Examples.Basics.ProofTests:f4 from sbv-4.4

Time bar (total: 4.3s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB 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 15 to 11 computations (26.7% saved)

sample903.0ms (21%)

Memory
1.8MiB live, 1 113.3MiB allocated
Samples
640.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 463.0ms
ival-mult: 383.0ms (82.6% of total)
ival-add: 67.0ms (14.5% of total)
ival-true: 5.0ms (1.1% of total)
exact: 5.0ms (1.1% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

explain141.0ms (3.3%)

Memory
-17.0MiB live, 186.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
100-0-(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
90-0-(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
00-0-(*.f64 x #s(literal 2 binary64))
00-0-(*.f64 x x)
00-0-(*.f64 (*.f64 x #s(literal 2 binary64)) y)
00-0-y
00-0-#s(literal 2 binary64)
00-0-(*.f64 y y)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
+.f64(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))nan-rescue100
(*.f64 x x)overflow54
(*.f64 (*.f64 x #s(literal 2 binary64)) y)overflow32
+.f64(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))nan-rescue90
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))overflow64
(*.f64 x x)overflow54
(*.f64 (*.f64 x #s(literal 2 binary64)) y)overflow32
(*.f64 y y)overflow66
Confusion
Predicted +Predicted -
+160
-0240
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+1600
-00240
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0240
113
23
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
33.0ms512×0valid
Compiler

Compiled 95 to 31 computations (67.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-mult: 12.0ms (70.5% of total)
ival-add: 4.0ms (23.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess175.0ms (4.1%)

Memory
37.2MiB live, 107.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
02371
19557
231457
361155
4103155
5155535
6224835
7300835
8367435
9399635
10400435
11400435
12404635
13408835
14410235
0913
01513
13811
212711
333011
463411
59717
612977
718557
825037
927947
1030487
1130667
030667
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Outputs
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(*.f64 (+.f64 y x) (+.f64 y x))
Symmetry

(sort x y)

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
93.7%
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify62.0ms (1.4%)

Memory
11.4MiB live, 45.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
cost-diff0
(*.f64 x x)
cost-diff3
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
cost-diff3
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0939
01539
13835
212735
333035
463435
597131
6129731
7185531
8250331
9279431
10304831
11306631
0306630
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
x
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
y
(*.f64 y y)
Outputs
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(*.f64 x x)
x
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
(*.f64 y (*.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
y
(*.f64 y y)

localize34.0ms (0.8%)

Memory
-28.2MiB live, 21.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.0
(*.f64 x #s(literal 2 binary64))
accuracy1.0000000000000002
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
accuracy2.949212557490618
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
Samples
28.0ms256×0valid
Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 12.0ms (56.4% of total)
ival-add: 9.0ms (42.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory
9.2MiB live, 9.2MiB allocated
Counts
5 → 17
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(* 2 (* x y))
(* x (+ x (* 2 y)))
(pow x 2)
(* 2 x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
Calls

6 calls:

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

simplify157.0ms (3.6%)

Memory
-16.1MiB live, 179.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056177
1194169
2746157
33571149
08118140
Stop Event
iter limit
node limit
Counts
17 → 17
Calls
Call 1
Inputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(* 2 (* x y))
(* x (+ x (* 2 y)))
(pow x 2)
(* 2 x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
Outputs
(pow y 2)
(*.f64 y y)
(+ (* 2 (* x y)) (pow y 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(+ (* x (+ x (* 2 y))) (pow y 2))
(*.f64 (+.f64 y x) (+.f64 y x))
(* 2 (* x y))
(*.f64 (*.f64 y x) #s(literal 2 binary64))
(* x (+ x (* 2 y)))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(pow x 2)
(*.f64 x x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x)
(+ (* 2 (* x y)) (pow x 2))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(+ (* y (+ y (* 2 x))) (pow x 2))
(*.f64 (+.f64 y x) (+.f64 y x))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(*.f64 (*.f64 (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal 1 binary64)) y) y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) y) y)
(* y (+ (* 2 x) (/ (pow x 2) y)))
(*.f64 (*.f64 y x) (-.f64 (/.f64 x y) #s(literal -2 binary64)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(*.f64 (*.f64 (fma.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) y) y)
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(*.f64 (*.f64 y x) (-.f64 (/.f64 x y) #s(literal -2 binary64)))

rewrite167.0ms (3.9%)

Memory
15.9MiB live, 213.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0933
01533
16529
256829
0928626
Stop Event
iter limit
node limit
iter limit
Counts
5 → 255
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 (*.f64 y y) (fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x)))))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 4 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 y y) x) (fma.f64 y #s(literal 2 binary64) x))) #s(literal 2 binary64)))) (+.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 (*.f64 y y) (fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x)))))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 6 binary64)) (*.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (*.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x))) #s(literal 3 binary64))))) (+.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 4 binary64)) (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 y y) x) (fma.f64 y #s(literal 2 binary64) x))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 y y) x) (fma.f64 y #s(literal 2 binary64) x))) (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 (neg.f64 y) y))) (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 (neg.f64 y) y)))) (*.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y))))) (fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (+.f64 (fma.f64 y y (*.f64 x x)) (*.f64 (*.f64 #s(literal -2 binary64) x) y)))
(/.f64 (-.f64 (*.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (fma.f64 y y (*.f64 x x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 3 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x))) (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 3 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x))) (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64))))) (*.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x))) (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (*.f64 y y) (fma.f64 y y (*.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x))) (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)))))) (fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 (*.f64 y (fma.f64 #s(literal 2 binary64) x y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 y (fma.f64 #s(literal 2 binary64) x y)) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 (fma.f64 x x (*.f64 y y)) (fma.f64 x x (*.f64 y y)))) (-.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) (fma.f64 x x (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) y) #s(literal 3 binary64))) (fma.f64 (fma.f64 y y (*.f64 x x)) (fma.f64 y y (*.f64 x x)) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (fma.f64 y y (*.f64 x x)) (*.f64 (*.f64 #s(literal -2 binary64) x) y)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 (neg.f64 y) y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 (neg.f64 y) y))) (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 (neg.f64 y) y))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y))) (*.f64 (/.f64 (pow.f64 (*.f64 x (fma.f64 y #s(literal 2 binary64) x)) #s(literal 2 binary64)) (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 (neg.f64 y) y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y)))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 y (-.f64 (*.f64 #s(literal -2 binary64) x) y)) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 (*.f64 y (fma.f64 #s(literal 2 binary64) x y)) #s(literal 2 binary64)) (*.f64 (*.f64 x x) (*.f64 y (-.f64 (*.f64 #s(literal -2 binary64) x) y))))))
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(fma.f64 (*.f64 #s(literal 2 binary64) x) y (*.f64 x x))
(fma.f64 #s(literal 2 binary64) (*.f64 x y) (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal 2 binary64) (*.f64 x y) (*.f64 x x))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) (*.f64 x x))
(fma.f64 x (*.f64 y #s(literal 2 binary64)) (*.f64 (neg.f64 x) x))
(fma.f64 x (*.f64 y #s(literal 2 binary64)) (*.f64 x x))
(fma.f64 x x (*.f64 (neg.f64 y) (*.f64 #s(literal -2 binary64) x)))
(fma.f64 x x (*.f64 (*.f64 #s(literal -2 binary64) x) y))
(fma.f64 x x (*.f64 y (*.f64 #s(literal 2 binary64) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 x (fma.f64 y #s(literal 2 binary64) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 y #s(literal 2 binary64) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 y #s(literal 2 binary64) x))) (/.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 x (fma.f64 y #s(literal 2 binary64) x))))
(-.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) (*.f64 (neg.f64 x) x))
(-.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) (*.f64 x x))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 y) (*.f64 #s(literal -2 binary64) x)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal -2 binary64) x) y))
(-.f64 (*.f64 x x) (*.f64 y (*.f64 #s(literal 2 binary64) x)))
(+.f64 (/.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) x) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (fma.f64 y #s(literal 2 binary64) x))) (/.f64 (neg.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 x (fma.f64 y #s(literal 2 binary64) x))))
(+.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) (*.f64 x x))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 y) (*.f64 #s(literal -2 binary64) x)))
(+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal -2 binary64) x) y))
(+.f64 (*.f64 x x) (*.f64 y (*.f64 #s(literal 2 binary64) x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 (*.f64 y x) #s(literal 2 binary64))
(*.f64 (*.f64 y #s(literal 2 binary64)) x)
(*.f64 y (*.f64 #s(literal 2 binary64) x))
(*.f64 (*.f64 #s(literal 2 binary64) x) y)
(*.f64 #s(literal 2 binary64) (*.f64 x y))
(*.f64 #s(literal 2 binary64) (*.f64 y x))
(*.f64 x (*.f64 y #s(literal 2 binary64)))
(neg.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) y))
(fma.f64 y x (*.f64 y x))
(fma.f64 x y (*.f64 x y))
(+.f64 (*.f64 x y) (*.f64 x y))
(+.f64 (*.f64 y x) (*.f64 y x))
(*.f64 #s(literal -2 binary64) (neg.f64 x))
(*.f64 (neg.f64 x) #s(literal -2 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x x))
(/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x))))
(neg.f64 (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(+.f64 x x)

eval65.0ms (1.5%)

Memory
19.3MiB live, 55.2MiB allocated
Compiler

Compiled 8 056 to 793 computations (90.2% saved)

prune8.0ms (0.2%)

Memory
-30.4MiB live, 13.4MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2644268
Fresh000
Picked101
Done000
Total2654269
Accuracy
100.0%
Counts
269 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
95.7%
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
100.0%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
52.3%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify60.0ms (1.4%)

Memory
14.6MiB live, 52.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 y #s(literal 2 binary64) x)
cost-diff0
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
cost-diff2
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
cost-diff0
(fma.f64 #s(literal 2 binary64) x y)
cost-diff0
(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
cost-diff2
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
cost-diff0
(+.f64 y x)
cost-diff0
(*.f64 (+.f64 y x) (+.f64 y x))
cost-diff0
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
cost-diff0
(*.f64 y y)
cost-diff0
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02098
03186
18486
224582
365682
4107582
5137082
6188382
7250582
8283882
9309082
10317682
0317682
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
y
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
y
x
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
x
(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
y
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
y
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
x
(fma.f64 y #s(literal 2 binary64) x)
#s(literal 2 binary64)
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
y
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
y
x
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
(*.f64 (+.f64 y x) (+.f64 y x))
x
(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
y
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
(*.f64 (+.f64 y x) (+.f64 y x))
y
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
x
(fma.f64 y #s(literal 2 binary64) x)
#s(literal 2 binary64)

localize110.0ms (2.6%)

Memory
0.8MiB live, 72.8MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(fma.f64 y #s(literal 2 binary64) x)
accuracy0.01171875
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
accuracy1.249986238027801
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
accuracy0.0
(fma.f64 #s(literal 2 binary64) x y)
accuracy0.0078125
(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
accuracy2.757782223661162
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
accuracy0.0
(+.f64 y x)
accuracy0.0
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
accuracy0.01171875
(*.f64 (+.f64 y x) (+.f64 y x))
accuracy0.0
(*.f64 y y)
accuracy30.521674656137936
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Samples
77.0ms256×0valid
Compiler

Compiled 96 to 21 computations (78.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-add: 51.0ms (79% of total)
ival-mult: 13.0ms (20.1% 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
11.9MiB live, 11.9MiB allocated
Counts
11 → 38
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
(fma.f64 #s(literal 2 binary64) x y)
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
(fma.f64 y #s(literal 2 binary64) x)
Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
y
(+ x y)
(+ y (* 2 x))
(* 2 (* x y))
(* x (+ x (* 2 y)))
(* 2 y)
(+ x (* 2 y))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
x
(* x (+ 1 (/ y x)))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* 2 x)
(* x (+ 2 (/ y x)))
(* x (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(* -1 (* x (- (* -2 (/ y x)) 1)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (/ x y)))
(* y (+ 1 (* 2 (/ x y))))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* y (+ 2 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* -1 (* y (- (* -1 (/ x y)) 2)))
Calls

6 calls:

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

simplify196.0ms (4.6%)

Memory
-26.4MiB live, 225.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093326
1317318
21075302
34184302
08302282
Stop Event
iter limit
node limit
Counts
38 → 36
Calls
Call 1
Inputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
y
(+ x y)
(+ y (* 2 x))
(* 2 (* x y))
(* x (+ x (* 2 y)))
(* 2 y)
(+ x (* 2 y))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
x
(* x (+ 1 (/ y x)))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* 2 x)
(* x (+ 2 (/ y x)))
(* x (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(* -1 (* x (- (* -2 (/ y x)) 1)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (/ x y)))
(* y (+ 1 (* 2 (/ x y))))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* y (+ 2 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* -1 (* y (- (* -1 (/ x y)) 2)))
Outputs
(pow y 2)
(*.f64 y y)
(+ (* 2 (* x y)) (pow y 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(+ (* x (+ x (* 2 y))) (pow y 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
y
(+ x y)
(+.f64 y x)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(* 2 (* x y))
(*.f64 (*.f64 y x) #s(literal 2 binary64))
(* x (+ x (* 2 y)))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(+ x (* 2 y))
(fma.f64 y #s(literal 2 binary64) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (+.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) x)
x
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x x)
(* x (+ (* 2 y) (/ (pow y 2) x)))
(*.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ y x)))
(*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x)
(* x (+ 1 (* 2 (/ y x))))
(*.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal 1 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) (+.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 1 binary64)))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(*.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 2 binary64)))
(* -1 (* x (- (* -2 (/ y x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 y x)) #s(literal 1 binary64)))
(+ (* 2 (* x y)) (pow x 2))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(+ (* y (+ y (* 2 x))) (pow x 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(* y (+ y (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(*.f64 (*.f64 (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal 1 binary64)) y) y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64))) y y) y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(* y (+ 1 (* 2 (/ x y))))
(*.f64 (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal 1 binary64)) y)
(* y (+ (* 2 x) (/ (pow x 2) y)))
(*.f64 x (*.f64 (+.f64 (/.f64 x y) #s(literal 2 binary64)) y))
(* y (+ 2 (/ x y)))
(*.f64 (+.f64 (/.f64 x y) #s(literal 2 binary64)) y)
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(*.f64 (fma.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64))) y y) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 (neg.f64 y) (-.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64)))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(*.f64 (neg.f64 y) (-.f64 (*.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(*.f64 x (*.f64 (+.f64 (/.f64 x y) #s(literal 2 binary64)) y))
(* -1 (* y (- (* -1 (/ x y)) 2)))
(*.f64 (neg.f64 y) (-.f64 (/.f64 (neg.f64 x) y) #s(literal 2 binary64)))

rewrite220.0ms (5.1%)

Memory
34.7MiB live, 264.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02089
03177
116677
2142677
0871977
Stop Event
iter limit
node limit
iter limit
Counts
11 → 811
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
(fma.f64 #s(literal 2 binary64) x y)
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
(fma.f64 y #s(literal 2 binary64) x)
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 (neg.f64 (neg.f64 (neg.f64 y))) (neg.f64 (neg.f64 (neg.f64 y))))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 y)))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(sqrt.f64 (pow.f64 y #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 y) y))
(fabs.f64 (*.f64 y y))
(exp.f64 (*.f64 (log.f64 (neg.f64 y)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 y) #s(literal 2 binary64))))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 (+.f64 y x))) (exp.f64 (log.f64 (+.f64 y x))))
(*.f64 (+.f64 y x) (+.f64 y x))
(pow.f64 (exp.f64 (log.f64 (+.f64 y x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (+.f64 y x) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 x) (+.f64 y x)) (*.f64 (neg.f64 x) (+.f64 y x)))) (fma.f64 (+.f64 y x) y (*.f64 (neg.f64 x) (+.f64 y x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 2 binary64))) (-.f64 (*.f64 (+.f64 y x) x) (*.f64 (+.f64 y x) y)))
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 x) (+.f64 y x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 2 binary64)) (fma.f64 (*.f64 (neg.f64 x) (+.f64 y x)) (*.f64 (neg.f64 x) (+.f64 y x)) (*.f64 (*.f64 (+.f64 y x) y) (*.f64 (neg.f64 x) (+.f64 y x))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 y x) y) (*.f64 (+.f64 y x) x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 y x) x) (*.f64 (+.f64 y x) y)))))
(/.f64 (fma.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y)) (-.f64 y x))
(/.f64 (fma.f64 x (*.f64 (+.f64 y x) (-.f64 y x)) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y)) (-.f64 y x))
(/.f64 (fma.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y)) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fma.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y)) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fma.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x)))) (-.f64 y x))
(/.f64 (fma.f64 x (*.f64 (+.f64 y x) (-.f64 y x)) (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x)))) (-.f64 y x))
(/.f64 (fma.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fma.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fma.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x)) (-.f64 y x))
(/.f64 (fma.f64 y (*.f64 (+.f64 y x) (-.f64 y x)) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x)) (-.f64 y x))
(/.f64 (fma.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x)) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fma.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x)) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fma.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x)))) (-.f64 y x))
(/.f64 (fma.f64 y (*.f64 (+.f64 y x) (-.f64 y x)) (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x)))) (-.f64 y x))
(/.f64 (fma.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y (*.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fma.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (neg.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (+.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 y x))) (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (*.f64 (+.f64 y x) (-.f64 y x)))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 2 binary64)))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (+.f64 y x) y) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (+.f64 y x) x) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 y x) y) (*.f64 (+.f64 y x) x))))))
(/.f64 (neg.f64 (pow.f64 (*.f64 (+.f64 y x) (-.f64 y x)) #s(literal 2 binary64))) (neg.f64 (pow.f64 (-.f64 y x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (+.f64 y x) (-.f64 y x)))) (neg.f64 (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 y x))))
(/.f64 (neg.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))) (neg.f64 (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal 2 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y) (-.f64 y x)) (*.f64 (-.f64 y x) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (-.f64 y x) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x))) (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y) (-.f64 y x)) (*.f64 (-.f64 y x) (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x))))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (-.f64 y x) (*.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y) (-.f64 y x)) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 y x)))
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x))) (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y) (-.f64 y x)) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x))))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 y x)))
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x)) (*.f64 (-.f64 y x) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (-.f64 y x) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x))) (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (-.f64 (*.f64 (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x)) (*.f64 (-.f64 y x) (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x))))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (-.f64 y x) (*.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (-.f64 (*.f64 (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 y x)) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 y x)))
(/.f64 (-.f64 (*.f64 (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x))) (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 y x)) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x))))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 y x)))
(/.f64 (-.f64 (*.f64 (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x) (-.f64 y x) (*.f64 (-.f64 y x) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x) (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (-.f64 y x) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y))) (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (fma.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x) (-.f64 y x) (*.f64 (-.f64 y x) (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x))))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) x) (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (-.f64 y x) (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (fma.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x) (-.f64 y x) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 y x)))
(/.f64 (fma.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y))) (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x) (-.f64 y x) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 y (*.f64 (+.f64 y x) (-.f64 y x))))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 y x)))
(/.f64 (fma.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (pow.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x) (*.f64 (-.f64 y x) (*.f64 (*.f64 (+.f64 y x) (-.f64 y x)) y))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (*.f64 x (*.f64 (+.f64 y x) (-.f64 y x))) (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (-.f64 y x) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y))) (*.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (*.f64 y y))))
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(fma.f64 #s(literal 2 binary64) y x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 y #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (-.f64 x (*.f64 y #s(literal 2 binary64)))))
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 y #s(literal 2 binary64)) x)))
(-.f64 x (*.f64 (neg.f64 y) #s(literal 2 binary64)))
(-.f64 x (*.f64 #s(literal -2 binary64) y))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (*.f64 (*.f64 y x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 x x (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (*.f64 (*.f64 y x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 x x (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (*.f64 (*.f64 y x) #s(literal 2 binary64))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (*.f64 (*.f64 y x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 #s(literal 4 binary64) (*.f64 y y)))) (/.f64 (pow.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 #s(literal 4 binary64) (*.f64 y y)))))
(+.f64 (/.f64 (pow.f64 (*.f64 y #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 #s(literal 4 binary64) (*.f64 y y)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 #s(literal 4 binary64) (*.f64 y y)))))
(+.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (/.f64 (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)))
(+.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (/.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 y #s(literal 2 binary64)) x)))
(+.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (/.f64 (*.f64 x (neg.f64 x)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)))
(+.f64 (*.f64 y #s(literal 2 binary64)) x)
(+.f64 x (*.f64 y #s(literal 2 binary64)))

eval191.0ms (4.5%)

Memory
11.9MiB live, 165.8MiB allocated
Compiler

Compiled 25 265 to 2 491 computations (90.1% saved)

prune48.0ms (1.1%)

Memory
-17.2MiB live, 33.6MiB allocated
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New7522754
Fresh000
Picked044
Done000
Total7526758
Accuracy
100.0%
Counts
758 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
95.7%
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
58.1%
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
100.0%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
52.3%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
62.0%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify58.0ms (1.3%)

Memory
-13.8MiB live, 24.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 2 binary64) x)
cost-diff0
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
cost-diff0
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))
cost-diff0
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01761
02161
15259
216059
343759
480255
5115755
6153855
7216355
8276555
9302955
10321355
0321352
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
x
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))
y
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y (*.f64 x x))
x
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))
(*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y)
y
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)

localize49.0ms (1.1%)

Memory
17.4MiB live, 51.6MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 2 binary64) x)
accuracy0.0078125
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))
accuracy2.757782223661162
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
accuracy27.468130174478503
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
accuracy0.0
(*.f64 x x)
accuracy24.331649884996025
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Samples
42.0ms256×0valid
Compiler

Compiled 48 to 15 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-add: 23.0ms (72.3% of total)
ival-mult: 9.0ms (28.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
10.7MiB live, 10.7MiB allocated
Counts
6 → 23
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(pow x 2)
y
(+ y (* 2 x))
(* 2 x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* 2 (* x y))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* x (+ 2 (/ y x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -2 (/ x y)) 1)))
Calls

6 calls:

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

simplify305.0ms (7.1%)

Memory
-42.3MiB live, 229.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067220
1231210
2830198
33689198
08262183
Stop Event
iter limit
node limit
Counts
23 → 22
Calls
Call 1
Inputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(pow x 2)
y
(+ y (* 2 x))
(* 2 x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* 2 (* x y))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* x (+ 2 (/ y x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -2 (/ x y)) 1)))
Outputs
(pow y 2)
(*.f64 y y)
(+ (* 2 (* x y)) (pow y 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(+ (* x (+ x (* 2 y))) (pow y 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
y
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -2 binary64))) x x) x)
(* 2 (* x y))
(*.f64 (*.f64 y x) #s(literal 2 binary64))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(*.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x))
(* x (+ 2 (/ y x)))
(*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(*.f64 (fma.f64 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -2 binary64))) x x) x)
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(*.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 2 binary64)))
(+ (* 2 (* x y)) (pow x 2))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(+ (* y (+ y (* 2 x))) (pow x 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(* y (+ y (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(*.f64 (*.f64 (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal 1 binary64)) y) y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64))) y y) y)
(* y (+ 1 (* 2 (/ x y))))
(*.f64 (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal 1 binary64)) y)
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(*.f64 (fma.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64))) y y) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(*.f64 (neg.f64 y) (-.f64 (*.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))

rewrite193.0ms (4.5%)

Memory
12.2MiB live, 171.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01757
02157
110055
285955
0922950
Stop Event
iter limit
node limit
iter limit
Counts
6 → 120
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x (neg.f64 (neg.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))))) (*.f64 (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))))))
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(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))))
(-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) (*.f64 (neg.f64 x) x))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 (neg.f64 y))) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))
(+.f64 (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))))) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))))))
(+.f64 (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) (fma.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) (fma.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) (fma.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) (fma.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64))) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))))
(+.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) (*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 x)))
(+.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) (*.f64 x x))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))) y))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))) (neg.f64 y)))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))))
(+.f64 (*.f64 x x) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y))
(*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y)
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)))
#s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) (neg.f64 x))
(*.f64 #s(literal -2 binary64) x)
(*.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(*.f64 (neg.f64 x) #s(literal -2 binary64))
(*.f64 (neg.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 x)))
(*.f64 #s(literal 2 binary64) (neg.f64 x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x))) (neg.f64 (-.f64 x x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x)))))
(/.f64 (fabs.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x))) (fabs.f64 (-.f64 x x)))
(/.f64 (fabs.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fabs.f64 (fma.f64 x x (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x)))))
(/.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x)) (-.f64 (neg.f64 x) (neg.f64 x)))
(/.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x))))
(neg.f64 (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 x))) (sqrt.f64 (neg.f64 (neg.f64 x))) x)
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(sqrt.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x x)) (/.f64 (*.f64 x x) (-.f64 x x)))
(fabs.f64 (*.f64 #s(literal -2 binary64) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (*.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 x x)))))
(+.f64 (neg.f64 x) (neg.f64 x))
(+.f64 x x)

eval20.0ms (0.5%)

Memory
-7.5MiB live, 30.4MiB allocated
Compiler

Compiled 4 415 to 428 computations (90.3% saved)

prune4.0ms (0.1%)

Memory
9.8MiB live, 9.8MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New1371138
Fresh000
Picked112
Done044
Total1386144
Accuracy
100.0%
Counts
144 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
95.7%
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
58.1%
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
100.0%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
52.3%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
62.0%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Compiler

Compiled 87 to 55 computations (36.8% saved)

simplify10.0ms (0.2%)

Memory
-23.9MiB live, 13.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x x)
cost-diff0
#s(approx (+ (* 2 x) y) (+.f64 x x))
cost-diff0
(*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)))
cost-diff0
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0939
01339
12739
26639
311139
415139
516939
617139
717339
017336
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
x
(*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)))
y
#s(approx (+ (* 2 x) y) (+.f64 x x))
(+.f64 x x)
Outputs
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
(fma.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y (*.f64 x x))
x
(*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)))
(*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y)
y
#s(approx (+ (* 2 x) y) (+.f64 x x))
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)

localize41.0ms (1%)

Memory
-0.4MiB live, 35.5MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x x)
accuracy0.0078125
(*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)))
accuracy2.757782223661162
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
accuracy27.468130174478503
#s(approx (+ (* 2 x) y) (+.f64 x x))
Samples
35.0ms256×0valid
Compiler

Compiled 30 to 11 computations (63.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-mult: 5.0ms (61.9% of total)
ival-add: 3.0ms (37.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
5.2MiB live, 5.2MiB allocated
Counts
4 → 23
Calls
Call 1
Inputs
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
(*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)))
#s(approx (+ (* 2 x) y) (+.f64 x x))
(+.f64 x x)
Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
y
(+ y (* 2 x))
(* 2 x)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* 2 (* x y))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* x (+ 2 (/ y x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -2 (/ x y)) 1)))
Calls

6 calls:

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

simplify321.0ms (7.5%)

Memory
-5.5MiB live, 241.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067220
1231210
2830198
33686198
08269183
Stop Event
iter limit
node limit
Counts
23 → 22
Calls
Call 1
Inputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
y
(+ y (* 2 x))
(* 2 x)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* 2 (* x y))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* x (+ 2 (/ y x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -2 (/ x y)) 1)))
Outputs
(pow y 2)
(*.f64 y y)
(+ (* 2 (* x y)) (pow y 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(+ (* x (+ x (* 2 y))) (pow y 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
y
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(*.f64 (*.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -2 binary64))) x x) x)
(* 2 (* x y))
(*.f64 (*.f64 y x) #s(literal 2 binary64))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(*.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x))
(* x (+ 2 (/ y x)))
(*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(*.f64 (fma.f64 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) #s(literal -2 binary64))) x x) x)
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(*.f64 y (*.f64 (+.f64 (/.f64 y x) #s(literal 2 binary64)) x))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 2 binary64)))
(+ (* 2 (* x y)) (pow x 2))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(+ (* y (+ y (* 2 x))) (pow x 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(* y (+ y (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(*.f64 (*.f64 (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal 1 binary64)) y) y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(*.f64 (fma.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64))) y y) y)
(* y (+ 1 (* 2 (/ x y))))
(*.f64 (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal 1 binary64)) y)
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(*.f64 (fma.f64 (*.f64 (/.f64 x y) (-.f64 (/.f64 x y) #s(literal -2 binary64))) y y) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(*.f64 (neg.f64 y) (-.f64 (*.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))

rewrite44.0ms (1%)

Memory
26.9MiB live, 63.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0937
01337
16037
055234
Stop Event
iter limit
iter limit
node limit
iter limit
Counts
4 → 71
Calls
Call 1
Inputs
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
(*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)))
#s(approx (+ (* 2 x) y) (+.f64 x x))
(+.f64 x x)
Outputs
(/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 2 binary64)) (*.f64 (*.f64 x x) (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 2 binary64)))) (neg.f64 (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 2 binary64))) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y (*.f64 x x))
(fma.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) (*.f64 x x))
(fma.f64 x x (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 2 binary64)) (fma.f64 x x (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))) y))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 (neg.f64 x) x))
(-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 x (neg.f64 x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (-.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 y)) #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(+.f64 (*.f64 x x) (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(+.f64 (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y) (*.f64 x x))
(*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y)
(*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3/2 binary64)))
(*.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (fabs.f64 (*.f64 #s(literal 2 binary64) x)) (fabs.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 #s(literal 4 binary64) (*.f64 x x))
(*.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64))
(*.f64 (*.f64 x x) #s(literal 4 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 #s(literal 2 binary64) x)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))
(*.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 2 binary64) x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x (*.f64 (*.f64 #s(literal 2 binary64) x) x))
(fma.f64 x (*.f64 #s(literal 2 binary64) x) (*.f64 x (*.f64 #s(literal 2 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))
(+.f64 (*.f64 x (*.f64 #s(literal 2 binary64) x)) (*.f64 x (*.f64 #s(literal 2 binary64) x)))
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) x) (*.f64 (*.f64 #s(literal 2 binary64) x) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 x x)

eval13.0ms (0.3%)

Memory
-14.8MiB live, 22.8MiB allocated
Compiler

Compiled 1 922 to 327 computations (83% saved)

prune4.0ms (0.1%)

Memory
9.4MiB live, 9.4MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New89089
Fresh000
Picked011
Done055
Total89695
Accuracy
100.0%
Counts
95 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
95.7%
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
58.1%
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
100.0%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
52.3%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
62.0%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Compiler

Compiled 201 to 92 computations (54.2% saved)

regimes44.0ms (1%)

Memory
-28.9MiB live, 18.7MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x))))
(fma.f64 x x (*.f64 y #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))))
(fma.f64 x x (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
(fma.f64 y y (*.f64 x (fma.f64 y #s(literal 2 binary64) x)))
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
Calls

3 calls:

38.0ms
y
3.0ms
x
3.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes4.0ms (0.1%)

Memory
8.3MiB live, 8.3MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Calls

3 calls:

1.0ms
y
1.0ms
x
1.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Results
AccuracySegmentsBranch
91.1%2x
88.8%2y
62.0%1(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes2.0ms (0.1%)

Memory
5.6MiB live, 5.6MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

2 calls:

1.0ms
x
1.0ms
y
Results
AccuracySegmentsBranch
62.0%1y
62.0%1x
Compiler

Compiled 2 to 4 computations (-100% saved)

bsearch20.0ms (0.5%)

Memory
-15.1MiB live, 21.3MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
19.0ms
-1.9232842247540702e-142
-5.143777589418308e-145
Samples
14.0ms128×0valid
Compiler

Compiled 288 to 206 computations (28.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 10.0ms (90% of total)
ival-add: 1.0ms (9% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify59.0ms (1.4%)

Memory
6.6MiB live, 44.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01976
14268
213068
333868
466168
5101952
6149752
7384852
8612052
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(if (<=.f64 x #s(literal -5217246221699263/27459190640522438859927603196325572869077741200573221637577853836742172733590624208490238562645818219909185245565923432148487951998866575250296113164460228608 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(if (<=.f64 x #s(literal -5217246221699263/27459190640522438859927603196325572869077741200573221637577853836742172733590624208490238562645818219909185245565923432148487951998866575250296113164460228608 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

soundness447.0ms (10.4%)

Memory
-3.5MiB live, 193.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056177
1194169
2746157
33571149
08118140
093326
1317318
21075302
34184302
08302282
Stop Event
done
iter limit
node limit
iter limit
node limit
Compiler

Compiled 98 to 38 computations (61.2% saved)

preprocess92.0ms (2.2%)

Memory
5.8MiB live, 89.8MiB allocated
Remove

(sort x y)

Compiler

Compiled 246 to 98 computations (60.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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