Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Time bar (total: 3.9s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 11 to 10 computations (9.1% saved)

sample738.0ms (18.8%)

Memory
21.5MiB live, 1 399.8MiB allocated
Samples
503.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 223.0ms
ival-add: 80.0ms (35.8% of total)
ival-mult: 68.0ms (30.5% of total)
ival-div: 61.0ms (27.3% of total)
ival-true: 6.0ms (2.7% of total)
exact: 4.0ms (1.8% of total)
ival-assert: 3.0ms (1.3% of total)
Bogosity

explain87.0ms (2.2%)

Memory
4.4MiB live, 125.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
00-0-#s(literal 2 binary64)
00-0-y
00-0-(/.f64 x #s(literal 2 binary64))
00-0-z
00-0-(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
00-0-(*.f64 y 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
33.0ms512×0valid
Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-add: 10.0ms (54.8% of total)
ival-mult: 4.0ms (21.9% of total)
ival-div: 3.0ms (16.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess89.0ms (2.3%)

Memory
-3.5MiB live, 30.7MiB allocated
Algorithm
egg-herbie
Rules
386×distribute-rgt-in
336×sub-neg
268×unsub-neg
230×associate-+l-
226×cancel-sign-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03288
18882
223281
366269
4116665
5171463
6219063
7237663
8242463
9243263
10243263
089
0129
1179
2249
3269
0268
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
Outputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 z (fma.f64 y x (/.f64 x #s(literal 2 binary64))))
Compiler

Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Memory
2.8MiB live, 2.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y x)
cost-diff0
(/.f64 x #s(literal 2 binary64))
cost-diff0
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
cost-diff128
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
Rules
24×lower-+.f32
20×lower-+.f64
12×lower-fma.f64
12×lower-fma.f32
10×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0826
01226
11726
22426
32626
02624
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 y x)
y
z
Outputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 z (fma.f64 y x (/.f64 x #s(literal 2 binary64))))
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
(fma.f64 y x (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 y x)
y
z

localize18.0ms (0.5%)

Memory
17.7MiB live, 17.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(/.f64 x #s(literal 2 binary64))
accuracy0
(*.f64 y x)
accuracy0.00390625
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
accuracy0.00390625
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
Samples
13.0ms256×0valid
Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-div: 2.0ms (33.3% of total)
ival-add: 2.0ms (33.3% of total)
ival-mult: 2.0ms (33.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory
8.2MiB live, 8.2MiB allocated
Counts
4 → 96
Calls
Call 1
Inputs
#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())
#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())
#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())
Outputs
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt z (taylor inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt z (taylor -inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y))))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y))))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y))))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor 0 x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor 0 x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor 0 x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor 0 x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt z (taylor 0 x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (* x (+ 1/2 y))) (taylor 0 x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (* x (+ 1/2 y))) (taylor 0 x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (+ z (* x (+ 1/2 y))) (taylor 0 x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (+ y (/ z x)))) (taylor inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (+ y (/ z x)))) (taylor inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (+ y (/ z x)))) (taylor inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
1.0ms
x
@inf
((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
1.0ms
y
@-inf
((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
1.0ms
x
@0
((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
0.0ms
y
@0
((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))

simplify172.0ms (4.4%)

Memory
-39.4MiB live, 168.3MiB allocated
Algorithm
egg-herbie
Rules
6 434×lower-fma.f64
6 434×lower-fma.f32
2 474×lower-*.f64
2 474×lower-*.f32
1 356×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057440
1174440
2488440
31308440
43609440
56674440
08210412
Stop Event
iter limit
node limit
Counts
96 → 93
Calls
Call 1
Inputs
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* 1/2 x)
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x y)
(* x y)
(* x y)
(* x y)
Outputs
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x y)
(*.f64 y x)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x y)
(*.f64 y x)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
z
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)

rewrite256.0ms (6.5%)

Memory
25.2MiB live, 180.5MiB allocated
Rules
7 074×lower-fma.f64
7 074×lower-fma.f32
4 356×lower-*.f32
4 354×lower-*.f64
2 578×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0822
01222
15218
245218
3607718
0804017
Stop Event
iter limit
node limit
iter limit
Counts
4 → 242
Calls
Call 1
Inputs
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(/.f64 x #s(literal 2 binary64))
(*.f64 y x)
Outputs
(*.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 y y))) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 y y) y)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 y x) x) (+.f64 #s(literal 1/2 binary64) y))))
(*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x)) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x))))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (*.f64 (*.f64 (neg.f64 x) y) (*.f64 x (-.f64 y #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x)) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x))) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x))))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/16 binary64) (*.f64 (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x)) (-.f64 (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
(*.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 y y))) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 y y)))) (*.f64 (+.f64 #s(literal 1/2 binary64) y) x))
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) x) (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) y) x) (-.f64 #s(literal 1/2 binary64) y)))
(*.f64 (+.f64 #s(literal 1/2 binary64) y) x)
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(fma.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (*.f64 (+.f64 #s(literal 1/2 binary64) y) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z))) (neg.f64 (/.f64 (*.f64 z z) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z)))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x))) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x)))) z)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x))) (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x))))) z)
(fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (*.f64 (*.f64 x (-.f64 y #s(literal 1/2 binary64))) (*.f64 y x)))) z)
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (fma.f64 y x z))
(fma.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z))) (neg.f64 (/.f64 (*.f64 z z) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z)))))
(fma.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) y) x) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)) z)
(fma.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (*.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))) z)
(fma.f64 (*.f64 y x) #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) (fma.f64 y x z))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y x z))
(fma.f64 x y (fma.f64 #s(literal 1/2 binary64) x z))
(-.f64 (+.f64 z (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))) (/.f64 (*.f64 (*.f64 x x) (*.f64 y y)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)))
(-.f64 (/.f64 (*.f64 z z) (-.f64 z (*.f64 (+.f64 #s(literal 1/2 binary64) y) x))) (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (*.f64 (+.f64 #s(literal 1/2 binary64) y) x)) (-.f64 z (*.f64 (+.f64 #s(literal 1/2 binary64) y) x))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) y) x) z)) (/.f64 (*.f64 (fma.f64 y x z) (fma.f64 y x z)) (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) y) x) z)))
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (*.f64 (+.f64 #s(literal 1/2 binary64) y) x)) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z))) (/.f64 (*.f64 z z) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)) (-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 y y)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)) z))
(-.f64 (fma.f64 y x z) (*.f64 #s(literal -1/2 binary64) x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z))) #s(literal -1 binary64)))
(+.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 y x))
(+.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) (*.f64 (+.f64 #s(literal 1/2 binary64) y) x)) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z))) (neg.f64 (/.f64 (*.f64 z z) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x (neg.f64 z)))))
(+.f64 (fma.f64 y x z) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 z (*.f64 (+.f64 #s(literal 1/2 binary64) y) x))
(+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) y) x) z)
(+.f64 (*.f64 y x) (fma.f64 #s(literal 1/2 binary64) x z))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 y x z))
(*.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) x))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) y) x)
(*.f64 #s(literal 1 binary64) (*.f64 y x))
(*.f64 (*.f64 y x) #s(literal 1 binary64))
(*.f64 y x)
(*.f64 x y)

eval153.0ms (3.9%)

Memory
-13.2MiB live, 68.7MiB allocated
Compiler

Compiled 7 883 to 738 computations (90.6% saved)

prune49.0ms (1.2%)

Memory
-12.3MiB live, 65.6MiB allocated
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3296335
Fresh000
Picked101
Done000
Total3306336
Accuracy
100.0%
Counts
336 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
100.0%
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
69.1%
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
68.8%
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
62.7%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
33.1%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
Compiler

Compiled 104 to 64 computations (38.5% saved)

simplify6.0ms (0.2%)

Memory
5.9MiB live, 5.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y x)
cost-diff0
#s(approx (+ (/ x 2) (* y x)) (*.f64 y x))
cost-diff0
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
cost-diff0
(-.f64 y #s(literal -1/2 binary64))
cost-diff0
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
cost-diff0
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
cost-diff0
(fma.f64 x #s(literal 1/2 binary64) z)
cost-diff0
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
cost-diff0
(*.f64 y x)
cost-diff0
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
cost-diff0
(fma.f64 #s(literal 1/2 binary64) x z)
cost-diff192
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
Rules
52×lower-+.f32
50×lower-+.f64
36×lower-fma.f32
30×lower-fma.f64
24×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021110
030110
145110
260110
362110
062104
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
y
x
(fma.f64 #s(literal 1/2 binary64) x z)
#s(literal 1/2 binary64)
z
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
(*.f64 y x)
y
x
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
(fma.f64 x #s(literal 1/2 binary64) z)
x
#s(literal 1/2 binary64)
z
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(-.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
x
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
#s(approx (+ (/ x 2) (* y x)) (*.f64 y x))
(*.f64 y x)
y
x
z
Outputs
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
y
x
(fma.f64 #s(literal 1/2 binary64) x z)
#s(literal 1/2 binary64)
z
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y))
(*.f64 y x)
(*.f64 x y)
y
x
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 x #s(literal 1/2 binary64) z)
(fma.f64 #s(literal 1/2 binary64) x z)
x
#s(literal 1/2 binary64)
z
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(-.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
x
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)
#s(approx (+ (/ x 2) (* y x)) (*.f64 y x))
#s(approx (+ (/ x 2) (* y x)) (*.f64 x y))
(*.f64 y x)
(*.f64 x y)
y
x
z

localize40.0ms (1%)

Memory
7.8MiB live, 45.8MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 y x)
accuracy0.00390625
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
accuracy34.16106322160491
#s(approx (+ (/ x 2) (* y x)) (*.f64 y x))
accuracy0
(-.f64 y #s(literal -1/2 binary64))
accuracy0.0078125
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
accuracy23.88484690290038
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
accuracy0
(fma.f64 x #s(literal 1/2 binary64) z)
accuracy19.961262715191165
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
accuracy0
(*.f64 y x)
accuracy42.837006664021835
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
accuracy0
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
accuracy0
(fma.f64 #s(literal 1/2 binary64) x z)
Samples
30.0ms256×0valid
Compiler

Compiled 93 to 19 computations (79.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-mult: 6.0ms (34.7% of total)
ival-add: 5.0ms (28.9% of total)
ival-sub: 3.0ms (17.4% of total)
ival-div: 1.0ms (5.8% of total)
exact: 1.0ms (5.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series14.0ms (0.4%)

Memory
17.9MiB live, 17.9MiB allocated
Counts
11 → 312
Calls
Call 1
Inputs
#s(alt (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) (patch (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x z) (patch (fma.f64 #s(literal 1/2 binary64) x z) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) #<representation binary64>) () ())
#s(alt (*.f64 y x) (patch (*.f64 y x) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (patch (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 y #s(literal -1/2 binary64)) (patch (-.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) (patch (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) #<representation binary64>) () ())
#s(alt #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) (patch #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) #<representation binary64>) () ())
Outputs
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 z) (#s(alt (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) (patch (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) (patch (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) (patch (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) (patch (fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 z) (#s(alt (fma.f64 #s(literal 1/2 binary64) x z) (patch (fma.f64 #s(literal 1/2 binary64) x z) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt (fma.f64 #s(literal 1/2 binary64) x z) (patch (fma.f64 #s(literal 1/2 binary64) x z) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt (fma.f64 #s(literal 1/2 binary64) x z) (patch (fma.f64 #s(literal 1/2 binary64) x z) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt (fma.f64 #s(literal 1/2 binary64) x z) (patch (fma.f64 #s(literal 1/2 binary64) x z) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 z) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ z x)) 1/2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ z x)) 1/2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ z x)) 1/2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor -inf x) (#s(alt (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (patch (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor -inf x) (#s(alt (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (patch (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor -inf x) (#s(alt (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (patch (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor -inf x) (#s(alt (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (patch (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) (patch (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) (patch (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) (patch (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2))) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) (patch (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) (patch #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) (patch #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) (patch #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 y) 1/2))) (taylor -inf x) (#s(alt #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) (patch #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms
x
@inf
((+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms
y
@-inf
((+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms
x
@0
((+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms
y
@inf
((+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))

simplify142.0ms (3.6%)

Memory
-11.0MiB live, 66.8MiB allocated
Algorithm
egg-herbie
Rules
6 334×lower-fma.f64
6 334×lower-fma.f32
2 392×lower-*.f64
2 392×lower-*.f32
1 382×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0721624
12231624
25981624
317581624
437791624
557921624
672441624
080301448
Stop Event
iter limit
node limit
Counts
312 → 289
Calls
Call 1
Inputs
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* 1/2 x)
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* 1/2 x)
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
z
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
z
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* x y)
(* x y)
(* x y)
(* x y)
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* 1/2 x)
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
1/2
(+ 1/2 y)
(+ 1/2 y)
(+ 1/2 y)
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* 1/2 x)
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
z
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* x y)
(* x y)
(* x y)
(* x y)
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
z
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* 1/2 x)
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* 1/2 x)
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* 1/2 x)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* 1/2 x)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
Outputs
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ z (+ (* 1/2 x) (* x y)))
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(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ z x)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* x (+ 1/2 (/ z x)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* x (+ 1/2 (/ z x)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)

rewrite229.0ms (5.8%)

Memory
-4.1MiB live, 167.2MiB allocated
Rules
7 048×lower-fma.f32
7 042×lower-fma.f64
4 190×lower-/.f64
4 190×lower-/.f32
4 144×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02192
03086
113982
296082
0832478
Stop Event
iter limit
node limit
iter limit
Counts
11 → 375
Calls
Call 1
Inputs
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 #s(literal 1/2 binary64) x z)
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
(*.f64 y x)
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
(fma.f64 x #s(literal 1/2 binary64) z)
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(-.f64 y #s(literal -1/2 binary64))
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
#s(approx (+ (/ x 2) (* y x)) (*.f64 y x))
Outputs
(*.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 x y z))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 x y z))))
(*.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (-.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 x y))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 x y))))
(*.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (-.f64 z (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (-.f64 z (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (fma.f64 x y z) (fma.f64 x y z)) (fma.f64 x y z))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (fma.f64 (fma.f64 x y z) (fma.f64 x y z) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (fma.f64 x y z))))))
(*.f64 (*.f64 (neg.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z)))))
(*.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (fma.f64 (neg.f64 x) y (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) y (fma.f64 #s(literal 1/2 binary64) x z))))
(*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (*.f64 z z) z))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) (-.f64 y #s(literal -1/2 binary64))) (*.f64 x x) (*.f64 z (-.f64 z (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 y y) y) (*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (fma.f64 #s(literal 1/2 binary64) x z)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 (*.f64 x y) x) y (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (-.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 x y)))))))
(*.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))))
(*.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) y (fma.f64 #s(literal 1/2 binary64) x z))))
(*.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z))
(*.f64 (fma.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (*.f64 z z) z)) (/.f64 #s(literal 1 binary64) (fma.f64 z z (-.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) z)))))
(*.f64 (fma.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (*.f64 z z) z)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) (-.f64 y #s(literal -1/2 binary64))) (*.f64 x x) (*.f64 z (-.f64 z (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 y y) y) (*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z) (-.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (*.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 y y) y) (*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x y) x) y (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (-.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 x y))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z)))) (*.f64 (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))))) (+.f64 (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z)))) (*.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))))) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z)))))
(/.f64 (-.f64 (*.f64 (fma.f64 x y z) (fma.f64 x y z)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (-.f64 (fma.f64 x y z) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (fma.f64 (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (*.f64 (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (fma.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 x y) x) y) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z))) (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x z) (fma.f64 #s(literal 1/2 binary64) x z)) (-.f64 (*.f64 x y) (fma.f64 #s(literal 1/2 binary64) x z)))))))
(/.f64 (fma.f64 (*.f64 (fma.f64 x y z) (fma.f64 x y z)) (fma.f64 x y z) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 (fma.f64 x y z) (fma.f64 x y z) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 x y z) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 x y z)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 x y z))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (-.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 x y)))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 x y))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (-.f64 z (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)))) (neg.f64 (-.f64 z (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (fma.f64 x y z) (fma.f64 x y z)) (fma.f64 x y z)))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (fma.f64 (fma.f64 x y z) (fma.f64 x y z) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (fma.f64 x y z))))))
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(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 z z (fma.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 (neg.f64 z) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))))) (fma.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 (*.f64 z z) z))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)))
(/.f64 (fma.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 (*.f64 z z) z)) (fma.f64 z z (fma.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 (neg.f64 z) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))))))
(/.f64 (fma.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 (*.f64 z z) z)) (fma.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 z (-.f64 z #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))))))
(neg.f64 (/.f64 (*.f64 (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z) (neg.f64 (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z))) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 (*.f64 z z) z))) (fma.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 z (-.f64 z #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)))))))
(neg.f64 (/.f64 (*.f64 (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)) (neg.f64 (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z))))
(neg.f64 (/.f64 (fma.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 (*.f64 z z) z)) (neg.f64 (fma.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) (*.f64 z (-.f64 z #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))))))))
(fma.f64 #s(literal 1 binary64) z #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)))
(fma.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)) (neg.f64 (/.f64 (*.f64 z z) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z))))
(-.f64 (/.f64 (*.f64 z z) (-.f64 z #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)))) (/.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) (-.f64 z #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)))))
(-.f64 (/.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)) (/.f64 (*.f64 z z) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)))
(+.f64 (/.f64 (*.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) #s(approx (+ (/ x 2) (* y x)) (*.f64 x y))) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)) (neg.f64 (/.f64 (*.f64 z z) (-.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z))))
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)
(+.f64 z #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)))
#s(approx (+ (/ x 2) (* y x)) (*.f64 x y))

eval84.0ms (2.1%)

Memory
3.4MiB live, 160.4MiB allocated
Compiler

Compiled 11 662 to 908 computations (92.2% saved)

prune79.0ms (2%)

Memory
9.2MiB live, 129.5MiB allocated
Pruning

8 alts after pruning (3 fresh and 5 done)

PrunedKeptTotal
New6883691
Fresh101
Picked055
Done000
Total6898697
Accuracy
100.0%
Counts
697 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
100.0%
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
62.7%
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
69.1%
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
68.8%
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
62.7%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
31.9%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
33.1%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
Compiler

Compiled 70 to 43 computations (38.6% saved)

simplify9.0ms (0.2%)

Memory
-30.9MiB live, 8.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 y #s(literal -1/2 binary64))
cost-diff0
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
cost-diff0
(*.f64 x #s(literal 1/2 binary64))
cost-diff0
#s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))
cost-diff0
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
cost-diff0
#s(approx (- y -1/2) #s(literal 1/2 binary64))
cost-diff0
(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
Rules
52×lower-+.f64
52×lower-+.f32
40×lower-fma.f32
36×lower-fma.f64
18×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02171
02771
14071
24971
35471
45671
05668
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
#s(approx (- y -1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
y
x
#s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(-.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
x
z
Outputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
#s(approx (- y -1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))
y
x
#s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(-.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
x
z

localize35.0ms (0.9%)

Memory
21.5MiB live, 60.2MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 y #s(literal -1/2 binary64))
accuracy0.0078125
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
accuracy0
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
accuracy0
(*.f64 x #s(literal 1/2 binary64))
accuracy30.22529832224339
#s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))
accuracy0.0078125
(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
accuracy23.88484690290038
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
accuracy28.406650472667717
#s(approx (- y -1/2) #s(literal 1/2 binary64))
Samples
26.0ms256×0valid
Compiler

Compiled 55 to 19 computations (65.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 6.0ms (39.6% of total)
ival-add: 5.0ms (33% of total)
ival-div: 2.0ms (13.2% of total)
ival-sub: 1.0ms (6.6% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory
14.1MiB live, 14.1MiB allocated
Counts
8 → 192
Calls
Call 1
Inputs
#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x) (patch (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (- y -1/2) #s(literal 1/2 binary64)) (patch #s(approx (- y -1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 1/2 binary64)) (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())
#s(alt (-.f64 y #s(literal -1/2 binary64)) (patch (-.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* x y)) (taylor 0 z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ z (+ (* 1/2 x) (* x y))) (taylor 0 z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ z (* 1/2 x)) (taylor 0 z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 y)) (taylor 0 z) (#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())) ())
#s(alt (+ z (* x (+ 1/2 y))) (taylor 0 z) (#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())) ())
#s(alt (+ z (* x (+ 1/2 y))) (taylor 0 z) (#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())) ())
#s(alt (+ z (* x (+ 1/2 y))) (taylor 0 z) (#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())) ())
#s(alt z (taylor inf z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt z (taylor inf z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z)))) (taylor inf z) (#s(alt (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) (patch (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt z (taylor inf z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (* 1/2 (/ x z)))) (taylor inf z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (* 1/2 (/ x z)))) (taylor inf z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (* 1/2 (/ x z)))) (taylor inf z) (#s(alt #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt z (taylor inf z) (#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (/ (* x (+ 1/2 y)) z))) (taylor inf z) (#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x))))) (taylor -inf x) (#s(alt (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) (patch (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (* x 1/2) (+ (* (- y -1/2) x) z) (- y -1/2))
1.0ms
x
@inf
((+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (* x 1/2) (+ (* (- y -1/2) x) z) (- y -1/2))
0.0ms
y
@-inf
((+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (* x 1/2) (+ (* (- y -1/2) x) z) (- y -1/2))
0.0ms
z
@inf
((+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (* x 1/2) (+ (* (- y -1/2) x) z) (- y -1/2))
0.0ms
x
@0
((+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (* y x) (+ (* 1/2 x) z)) (+ (* 1/2 x) z) (* x 1/2) (+ (* (- y -1/2) x) z) (- y -1/2))

simplify201.0ms (5.1%)

Memory
-2.6MiB live, 151.4MiB allocated
Algorithm
egg-herbie
Rules
6 552×lower-fma.f64
6 552×lower-fma.f32
2 372×lower-*.f64
2 372×lower-*.f32
1 408×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083966
1270966
2723966
32011966
44157966
56218966
67531966
08023864
Stop Event
iter limit
node limit
Counts
192 → 176
Calls
Call 1
Inputs
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* 1/2 x)
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(* x (+ 1/2 y))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
z
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
z
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
z
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* 1/2 x)
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
1/2
(+ 1/2 y)
(+ 1/2 y)
(+ 1/2 y)
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
1/2
(+ 1/2 y)
(+ 1/2 y)
(+ 1/2 y)
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
z
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* 1/2 x)
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* 1/2 x)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 y))
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
Outputs
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* z (+ 1 (* 1/2 (/ x z))))
(fma.f64 x #s(literal 1/2 binary64) z)
(* z (+ 1 (* 1/2 (/ x z))))
(fma.f64 x #s(literal 1/2 binary64) z)
(* z (+ 1 (* 1/2 (/ x z))))
(fma.f64 x #s(literal 1/2 binary64) z)
z
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(fma.f64 x #s(literal 1/2 binary64) z)
z
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(+ (* 1/2 x) (* x y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 y)
(-.f64 y #s(literal -1/2 binary64))
(+ 1/2 y)
(-.f64 y #s(literal -1/2 binary64))
(+ 1/2 y)
(-.f64 y #s(literal -1/2 binary64))
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
1/2
#s(literal 1/2 binary64)
(+ 1/2 y)
(-.f64 y #s(literal -1/2 binary64))
(+ 1/2 y)
(-.f64 y #s(literal -1/2 binary64))
(+ 1/2 y)
(-.f64 y #s(literal -1/2 binary64))
(* x y)
(*.f64 y x)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* x y)
(*.f64 y x)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* x y)
(*.f64 y x)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* x y)
(*.f64 y x)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x y)
(*.f64 y x)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
(* y (+ 1 (* 1/2 (/ 1 y))))
(-.f64 y #s(literal -1/2 binary64))
z
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
z
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
z
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
z
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(+ z (* x (+ 1/2 y)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ z x)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* x (+ 1/2 (/ z x)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* x (+ 1/2 (/ z x)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 x #s(literal 1/2 binary64) z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 y))
(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)

rewrite194.0ms (4.9%)

Memory
-8.2MiB live, 311.1MiB allocated
Rules
12 994×lower-fma.f32
12 990×lower-fma.f64
5 638×lower-*.f32
5 634×lower-*.f64
3 354×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02162
02762
112459
295159
0858457
Stop Event
iter limit
node limit
iter limit
Counts
8 → 225
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
#s(approx (- y -1/2) #s(literal 1/2 binary64))
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(-.f64 y #s(literal -1/2 binary64))
Outputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
(*.f64 x #s(approx (- y -1/2) #s(literal 1/2 binary64)))
#s(approx (- y -1/2) #s(literal 1/2 binary64))
(*.f64 (*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x))))
(*.f64 (*.f64 (neg.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 y y)) y (*.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)) (*.f64 (*.f64 (*.f64 y y) x) x)))))
(*.f64 (*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))))
(*.f64 #s(literal 1 binary64) (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))
(*.f64 (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)) (*.f64 (*.f64 (*.f64 y y) x) x)) (*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)) (*.f64 (*.f64 (*.f64 y y) x) x)))))
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 y y)) y (*.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 (*.f64 y x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))))))
(*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 y y)) y (*.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)) (*.f64 (*.f64 (*.f64 y y) x) x))))
(*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (*.f64 (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))) (*.f64 (/.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))))) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (fma.f64 (/.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (/.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)))) (neg.f64 (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))) (neg.f64 (neg.f64 (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 y y)) y (*.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))))) (neg.f64 (neg.f64 (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)) (*.f64 (*.f64 (*.f64 y y) x) x)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 y y) x) x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (*.f64 (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))) (*.f64 (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x))) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)))
(/.f64 (*.f64 (neg.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (neg.f64 (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 y y)) y (*.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))) (neg.f64 (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 (*.f64 y x) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 y y)) y (*.f64 (*.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))) (neg.f64 (fma.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)) (*.f64 (*.f64 (*.f64 y y) x) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) (-.f64 (*.f64 y x) #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)) (*.f64 (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 1 binary64)))
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(-.f64 (fma.f64 y x z) (*.f64 #s(literal -1/2 binary64) x))
(+.f64 (/.f64 (*.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z))) (neg.f64 (/.f64 (*.f64 z z) (fma.f64 (-.f64 y #s(literal -1/2 binary64)) x (neg.f64 z)))))
(+.f64 (fma.f64 y x z) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 y x))
(+.f64 z (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
(+.f64 (*.f64 (-.f64 y #s(literal -1/2 binary64)) x) z)
(+.f64 (*.f64 y x) (fma.f64 #s(literal 1/2 binary64) x z))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 y x z))
(*.f64 (neg.f64 (fma.f64 y y #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) y)))
(*.f64 (neg.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))))
(*.f64 (fma.f64 y y #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 y #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (-.f64 y #s(literal -1/2 binary64)))
(*.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y y (-.f64 #s(literal 1/4 binary64) (*.f64 y #s(literal 1/2 binary64))))))
(*.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 y #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64))))) (+.f64 (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))) (*.f64 (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))))) (+.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 y y)) (-.f64 #s(literal 1/2 binary64) y))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64))) (*.f64 (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (*.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 y y) y)) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 y y) (*.f64 #s(literal 1/2 binary64) y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 y y #s(literal -1/4 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) y)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (*.f64 (-.f64 y #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (-.f64 y #s(literal 1/2 binary64)) (-.f64 y #s(literal 1/2 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (*.f64 (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))) #s(literal -1/8 binary64))) (*.f64 (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 y y #s(literal -1/4 binary64))) (-.f64 #s(literal 1/2 binary64) y))
(/.f64 (neg.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))) (neg.f64 (fma.f64 y y (-.f64 #s(literal 1/4 binary64) (*.f64 y #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))) (neg.f64 (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 y #s(literal -1/2 binary64)))))
(/.f64 (fma.f64 y y #s(literal -1/4 binary64)) (-.f64 y #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 y #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y (-.f64 #s(literal 1/4 binary64) (*.f64 y #s(literal 1/2 binary64)))) (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 y #s(literal -1/2 binary64))))
(/.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64)) (fma.f64 y y (-.f64 #s(literal 1/4 binary64) (*.f64 y #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64)) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 y y #s(literal -1/4 binary64))) (-.f64 y #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64))) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (fma.f64 y y #s(literal -1/4 binary64)) (-.f64 #s(literal 1/2 binary64) y)))
(neg.f64 (/.f64 (fma.f64 (*.f64 y y) y #s(literal 1/8 binary64)) (neg.f64 (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))))
(fma.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) (-.f64 y #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 (*.f64 y y) y) (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (neg.f64 (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))))
(-.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (-.f64 #s(literal 1/4 binary64) (*.f64 y #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (-.f64 #s(literal 1/4 binary64) (*.f64 y #s(literal 1/2 binary64))))))
(-.f64 (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))))
(-.f64 y #s(literal -1/2 binary64))
(+.f64 (/.f64 (*.f64 y y) (-.f64 y #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 y #s(literal 1/2 binary64)))))
(+.f64 (/.f64 (*.f64 (*.f64 y y) y) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64)))) (neg.f64 (/.f64 #s(literal -1/8 binary64) (fma.f64 y y (fma.f64 #s(literal -1/2 binary64) y #s(literal 1/4 binary64))))))
(+.f64 #s(literal 1/2 binary64) y)
(+.f64 y #s(literal 1/2 binary64))

eval46.0ms (1.2%)

Memory
4.1MiB live, 127.0MiB allocated
Compiler

Compiled 7 094 to 665 computations (90.6% saved)

prune47.0ms (1.2%)

Memory
5.9MiB live, 83.4MiB allocated
Pruning

8 alts after pruning (0 fresh and 8 done)

PrunedKeptTotal
New4010401
Fresh000
Picked033
Done055
Total4018409
Accuracy
100.0%
Counts
409 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
100.0%
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
62.7%
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
69.1%
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
68.8%
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
62.7%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
31.9%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
33.1%
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
Compiler

Compiled 134 to 65 computations (51.5% saved)

regimes20.0ms (0.5%)

Memory
6.5MiB live, 49.2MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
Outputs
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
Calls

5 calls:

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

Compiled 34 to 24 computations (29.4% saved)

regimes18.0ms (0.4%)

Memory
-4.6MiB live, 34.4MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
(fma.f64 (-.f64 y #s(literal -1/2 binary64)) x z)
(fma.f64 y x #s(approx (+ (* 1/2 x) z) (*.f64 x #s(literal 1/2 binary64))))
Outputs
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
Calls

5 calls:

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

Compiled 34 to 24 computations (29.4% saved)

regimes87.0ms (2.2%)

Memory
-5.2MiB live, 33.7MiB allocated
Counts
5 → 3
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
Outputs
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
Calls

5 calls:

76.0ms
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
3.0ms
z
2.0ms
x
2.0ms
y
2.0ms
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
Results
AccuracySegmentsBranch
88.6%3x
98.9%3y
87.5%3z
80.8%3(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
91.4%4(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes5.0ms (0.1%)

Memory
11.9MiB live, 11.9MiB allocated
Counts
4 → 3
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
Outputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
Calls

2 calls:

2.0ms
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
2.0ms
y
Results
AccuracySegmentsBranch
89.5%3(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
86.7%3y
Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes18.0ms (0.5%)

Memory
-10.8MiB live, 26.8MiB allocated
Counts
3 → 3
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
Outputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
Calls

4 calls:

12.0ms
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
2.0ms
z
2.0ms
y
2.0ms
x
Results
AccuracySegmentsBranch
86.6%3y
68.8%1z
68.8%1x
80.4%3(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
Compiler

Compiled 22 to 16 computations (27.3% saved)

regimes45.0ms (1.1%)

Memory
-11.4MiB live, 69.1MiB allocated
Counts
2 → 3
Calls
Call 1
Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
Outputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
Calls

5 calls:

38.0ms
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
2.0ms
y
2.0ms
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
2.0ms
z
2.0ms
x
Results
AccuracySegmentsBranch
40.4%3x
39.9%3z
43.9%3(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
43.8%3(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
61.8%3y
Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes7.0ms (0.2%)

Memory
21.1MiB live, 21.1MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

5 calls:

1.0ms
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
1.0ms
x
1.0ms
y
1.0ms
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
1.0ms
z
Results
AccuracySegmentsBranch
33.1%1z
33.1%1x
33.1%1(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
33.1%1(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
33.1%1y
Compiler

Compiled 34 to 24 computations (29.4% saved)

bsearch35.0ms (0.9%)

Memory
-29.6MiB live, 46.6MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
10.0ms
0.00014138685008050479
1.9769181253425554
16.0ms
-16285217637975462.0
-1614421.0194843044
Samples
13.0ms288×0valid
Compiler

Compiled 357 to 230 computations (35.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-div: 2.0ms (29.4% of total)
ival-add: 2.0ms (29.4% of total)
ival-mult: 2.0ms (29.4% 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
0.6MiB live, 0.6MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
2.370148426146294e+84
6.09113032174703e+90
0.0ms
-1.1066851969256255e+75
-1.6362523695492225e+72
Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch16.0ms (0.4%)

Memory
26.7MiB live, 26.7MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
4.0ms
8908139883087448000.0
10909593000565883000.0
11.0ms
-16285217637975462.0
-1614421.0194843044
Samples
8.0ms176×0valid
Compiler

Compiled 236 to 157 computations (33.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-add: 2.0ms (47.9% of total)
ival-div: 1.0ms (24% of total)
ival-mult: 1.0ms (24% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch26.0ms (0.7%)

Memory
-24.6MiB live, 20.9MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
1.0ms
0.00014138685008050479
1.9769181253425554
24.0ms
-2.287326427673324e-7
-1.0162561533376278e-9
Samples
20.0ms112×0valid
Compiler

Compiled 270 to 179 computations (33.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-div: 16.0ms (91.3% of total)
ival-add: 1.0ms (5.7% of total)
ival-mult: 1.0ms (5.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify9.0ms (0.2%)

Memory
22.8MiB live, 22.8MiB allocated
Algorithm
egg-herbie
Rules
10×+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050237
158237
263237
365237
466237
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
(if (<=.f64 y #s(literal -1620000 binary64)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)))
(if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #s(literal -999999999999999926539781176481198923508803215199467887262646419780362305536 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #s(literal 4000000000000000231066439592463586809749068508384256548392167452938849336067698458624 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(if (<=.f64 y #s(literal -5200000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (if (<=.f64 y #s(literal 10200000000000000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))))
(if (<=.f64 y #s(literal -8500259669165361/37778931862957161709568 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
Outputs
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
(if (<=.f64 y #s(literal -1620000 binary64)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)))
(if (<=.f64 y #s(literal -1620000 binary64)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)))
(if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #s(literal -999999999999999926539781176481198923508803215199467887262646419780362305536 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) #s(literal 4000000000000000231066439592463586809749068508384256548392167452938849336067698458624 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 x y)) #s(literal -999999999999999926539781176481198923508803215199467887262646419780362305536 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 x y)) #s(literal 4000000000000000231066439592463586809749068508384256548392167452938849336067698458624 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(if (<=.f64 y #s(literal -5200000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (if (<=.f64 y #s(literal 10200000000000000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))))
(if (<=.f64 y #s(literal -5200000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y)) (if (<=.f64 y #s(literal 10200000000000000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y))))
(if (<=.f64 y #s(literal -8500259669165361/37778931862957161709568 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x)) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))))
(if (<=.f64 y #s(literal -8500259669165361/37778931862957161709568 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y)) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y))))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y))

soundness790.0ms (20.1%)

Memory
-7.8MiB live, 418.0MiB allocated
Rules
7 074×lower-fma.f64
7 074×lower-fma.f32
6 434×lower-fma.f64
6 434×lower-fma.f32
6 334×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0822
01222
15218
245218
3607718
0804017
057440
1174440
2488440
31308440
43609440
56674440
08210412
0721624
12231624
25981624
317581624
437791624
557921624
672441624
080301448
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 231 to 110 computations (52.4% saved)

preprocess140.0ms (3.6%)

Memory
12.4MiB live, 140.9MiB allocated
Compiler

Compiled 272 to 94 computations (65.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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