Numeric.Log:$clog1p from log-domain-0.10.2.1, A

Time bar (total: 4.1s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
1.3MiB live, 1.3MiB 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 13 to 10 computations (23.1% saved)

sample823.0ms (20.2%)

Memory
11.8MiB live, 1 054.2MiB allocated
Samples
575.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 337.0ms
ival-mult: 233.0ms (69.2% of total)
ival-add: 91.0ms (27% of total)
ival-true: 6.0ms (1.8% of total)
exact: 5.0ms (1.5% of total)
ival-assert: 3.0ms (0.9% of total)
Bogosity

explain172.0ms (4.2%)

Memory
-33.8MiB live, 124.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
00-0-(*.f64 x #s(literal 2 binary64))
00-0-#s(literal 2 binary64)
00-0-y
00-0-(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
00-0-(*.f64 y y)
00-0-(*.f64 x x)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
106.0ms512×0valid
Compiler

Compiled 77 to 28 computations (63.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 93.0ms
ival-mult: 88.0ms (94.9% of total)
ival-add: 4.0ms (4.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess40.0ms (1%)

Memory
22.1MiB live, 57.0MiB allocated
Algorithm
1×egg-herbie
Rules
266×sub-neg
198×unsub-neg
146×cancel-sign-sub-inv
142×associate-+l-
136×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02051
16849
221546
357845
4113245
5139645
6144545
0811
0139
1209
2309
3329
0328
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
Outputs
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
(fma.f64 (+.f64 #s(literal 2 binary64) x) x (*.f64 y y))
Symmetry

(abs y)

Compiler

Compiled 13 to 8 computations (38.5% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0.1%)

Memory
9.8MiB live, 9.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff128
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
cost-diff320
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
Rules
28×lower-fma.f64
28×lower-fma.f32
28×lower-+.f32
24×lower-+.f64
12×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0830
01326
12026
23026
33226
03225
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 x x)
(*.f64 y y)
y
Outputs
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
(fma.f64 (+.f64 #s(literal 2 binary64) x) x (*.f64 y y))
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (+.f64 #s(literal 2 binary64) x) x)
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)
(*.f64 x x)
(*.f64 y y)
y

localize48.0ms (1.2%)

Memory
-17.3MiB live, 58.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 y y)
accuracy0
(*.f64 x x)
accuracy0
(*.f64 x #s(literal 2 binary64))
accuracy0.0078125
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
Samples
40.0ms256×0valid
Compiler

Compiled 32 to 10 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 8.0ms (79% of total)
ival-add: 2.0ms (19.8% 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
13.2MiB live, 13.2MiB allocated
Counts
5 → 72
Calls
Call 1
Inputs
#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
Outputs
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 x)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 x)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 x)) (taylor 0 x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (patch (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x)))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x)))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) (patch (+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (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 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 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>) () ())) ())
Calls

18 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(+ (* x 2) (* x x))
0.0ms
x
@0
(+ (* x 2) (* x x))
0.0ms
y
@0
(+ (+ (* x 2) (* x x)) (* y y))
0.0ms
x
@-inf
(* x 2)
0.0ms
x
@0
(* x 2)

simplify161.0ms (3.9%)

Memory
-25.1MiB live, 188.2MiB allocated
Algorithm
1×egg-herbie
Rules
9 938×lower-fma.f64
9 938×lower-fma.f32
3 308×lower-*.f64
3 308×lower-*.f32
1 722×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036334
1101334
2272334
3917334
42774334
54851334
67645334
08375318
Stop Event
1×iter limit
1×node limit
Counts
72 → 72
Calls
Call 1
Inputs
(* 2 x)
(* x (+ 2 x))
(* x (+ 2 x))
(* x (+ 2 x))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
Outputs
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 y y (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.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)
(*.f64 y y)
(pow y 2)
(*.f64 y y)

rewrite182.0ms (4.5%)

Memory
11.2MiB live, 236.2MiB allocated
Rules
6 744×lower-fma.f64
6 744×lower-fma.f32
4 716×lower-*.f32
4 710×lower-*.f64
2 642×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0827
01323
14723
240623
3614823
0810222
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
5 → 219
Calls
Call 1
Inputs
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
(*.f64 x #s(literal 2 binary64))
(*.f64 x x)
(*.f64 y y)
Outputs
(*.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x))) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (*.f64 (*.f64 x x) x) (+.f64 #s(literal 2 binary64) x))))
(*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64))) (*.f64 (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64))))))) (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64))))))
(*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64))) (fma.f64 #s(literal 64 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (-.f64 x #s(literal 2 binary64))) (*.f64 x x)) (*.f64 x (-.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 x #s(literal 2 binary64)))))) (fma.f64 #s(literal 16 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (-.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (-.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(*.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (*.f64 (+.f64 #s(literal 2 binary64) x) x))
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) x) (/.f64 (*.f64 (-.f64 #s(literal 2 binary64) x) x) (-.f64 #s(literal 2 binary64) x)))
(*.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64)))) (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2 binary64) x) x))
(*.f64 (neg.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (-.f64 #s(literal 2 binary64) x))))
(*.f64 (neg.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64))))))
(*.f64 (+.f64 #s(literal 2 binary64) x) x)
(*.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 2 binary64) x) x)))
(*.f64 (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64)))))
(*.f64 (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64))))))
(*.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64)))))
(*.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) (/.f64 (*.f64 (-.f64 #s(literal 2 binary64) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x)))
(*.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) (*.f64 (*.f64 (-.f64 #s(literal 2 binary64) x) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 2 binary64) x) x))))
(*.f64 x (+.f64 #s(literal 2 binary64) x))
(pow.f64 (/.f64 (*.f64 x (-.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2 binary64) x) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2 binary64) x) x)) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) #s(literal 1 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) x) (-.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal 8 binary64)) x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64)))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 4 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 2 binary64) x) x))) (*.f64 (*.f64 x x) (+.f64 #s(literal 4 binary64) (*.f64 x x))))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64))) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 2 binary64) x) x))) (fma.f64 #s(literal 16 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) (+.f64 #s(literal 4 binary64) (*.f64 x x))))))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64))) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64))))) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))))
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) x #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64))))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))))
(/.f64 (*.f64 x (-.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 x (fma.f64 (*.f64 x x) x #s(literal 8 binary64))) (fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 4 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 2 binary64) x) x))) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x)))) (fma.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (*.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x))))))
(/.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x))) x) (-.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) #s(literal 4 binary64)))) (neg.f64 (*.f64 x (-.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 x x))))) (neg.f64 (*.f64 (neg.f64 x) (-.f64 #s(literal 2 binary64) x))))
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(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (-.f64 #s(literal 2 binary64) x) x)) (*.f64 y y)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 2 binary64) x) x (*.f64 y y)))) #s(literal -1 binary64)))
(+.f64 (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (*.f64 x x))
(+.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) (*.f64 (+.f64 #s(literal 2 binary64) x) x)) (fma.f64 (neg.f64 y) y (*.f64 (+.f64 #s(literal 2 binary64) x) x))) (neg.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 (neg.f64 y) y (*.f64 (+.f64 #s(literal 2 binary64) x) x)))))
(+.f64 (fma.f64 y y (*.f64 x x)) (*.f64 #s(literal 2 binary64) x))
(+.f64 (*.f64 y y) (*.f64 (+.f64 #s(literal 2 binary64) x) x))
(+.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) x) (*.f64 y y))
(+.f64 (*.f64 x x) (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
(+.f64 (*.f64 #s(literal 2 binary64) x) (fma.f64 y y (*.f64 x x)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.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)))

eval31.0ms (0.7%)

Memory
34.6MiB live, 71.6MiB allocated
Compiler

Compiled 8 903 to 676 computations (92.4% saved)

prune70.0ms (1.7%)

Memory
-28.4MiB live, 93.7MiB allocated
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2856291
Fresh000
Picked101
Done000
Total2866292
Accuracy
100.0%
Counts
292 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
83.9%
(+.f64 #s(approx (+ (* x 2) (* x x)) (*.f64 x x)) (*.f64 y y))
▶61.7%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
▶62.4%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
▶46.4%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
▶46.9%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
Compiler

Compiled 100 to 54 computations (46% saved)

simplify5.0ms (0.1%)

Memory
7.3MiB live, 7.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
cost-diff0
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
cost-diff0
(-.f64 x #s(literal -2 binary64))
cost-diff0
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
cost-diff0
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
cost-diff0
(*.f64 y y)
cost-diff0
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
cost-diff0
(*.f64 #s(literal 2 binary64) x)
cost-diff0
(fma.f64 y y (*.f64 #s(literal 2 binary64) x))
cost-diff192
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
Rules
28×lower-+.f64
28×lower-fma.f32
28×lower-+.f32
24×lower-fma.f64
14×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022116
030108
145108
249108
049103
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
x
(fma.f64 y y (*.f64 #s(literal 2 binary64) x))
y
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
(*.f64 y y)
y
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(-.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
y
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
Outputs
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
x
(fma.f64 y y (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 2 binary64) x (*.f64 y y))
y
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
(*.f64 y y)
y
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(-.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 #s(literal 2 binary64) x (*.f64 y y)))
(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) x (*.f64 y y))
y
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)

localize71.0ms (1.7%)

Memory
7.7MiB live, 84.2MiB allocated
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
accuracy0
(*.f64 x #s(literal 2 binary64))
accuracy24.54292647924658
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
accuracy0
(-.f64 x #s(literal -2 binary64))
accuracy0.01171875
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
accuracy24.07130873677366
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
accuracy0
(*.f64 y y)
accuracy34.27571489959532
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
accuracy0
(*.f64 x x)
accuracy34.00088511311027
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
accuracy0
(fma.f64 y y (*.f64 #s(literal 2 binary64) x))
accuracy0
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
accuracy0
(*.f64 #s(literal 2 binary64) x)
Samples
25.0ms256×0valid
Compiler

Compiled 101 to 17 computations (83.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 8.0ms (55% of total)
ival-add: 5.0ms (34.4% of total)
ival-sub: 1.0ms (6.9% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series12.0ms (0.3%)

Memory
-16.0MiB live, 20.1MiB allocated
Counts
13 → 240
Calls
Call 1
Inputs
#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) x) (patch (*.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)) #<representation binary64>) () ())
#s(alt (*.f64 (-.f64 x #s(literal -2 binary64)) x) (patch (*.f64 (-.f64 x #s(literal -2 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal -2 binary64)) (patch (-.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (pow y 2) (taylor 0 x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x)))) (taylor -inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x)))) (taylor -inf x) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (patch (fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) (patch (fma.f64 y y (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (pow y 2) x)) 2))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (pow y 2) x)) 2))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (pow y 2) x)) 2))) (taylor -inf x) (#s(alt (fma.f64 y y (*.f64 x #s(literal 2 binary64))) (patch (fma.f64 y y (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
Calls

60 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(* (- x -2) x)
0.0ms
x
@0
(* (- x -2) x)
0.0ms
x
@inf
(* (- x -2) x)
0.0ms
x
@0
(+ (* y y) (* 2 x))
0.0ms
x
@inf
(+ (* y y) (* 2 x))

simplify176.0ms (4.3%)

Memory
26.4MiB live, 185.9MiB allocated
Algorithm
1×egg-herbie
Rules
7 768×lower-fma.f64
7 768×lower-fma.f32
3 084×lower-*.f64
3 084×lower-*.f32
2 114×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0431472
11321472
23531376
312481376
434311376
574291376
083361260
Stop Event
1×iter limit
1×node limit
Counts
240 → 238
Calls
Call 1
Inputs
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* 2 x)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(* 2 x)
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* 2 x)
(* x (+ 2 x))
(* x (+ 2 x))
(* x (+ 2 x))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* 2 x)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(* 2 x)
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
Outputs
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.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)
(*.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)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
x
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
x
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))

rewrite210.0ms (5.2%)

Memory
5.1MiB live, 316.7MiB allocated
Rules
11 774×lower-fma.f32
11 770×lower-fma.f64
5 480×lower-*.f32
5 470×lower-*.f64
3 718×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022106
03098
111698
280798
0840393
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
13 → 352
Calls
Call 1
Inputs
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
(fma.f64 y y (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
(*.f64 x x)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
(*.f64 y y)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(-.f64 x #s(literal -2 binary64))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 (fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y)) (-.f64 (*.f64 x (-.f64 #s(literal 2 binary64) x)) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (-.f64 #s(literal 2 binary64) x)) (*.f64 y y))))
(*.f64 (*.f64 (fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y)) (-.f64 (*.f64 y y) (*.f64 (-.f64 x #s(literal -2 binary64)) x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y y) (*.f64 (-.f64 x #s(literal -2 binary64)) x))))
(*.f64 (*.f64 (fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y)) (fma.f64 y y (*.f64 x (-.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 y y (*.f64 x (-.f64 x #s(literal 2 binary64))))))
(*.f64 (*.f64 (fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y)) (fma.f64 y y (*.f64 x (-.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 y y (*.f64 x (-.f64 #s(literal 2 binary64) x)))))
(*.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y)))
(*.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x))) (fma.f64 y y (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x (-.f64 x #s(literal 2 binary64))))))))
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(*.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 (*.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 y y)) (*.f64 (fma.f64 y y (*.f64 #s(literal -2 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 y y))) #s(literal -1 binary64))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 #s(literal -4 binary64) (*.f64 x x))) #s(literal 1 binary64)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))
(/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y))) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 (*.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))) (*.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))))) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (fma.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) (*.f64 (*.f64 y y) y)))) (neg.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 #s(literal -4 binary64) (*.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y))))) (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 (*.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y)))))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (*.f64 (fma.f64 y y (*.f64 #s(literal -2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (*.f64 (fma.f64 y y (*.f64 #s(literal -2 binary64) x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 y y)))))
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) (*.f64 (*.f64 y y) y))) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y)) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) (*.f64 (*.f64 y y) y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 y y))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (*.f64 y y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))) (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 y y))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 #s(literal -4 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 y y (*.f64 #s(literal -2 binary64) x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y)))) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (*.f64 y y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y)))) (neg.f64 (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 (*.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y))))))
(/.f64 (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 #s(literal -4 binary64) (*.f64 x x))) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))
(/.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (*.f64 y y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (fma.f64 (*.f64 #s(literal 8 binary64) (*.f64 x x)) x (*.f64 (*.f64 (*.f64 y y) y) (*.f64 (*.f64 y y) y))) (fma.f64 (*.f64 (*.f64 y y) y) y (*.f64 (*.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y)))))
(neg.f64 (fma.f64 (neg.f64 y) y (*.f64 #s(literal -2 binary64) x)))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (/.f64 #s(literal 1 binary64) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (neg.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))))
(fma.f64 #s(literal 2 binary64) x (*.f64 y y))
(fma.f64 y y (*.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y))) (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 #s(literal 2 binary64) x (*.f64 (neg.f64 y) y))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) y) y) (fma.f64 y y (*.f64 #s(literal -2 binary64) x))) (neg.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 y y (*.f64 #s(literal -2 binary64) x)))))
(+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 y y))
(+.f64 (*.f64 y y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))

eval154.0ms (3.8%)

Memory
10.3MiB live, 168.2MiB allocated
Compiler

Compiled 11 558 to 805 computations (93% saved)

prune139.0ms (3.4%)

Memory
-25.6MiB live, 154.8MiB allocated
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New5873590
Fresh101
Picked145
Done000
Total5897596
Accuracy
100.0%
Counts
596 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶83.9%
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
▶62.4%
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
✓61.7%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
✓62.4%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
▶17.8%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
✓46.4%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
✓46.9%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
Compiler

Compiled 54 to 29 computations (46.3% saved)

simplify5.0ms (0.1%)

Memory
5.7MiB live, 5.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y y)
cost-diff0
#s(approx (+ (* y y) (* 2 x)) (*.f64 y y))
cost-diff0
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
#s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))
cost-diff0
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
cost-diff0
#s(approx (- x -2) #s(literal 2 binary64))
cost-diff0
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
cost-diff0
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
Rules
36×lower-+.f64
36×lower-+.f32
32×lower-fma.f32
28×lower-fma.f64
16×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02193
02691
14091
24791
04786
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
#s(approx (- x -2) #s(literal 2 binary64))
#s(literal 2 binary64)
x
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
x
#s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
x
#s(approx (+ (* y y) (* 2 x)) (*.f64 y y))
(*.f64 y y)
y
Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
#s(approx (- x -2) #s(literal 2 binary64))
#s(literal 2 binary64)
x
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)))
x
#s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))
#s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
x
#s(approx (+ (* y y) (* 2 x)) (*.f64 y y))
(*.f64 y y)
y

localize82.0ms (2%)

Memory
-10.3MiB live, 62.4MiB allocated
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
accuracy0
(*.f64 y y)
accuracy32.10492926775204
#s(approx (+ (* y y) (* 2 x)) (*.f64 y y))
accuracy0
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
accuracy0
(*.f64 x #s(literal 2 binary64))
accuracy30.442947279686635
#s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))
accuracy0.01171875
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
accuracy24.07130873677366
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
accuracy33.961614470513425
#s(approx (- x -2) #s(literal 2 binary64))
Samples
23.0ms256×0valid
Compiler

Compiled 69 to 16 computations (76.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-mult: 8.0ms (57.2% of total)
ival-add: 4.0ms (28.6% of total)
ival-sub: 1.0ms (7.2% 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
9.8MiB live, 9.8MiB allocated
Counts
9 → 168
Calls
Call 1
Inputs
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x) (patch (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (- x -2) #s(literal 2 binary64)) (patch #s(approx (- x -2) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())
Outputs
#s(alt (pow y 2) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x)))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (/ (pow y 2) x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (pow y 2) x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ 2 x)) (pow y 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (+ (* 2 x) (+ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2))))) (taylor -inf y) (#s(alt (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (patch (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor -inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor -inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x (pow y 2))))) (taylor -inf y) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (pow y 2)) (taylor 0 x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (/ (pow y 2) x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (/ (pow y 2) x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (patch #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt (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 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>) () ())) ())
Calls

42 calls:

TimeVariablePointExpression
0.0ms
y
@inf
(+ (* x x) (+ (* y y) (* 2 x)))
0.0ms
x
@0
(+ (+ (* x 2) (* x x)) (* y y))
0.0ms
y
@-inf
(+ (* x x) (+ (* y y) (* 2 x)))
0.0ms
x
@inf
(+ (+ (* x 2) (* x x)) (* y y))
0.0ms
y
@inf
(+ (+ (* x 2) (* x x)) (* y y))

simplify141.0ms (3.5%)

Memory
-5.1MiB live, 150.4MiB allocated
Algorithm
1×egg-herbie
Rules
7 768×lower-fma.f64
7 768×lower-fma.f32
3 084×lower-*.f64
3 084×lower-*.f32
2 114×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0431032
11321032
2353960
31256960
43436960
57419960
08331876
Stop Event
1×iter limit
1×node limit
Counts
168 → 166
Calls
Call 1
Inputs
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* 2 x)
(* x (+ 2 x))
(* x (+ 2 x))
(* x (+ 2 x))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* 2 x)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(* 2 x)
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(+ (* x (+ 2 x)) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(+ (* 2 x) (pow x 2))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* 2 x)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(pow y 2)
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(+ (* 2 x) (pow y 2))
(* 2 x)
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* x (+ 2 (/ (pow y 2) x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
Outputs
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* x (+ 2 x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
x
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
x
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* x (+ 2 x)) (pow y 2))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) 2) x))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (pow x 2))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(+ (* 2 x) (+ (pow x 2) (pow y 2)))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* (pow y 2) (+ 1 (+ (* 2 (/ x (pow y 2))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (-.f64 x #s(literal -2 binary64)) x (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (* 2 (/ x (pow y 2)))))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(+ (* 2 x) (pow y 2))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* x (+ 2 (/ (pow y 2) x)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
(* -1 (* x (- (* -1 (/ (pow y 2) x)) 2)))
(fma.f64 x #s(literal 2 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)
(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)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)

rewrite232.0ms (5.7%)

Memory
-0.0MiB live, 152.0MiB allocated
Rules
5 342×lower-fma.f32
5 338×lower-fma.f64
4 918×lower-*.f32
4 912×lower-*.f64
4 224×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02187
02685
111585
283785
0829880
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
9 → 98
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
#s(approx (- x -2) #s(literal 2 binary64))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
#s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
#s(approx (+ (* y y) (* 2 x)) (*.f64 y y))
(*.f64 y y)
Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
(*.f64 x #s(approx (- x -2) #s(literal 2 binary64)))
#s(approx (- x -2) #s(literal 2 binary64))
(*.f64 (*.f64 (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x))) (-.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)) (*.f64 x x))))
(*.f64 #s(literal 1 binary64) (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x))))
(*.f64 (*.f64 (neg.f64 (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)))) (-.f64 (*.f64 x x) #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 x x) #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)) #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x))) #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x)) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) x) x)))))
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(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 (*.f64 x x) #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))) (/.f64 (*.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (-.f64 (*.f64 x x) #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 (*.f64 x x) #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))) (neg.f64 (/.f64 (*.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))) (-.f64 (*.f64 x x) #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))))))
(+.f64 #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)) (*.f64 x x))
(+.f64 (*.f64 x x) #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
#s(approx (+ (* y y) (* 2 x)) (*.f64 y y))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval52.0ms (1.3%)

Memory
9.8MiB live, 59.8MiB allocated
Compiler

Compiled 5 110 to 280 computations (94.5% saved)

prune28.0ms (0.7%)

Memory
3.4MiB live, 40.9MiB allocated
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New2640264
Fresh000
Picked033
Done044
Total2647271
Accuracy
100.0%
Counts
271 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓83.9%
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
✓62.4%
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
✓61.7%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
✓62.4%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
✓17.8%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
✓46.4%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
✓46.9%
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
Compiler

Compiled 124 to 47 computations (62.1% saved)

regimes20.0ms (0.5%)

Memory
11.6MiB live, 47.3MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
(+.f64 #s(approx (+ (* x 2) (* x x)) (*.f64 x x)) (*.f64 y y))
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
Outputs
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
Calls

5 calls:

5.0ms
(*.f64 y y)
4.0ms
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
4.0ms
y
4.0ms
x
3.0ms
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
100.0%1(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
100.0%1(*.f64 y y)
Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes27.0ms (0.7%)

Memory
-5.9MiB live, 31.1MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
(+.f64 #s(approx (+ (* x 2) (* x x)) (*.f64 x x)) (*.f64 y y))
Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y)))
Calls

5 calls:

14.0ms
(*.f64 y y)
3.0ms
y
3.0ms
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
3.0ms
x
3.0ms
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
Results
AccuracySegmentsBranch
98.7%3x
97.2%2y
98.7%2(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
98.7%2(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
97.2%2(*.f64 y y)
Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes52.0ms (1.3%)

Memory
-48.2MiB live, 20.8MiB allocated
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
(fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64))))
Calls

5 calls:

40.0ms
(*.f64 y y)
3.0ms
x
3.0ms
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
3.0ms
y
3.0ms
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
Results
AccuracySegmentsBranch
93.4%3x
87.2%2y
87.2%2(*.f64 y y)
70.5%2(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
92.6%2(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes3.0ms (0.1%)

Memory
3.7MiB live, 3.7MiB allocated
Counts
5 → 2
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64))))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
Calls

1 calls:

2.0ms
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
Results
AccuracySegmentsBranch
92.6%2(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

regimes9.0ms (0.2%)

Memory
13.1MiB live, 13.1MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
Calls

4 calls:

2.0ms
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
2.0ms
x
2.0ms
y
2.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
87.1%2y
87.1%2(*.f64 y y)
78.3%3x
77.8%2(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
Compiler

Compiled 20 to 13 computations (35% saved)

regimes18.0ms (0.5%)

Memory
-20.1MiB live, 17.1MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
Calls

4 calls:

12.0ms
x
2.0ms
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
2.0ms
y
2.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
78.0%3x
76.7%2(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
71.6%2y
71.6%2(*.f64 y y)
Compiler

Compiled 20 to 13 computations (35% saved)

regimes7.0ms (0.2%)

Memory
21.0MiB live, 21.0MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

5 calls:

1.0ms
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
1.0ms
y
1.0ms
x
1.0ms
(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
1.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
46.9%1(+.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) (*.f64 y y))
46.9%1y
46.9%1(*.f64 y y)
46.9%1x
46.9%1(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))
Compiler

Compiled 33 to 21 computations (36.4% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0033335999839587695
270.2489161690043
Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
4.1967728499386024e-8
0.0033335999839587695
Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
4.1967728499386024e-8
0.0033335999839587695
Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch15.0ms (0.4%)

Memory
-0.1MiB live, 35.2MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
1.83166734850442e+39
5.639213386618228e+44
Samples
6.0ms144×0valid
Compiler

Compiled 142 to 94 computations (33.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 2.0ms (61% of total)
ival-add: 1.0ms (30.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.1084049941421173e+51
5.198834081153152e+58
Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify9.0ms (0.2%)

Memory
-14.9MiB live, 22.0MiB allocated
Algorithm
1×egg-herbie
Rules
6×*-commutative_binary64
6×+-commutative_binary64
4×sub-neg_binary64
2×neg-sub0_binary64
2×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042231
147231
252231
354231
455231
Stop Event
1×saturated
Calls
Call 1
Inputs
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 944473296573929/18889465931478580854784 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 944473296573929/18889465931478580854784 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)))
(if (<=.f64 (*.f64 y y) #s(literal 5099999999999999828520903201821992943616 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 1999999999999999986441897348723255952923416883888128 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x)))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
Outputs
(fma.f64 x x (fma.f64 y y (*.f64 #s(literal 2 binary64) x)))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))))
(if (<=.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 2 binary64) x)) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 y y))))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 944473296573929/18889465931478580854784 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 x #s(literal 2 binary64)))))
(if (<=.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 2 binary64) x)) #s(literal 944473296573929/18889465931478580854784 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) (fma.f64 x x #s(approx (+ (* y y) (* 2 x)) (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 944473296573929/18889465931478580854784 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 x #s(literal 2 binary64)))) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)))
(if (<=.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 2 binary64) x)) #s(literal 944473296573929/18889465931478580854784 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 y y (*.f64 #s(literal 2 binary64) x))) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)))
(if (<=.f64 (*.f64 y y) #s(literal 5099999999999999828520903201821992943616 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)))
(if (<=.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x)) #s(literal 1999999999999999986441897348723255952923416883888128 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x)))
(if (<=.f64 (+.f64 (*.f64 x x) (*.f64 #s(literal 2 binary64) x)) #s(literal 1999999999999999986441897348723255952923416883888128 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x)))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

soundness1.0s (24.9%)

Memory
-6.1MiB live, 559.3MiB allocated
Rules
9 938×lower-fma.f64
9 938×lower-fma.f32
7 768×lower-fma.f64
7 768×lower-fma.f32
6 744×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036334
1101334
2272334
3917334
42774334
54851334
67645334
08375318
0827
01323
14723
240623
3614823
0810222
0431472
11321472
23531376
312481376
434311376
574291376
083361260
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 287 to 112 computations (61% saved)

preprocess57.0ms (1.4%)

Memory
25.9MiB live, 144.9MiB allocated
Remove

(abs y)

Compiler

Compiled 314 to 98 computations (68.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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