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))))) (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)))
(*.f64 (*.f64 x (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64))))) (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (*.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)))) (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (fma.f64 (neg.f64 y) y #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 (*.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))) #s(literal 1 binary64)) (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 x (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (/.f64 x (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x (pow.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (fma.f64 y y #s(literal -1 binary64)))) (/.f64 x (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (/.f64 x (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))))
(*.f64 (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (fma.f64 y y #s(literal -1 binary64)))) (fma.f64 (neg.f64 y) y #s(literal -1 binary64)))
(*.f64 (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1/2 binary64))) (/.f64 x (neg.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (*.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)) x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 x (pow.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (hypot.f64 (*.f64 y y) y) x x))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.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))) (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (*.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))))
(*.f64 (/.f64 x (-.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))) (pow.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (*.f64 (fma.f64 y y #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1/2 binary64)) x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal 1/2 binary64)) (*.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) (*.f64 (*.f64 x (fma.f64 y y #s(literal -1 binary64))) (pow.f64 (*.f64 x (fma.f64 y y #s(literal -1 binary64))) #s(literal -1 binary64))))
(*.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal 1 binary64))
(*.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (fma.f64 y y #s(literal -1 binary64)) x)) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (pow.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 x (-.f64 x (*.f64 (pow.f64 y #s(literal 4 binary64)) x))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 (*.f64 y y) x))))
(*.f64 (pow.f64 (*.f64 x (fma.f64 y y #s(literal -1 binary64))) #s(literal -1 binary64)) (*.f64 x (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) x)))
(*.f64 (pow.f64 (-.f64 (hypot.f64 (*.f64 (*.f64 y y) x) x) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (neg.f64 (*.f64 x (-.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 y) (*.f64 y x) x)))
(*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (hypot.f64 (*.f64 (*.f64 y y) x) x) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(*.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (pow.f64 (fma.f64 y y #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (neg.f64 y) y #s(literal -1 binary64)) (neg.f64 x))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 y y #s(literal -1 binary64)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y #s(literal -1 binary64)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))))
(*.f64 (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)))))
(*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (/.f64 #s(literal -1 binary64) (fma.f64 y y #s(literal -1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (*.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
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(-.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y #s(literal 1 binary64))) #s(literal 1 binary64)))
(-.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+.f64 (*.f64 (*.f64 y y) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (fma.f64 y y #s(literal -1 binary64)))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (fma.f64 y y #s(literal -1 binary64)))))
(+.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (*.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (fma.f64 y y #s(literal -1 binary64))) (*.f64 y y)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (fma.f64 y y #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 y #s(literal 4 binary64))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(+.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 y #s(literal 4 binary64))))
(+.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1 binary64))) (*.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y))))
(+.f64 (pow.f64 (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (hypot.f64 (*.f64 y y) y) #s(literal 1 binary64)))))
(+.f64 (*.f64 (neg.f64 y) y) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y #s(literal 1 binary64)))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 y) y))

eval300.0ms (5.2%)

Memory
-0.5MiB live, 511.6MiB allocated
Compiler

Compiled 48 816 to 3 460 computations (92.9% saved)

prune47.0ms (0.8%)

Memory
-53.3MiB live, 133.1MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2 15022 152
Fresh000
Picked235
Done000
Total2 15252 157
Accuracy
100.0%
Counts
2 157 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.9%
(fma.f64 (*.f64 x y) y x)
▶42.6%
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
▶16.0%
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
✓42.6%
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
✓54.7%
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Compiler

Compiled 37 to 32 computations (13.5% saved)

simplify596.0ms (10.3%)

Memory
39.2MiB live, 153.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
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 (neg.f64 y) y)
cost-diff0
#s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))
cost-diff0
(/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))
cost-diff0
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
Rules
15 008×lower-fma.f64
15 008×lower-fma.f32
2 734×lower-*.f32
2 728×lower-*.f64
2 076×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02097
02997
14697
27197
311497
422197
534797
659697
7103497
8163397
9240897
10355897
11444897
12517297
13546697
14578497
15603297
16626197
17658497
18752097
19800097
0810595
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))
x
#s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
y
(-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))
#s(literal 1 binary64)
(pow.f64 y #s(literal 4 binary64))
#s(literal 4 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
Outputs
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))
(/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))
x
#s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
y
(-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))
#s(literal 1 binary64)
(pow.f64 y #s(literal 4 binary64))
#s(literal 4 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

localize244.0ms (4.2%)

Memory
-32.7MiB live, 49.0MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 y y)
accuracy0.2422371328237418
(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy4.293172583061458
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
accuracy32.64346132551062
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
accuracy0
(neg.f64 y)
accuracy3.387195650520581
(/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))
accuracy14.353552279669636
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
accuracy33.19040016803518
#s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))
Samples
78.0ms256×0valid
Compiler

Compiled 72 to 19 computations (73.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 44.0ms
ival-add: 25.0ms (57% of total)
ival-div: 5.0ms (11.4% of total)
ival-mult: 5.0ms (11.4% of total)
ival-pow: 5.0ms (11.4% of total)
ival-sub: 2.0ms (4.6% of total)
ival-neg: 1.0ms (2.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series11.0ms (0.2%)

Memory
15.6MiB live, 15.6MiB allocated
Counts
9 → 144
Calls
Call 1
Inputs
#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())
#s(alt (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) #<representation:binary64>) () ())
#s(alt #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) (patch #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #<representation:binary64>) () ())
#s(alt (*.f64 (neg.f64 y) y) (patch (*.f64 (neg.f64 y) y) #<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 (neg.f64 y) (patch (neg.f64 y) #<representation:binary64>) () ())
Outputs
#s(alt x (taylor 0 y) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.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 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (- (* x (pow y 2)) (* -1 x)))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (- (* (pow y 2) (- (* x (pow y 2)) (* -1 x))) (* -1 x)))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) (patch #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow y 2))) (taylor 0 y) (#s(alt #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) (patch #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow y 2))) (taylor 0 y) (#s(alt #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) (patch #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow y 2))) (taylor 0 y) (#s(alt #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) (patch #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor 0 y) (#s(alt (*.f64 (neg.f64 y) y) (patch (*.f64 (neg.f64 y) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor 0 y) (#s(alt (*.f64 (neg.f64 y) y) (patch (*.f64 (neg.f64 y) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor 0 y) (#s(alt (*.f64 (neg.f64 y) y) (patch (*.f64 (neg.f64 y) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor 0 y) (#s(alt (*.f64 (neg.f64 y) y) (patch (*.f64 (neg.f64 y) y) #<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>) () ())) ())
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#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#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 (+ 1 (pow y 2))) (taylor 0 x) (#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 (+ 1 (pow y 2))) (taylor 0 x) (#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 (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ x (- 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.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 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.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 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.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 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#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 (+ 1 (pow y 2))) (taylor inf x) (#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 (+ 1 (pow y 2))) (taylor inf x) (#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 (+ 1 (pow y 2))) (taylor inf x) (#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 (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ (* x (- 1 (pow y 4))) (- 1 (pow y 2))) (taylor -inf x) (#s(alt (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (/ x (- 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.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 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.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 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.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 (neg.f64 y) y))) (patch (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#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 (+ 1 (pow y 2))) (taylor -inf x) (#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 (+ 1 (pow y 2))) (taylor -inf x) (#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 (+ 1 (pow y 2))) (taylor -inf x) (#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>) () ())) ())
Calls

6 calls:

TimeVariablePointExpression
1.0ms
y
@inf
((* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)) (* (neg y) y) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (* y y) (neg y))
1.0ms
x
@-inf
((* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)) (* (neg y) y) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (* y y) (neg y))
1.0ms
y
@-inf
((* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)) (* (neg y) y) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (* y y) (neg y))
1.0ms
x
@0
((* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)) (* (neg y) y) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (* y y) (neg y))
1.0ms
x
@inf
((* (/ x (- 1 (* y y))) (- 1 (pow y 4))) (/ x (- 1 (* y y))) (- 1 (* y y)) (* (neg y) y) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (* y y) (neg y))

simplify223.0ms (3.9%)

Memory
14.1MiB live, 203.2MiB allocated
Algorithm
1×egg-herbie
Rules
12 948×lower-fma.f64
12 948×lower-fma.f32
3 102×lower-*.f64
3 102×lower-*.f32
1 526×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0661009
11781000
2433996
31602984
46390984
08229948
Stop Event
1×iter limit
1×node limit
Counts
144 → 141
Calls
Call 1
Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* (pow y 2) (- (* x (pow y 2)) (* -1 x))))
(+ x (* (pow y 2) (- (* (pow y 2) (- (* x (pow y 2)) (* -1 x))) (* -1 x))))
1
(+ 1 (* -1 (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))
(* -1 (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 (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)
(* -1 y)
(* -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)))) (/ x (pow y 2))) (pow y 2))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 6)))) (+ (/ x (pow y 2)) (/ x (pow y 4)))) (pow y 2))
(* -1 (pow y 2))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -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 (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)
(* -1 y)
(* -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)))) (/ x (pow y 2))) (pow y 2))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 6)))) (+ (/ x (pow y 2)) (/ x (pow y 4)))) (pow y 2))
(* -1 (pow y 2))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -1 (pow y 2))
(* -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 (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)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 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 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 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 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(/ (* x (- 1 (pow y 4))) (- 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
x
(+ x (* x (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(+ x (* x (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(+ x (* x (pow y 2)))
(fma.f64 (*.f64 y y) x x)
x
(+ x (* x (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(+ x (* (pow y 2) (- (* x (pow y 2)) (* -1 x))))
(fma.f64 (hypot.f64 (*.f64 y y) y) x x)
(+ x (* (pow y 2) (- (* (pow y 2) (- (* x (pow y 2)) (* -1 x))) (* -1 x))))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 y y) x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(+ 1 (* -1 (pow y 2)))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(+ 1 (* -1 (pow y 2)))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
x
(+ x (* x (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(+ x (* x (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(+ x (* x (pow y 2)))
(fma.f64 (*.f64 y y) x x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(+ 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)) (fma.f64 (neg.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)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* -1 (/ x (pow y 2)))
(/.f64 (/.f64 (neg.f64 x) y) y)
(/ (+ (* -1 x) (* -1 (/ x (pow y 2)))) (pow y 2))
(/.f64 (/.f64 (+.f64 (/.f64 x (*.f64 y y)) x) y) (neg.f64 y))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 4)))) (/ x (pow y 2))) (pow y 2))
(/.f64 (-.f64 (-.f64 (/.f64 (neg.f64 x) (pow.f64 y #s(literal 4 binary64))) x) (/.f64 x (*.f64 y y))) (*.f64 y y))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 6)))) (+ (/ x (pow y 2)) (/ x (pow y 4)))) (pow y 2))
(/.f64 (-.f64 (-.f64 (/.f64 (neg.f64 x) (pow.f64 y #s(literal 6 binary64))) x) (/.f64 (/.f64 (+.f64 (/.f64 x (*.f64 y y)) x) y) y)) (*.f64 y y))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x 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 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (/.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)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* -1 (/ x (pow y 2)))
(/.f64 (/.f64 (neg.f64 x) y) y)
(/ (+ (* -1 x) (* -1 (/ x (pow y 2)))) (pow y 2))
(/.f64 (/.f64 (+.f64 (/.f64 x (*.f64 y y)) x) y) (neg.f64 y))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 4)))) (/ x (pow y 2))) (pow y 2))
(/.f64 (-.f64 (-.f64 (/.f64 (neg.f64 x) (pow.f64 y #s(literal 4 binary64))) x) (/.f64 x (*.f64 y y))) (*.f64 y y))
(/ (- (+ (* -1 x) (* -1 (/ x (pow y 6)))) (+ (/ x (pow y 2)) (/ x (pow y 4)))) (pow y 2))
(/.f64 (-.f64 (-.f64 (/.f64 (neg.f64 x) (pow.f64 y #s(literal 6 binary64))) x) (/.f64 (/.f64 (+.f64 (/.f64 x (*.f64 y y)) x) y) y)) (*.f64 y y))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) 1))
(fma.f64 (neg.f64 y) y #s(literal 1 binary64))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* x (pow y 2))
(*.f64 (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 (*.f64 y y) x 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 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (/.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)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ (* x (- 1 (pow y 4))) (- 1 (pow y 2)))
(*.f64 (/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(/ x (- 1 (pow y 2)))
(/.f64 x (fma.f64 (neg.f64 y) y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)
(* x (+ 1 (pow y 2)))
(fma.f64 (*.f64 y y) x x)

rewrite220.0ms (3.8%)

Memory
7.2MiB live, 285.8MiB allocated
Rules
4 966×lower-fma.f64
4 966×lower-fma.f32
3 408×lower-*.f32
3 402×lower-*.f64
2 980×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02082
02982
111476
263576
3656376
0802774
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
9 → 338
Calls
Call 1
Inputs
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))
#s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(/.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)
(neg.f64 y)
Outputs
(*.f64 (/.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (+.f64 (pow.f64 y #s(literal 12 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (/.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (/.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y)) #s(literal 2 binary64)))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (/.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (+.f64 (pow.f64 (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y)) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y)) (-.f64 (hypot.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y y)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (neg.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))) (neg.f64 x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) #s(literal 1 binary64)) (pow.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 (neg.f64 x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) x)
(*.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) x) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (pow.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x) (pow.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (neg.f64 x) (neg.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 x (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (*.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) x))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (/.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) x)))
(*.f64 (pow.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) x))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (neg.f64 x) (*.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 x (*.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (*.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) x) (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y)) x)))
(*.f64 (neg.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 8 binary64))) (neg.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))))
(*.f64 (neg.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 12 binary64))) (*.f64 (+.f64 (+.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))))))
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(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64)))))
(*.f64 #s(literal 1 binary64) #s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64))))
#s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64)))
(/.f64 (neg.f64 #s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64)))) #s(literal -1 binary64))
(/.f64 #s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64))) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64)))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (pow (+ (* y y) 1) -1) (pow.f64 y #s(literal -2 binary64)))))
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) y) (neg.f64 (pow.f64 y #s(literal 3 binary64)))) (*.f64 y y))
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) y) (*.f64 (neg.f64 y) y)) y)
(*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -1 binary64) y))
(*.f64 (neg.f64 (pow.f64 y #s(literal -2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 y #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64)))
(*.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 y #s(literal -2 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -2 binary64)))
(pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 y y) #s(literal -1 binary64))
(pow.f64 y #s(literal -2 binary64))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (neg.f64 y))
(/.f64 (*.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 y))
(/.f64 (/.f64 #s(literal -1 binary64) y) (neg.f64 y))
(/.f64 (neg.f64 (pow.f64 y #s(literal -2 binary64))) #s(literal -1 binary64))
(/.f64 (pow.f64 y #s(literal -1 binary64)) (neg.f64 (neg.f64 y)))
(/.f64 (pow.f64 y #s(literal -1 binary64)) y)
(/.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 y) y))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(neg.f64 (neg.f64 (pow.f64 y #s(literal -2 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 y #s(literal -2 binary64))))
(exp.f64 (*.f64 (log.f64 y) #s(literal -2 binary64)))
(exp.f64 (*.f64 #s(literal -2 binary64) (log.f64 y)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (neg.f64 y))
(*.f64 (/.f64 y #s(literal -1 binary64)) (neg.f64 y))
(*.f64 (neg.f64 (neg.f64 y)) y)
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 y) y))
(*.f64 (*.f64 (neg.f64 y) y) #s(literal -1 binary64))
(*.f64 (neg.f64 y) (/.f64 y #s(literal -1 binary64)))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 (*.f64 y y) #s(literal 1 binary64))
(*.f64 y (neg.f64 (neg.f64 y)))
(*.f64 y y)
(*.f64 #s(literal 1 binary64) (*.f64 y y))
(pow.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 0 binary64)) (-.f64 (*.f64 y y) #s(literal 0 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 y y)))))
(/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 y y) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (pow.f64 y #s(literal 4 binary64))) (*.f64 (neg.f64 y) y))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 y #s(literal -2 binary64))))
(/.f64 (*.f64 (neg.f64 y) y) #s(literal -1 binary64))
(/.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) y))
(/.f64 (*.f64 y y) #s(literal 1 binary64))
(/.f64 y (pow.f64 y #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -2 binary64)))
(neg.f64 (*.f64 (neg.f64 y) y))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (neg.f64 y) #s(literal 0 binary64))
(fma.f64 (/.f64 y #s(literal -1 binary64)) (neg.f64 y) #s(literal 0 binary64))
(fma.f64 (neg.f64 (neg.f64 y)) y #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 y) y) #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 y) y) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (neg.f64 y) (/.f64 y #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 y) (neg.f64 y) #s(literal 0 binary64))
(fma.f64 (*.f64 y y) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 y (neg.f64 (neg.f64 y)) #s(literal 0 binary64))
(fma.f64 y y #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 y y) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 y) y))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)))
(+.f64 #s(literal 0 binary64) (*.f64 y y))
(+.f64 (*.f64 y y) #s(literal 0 binary64))
(*.f64 (neg.f64 (pow.f64 y #s(literal 3 binary64))) (pow.f64 y #s(literal -2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 y y) y))
(*.f64 #s(literal -1 binary64) y)
(*.f64 (*.f64 (neg.f64 y) y) (pow.f64 y #s(literal -1 binary64)))
(*.f64 (neg.f64 y) (/.f64 y y))
(*.f64 y (/.f64 (neg.f64 y) y))
(*.f64 y #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 y) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 y y) (*.f64 #s(literal 0 binary64) (neg.f64 y)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 y #s(literal 3 binary64)))) (*.f64 (neg.f64 y) y))
(/.f64 (neg.f64 (pow.f64 y #s(literal 3 binary64))) (*.f64 y y))
(/.f64 (*.f64 (neg.f64 y) y) (-.f64 #s(literal 0 binary64) (neg.f64 y)))
(/.f64 (*.f64 (neg.f64 y) y) y)
(/.f64 (*.f64 y y) (neg.f64 y))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) (neg.f64 (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 y (*.f64 (neg.f64 y) y)))
(neg.f64 (/.f64 (*.f64 y y) y))
(neg.f64 y)
(fma.f64 (neg.f64 (pow.f64 y #s(literal 3 binary64))) (pow.f64 y #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 y y) y) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) y #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 y) y) (pow.f64 y #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 y) (/.f64 y y) #s(literal 0 binary64))
(fma.f64 y (/.f64 (neg.f64 y) y) #s(literal 0 binary64))
(fma.f64 y #s(literal -1 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 y y)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (*.f64 y y)))
(-.f64 (/.f64 #s(literal 0 binary64) y) (/.f64 (*.f64 y y) y))
(-.f64 #s(literal 0 binary64) y)
(+.f64 #s(literal 0 binary64) (neg.f64 y))
(+.f64 (neg.f64 y) #s(literal 0 binary64))

eval54.0ms (0.9%)

Memory
-0.2MiB live, 115.3MiB allocated
Compiler

Compiled 7 459 to 1 091 computations (85.4% saved)

prune12.0ms (0.2%)

Memory
1.2MiB live, 37.5MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New4790479
Fresh000
Picked022
Done033
Total4795484
Accuracy
100.0%
Counts
484 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.9%
(fma.f64 (*.f64 x y) y x)
✓42.6%
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
✓16.0%
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
✓42.6%
(*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y)))
✓54.7%
(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))
Compiler

Compiled 102 to 62 computations (39.2% saved)

regimes16.0ms (0.3%)

Memory
6.3MiB live, 44.5MiB allocated
Counts
8 → 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 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(approx (- 1 (* y y)) (*.f64 (neg.f64 y) y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
Outputs
(fma.f64 (*.f64 x y) y x)
Calls

5 calls:

4.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
3.0ms
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
3.0ms
x
3.0ms
y
3.0ms
(*.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
12.0MiB live, 12.0MiB 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
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
1.0ms
y
1.0ms
x
1.0ms
(*.f64 y y)
1.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Results
AccuracySegmentsBranch
54.7%1x
92.6%2y
72.4%2(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
92.6%2(+.f64 #s(literal 1 binary64) (*.f64 y y))
92.6%2(*.f64 y y)
Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes92.0ms (1.6%)

Memory
-27.3MiB live, 11.1MiB 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:

87.0ms
(*.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
54.7%1x
54.7%1(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
54.7%1y
54.7%1(+.f64 #s(literal 1 binary64) (*.f64 y y))
54.7%1(*.f64 y y)
Compiler

Compiled 17 to 18 computations (-5.9% saved)

bsearch12.0ms (0.2%)

Memory
16.1MiB live, 16.1MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
11.0ms
0.007442014416868639
154362433.05445054
Samples
5.0ms160×0valid
Compiler

Compiled 90 to 121 computations (-34.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-add: 1.0ms (45.4% of total)
ival-mult: 1.0ms (45.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify28.0ms (0.5%)

Memory
-0.0MiB live, 46.0MiB allocated
Algorithm
1×egg-herbie
Rules
6×*-commutative-binary64-*.f64
2×1-exp-binary32-exp.f32
2×1-exp-binary64-exp.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01441
12041
Stop Event
1×saturated
Calls
Call 1
Inputs
(fma.f64 (*.f64 x y) y x)
(if (<=.f64 (*.f64 y 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 (*.f64 y 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 (*.f64 y 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)

soundness456.0ms (7.9%)

Memory
-1.6MiB live, 266.9MiB allocated
Rules
9 064×lower-fma.f64
9 064×lower-fma.f32
6 574×lower-*.f64
6 574×lower-*.f32
5 176×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

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

Compiled 50 to 32 computations (36% saved)

preprocess105.0ms (1.8%)

Memory
-13.0MiB live, 123.1MiB allocated
Remove

(negabs x)

(abs y)

Compiler

Compiled 152 to 94 computations (38.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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