Examples.Basics.ProofTests:f4 from sbv-4.4

Time bar (total: 3.9s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB 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)

sample1.1s (27.8%)

Memory
-105.9MiB live, 1 136.1MiB allocated
Samples
640.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 388.0ms
ival-mult: 273.0ms (70.3% of total)
ival-add: 100.0ms (25.7% of total)
ival-true: 6.0ms (1.5% of total)
exact: 6.0ms (1.5% of total)
ival-assert: 3.0ms (0.8% of total)
Bogosity

explain253.0ms (6.5%)

Memory
-10.9MiB live, 152.1MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
170-0-(+.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-rescue170
(*.f64 x x)overflow67
(*.f64 (*.f64 x #s(literal 2 binary64)) y)overflow37
+.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))overflow75
(*.f64 x x)overflow67
(*.f64 (*.f64 x #s(literal 2 binary64)) y)overflow37
(*.f64 y y)overflow68
Confusion
Predicted +Predicted -
+220
-0234
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+2200
-00234
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0234
118
24
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
55.0ms512×0valid
Compiler

Compiled 134 to 40 computations (70.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-mult: 17.0ms (76.2% of total)
ival-add: 5.0ms (22.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess40.0ms (1%)

Memory
-12.8MiB live, 23.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02371
17757
225055
363855
4121455
5150955
6153955
0913
01513
12311
24311
35111
0519
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))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
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
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
91.4%
(+.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)

simplify4.0ms (0.1%)

Memory
6.2MiB live, 6.2MiB 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-diff128
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
cost-diff448
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0939
01539
12335
24335
35135
05132
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))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
(+.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)

localize40.0ms (1%)

Memory
-4.2MiB live, 34.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.0
(*.f64 x #s(literal 2 binary64))
accuracy2.1992187500000004
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
accuracy3.6953001149812352
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
Samples
34.0ms256×0valid
Compiler

Compiled 80 to 20 computations (75% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 7.0ms (70.7% of total)
ival-add: 2.0ms (20.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory
10.7MiB live, 10.7MiB allocated
Counts
5 → 17
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(*.f64 x x)
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
Outputs
(* 2 (* x y))
(* x (+ x (* 2 y)))
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(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))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
Calls

6 calls:

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

simplify116.0ms (3%)

Memory
1.2MiB live, 115.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056129
1166129
2468129
31326129
43270129
56410129
08142110
Stop Event
iter limit
node limit
Counts
17 → 17
Calls
Call 1
Inputs
(* 2 (* x y))
(* x (+ x (* 2 y)))
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(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))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
Outputs
(* 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 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) y x) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2 binary64) y x) x (*.f64 y y))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(fma.f64 (fma.f64 #s(literal 2 binary64) y x) x (*.f64 y y))
(+ (* 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) y x) x (*.f64 y y))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 #s(literal 2 binary64) y x) x (*.f64 y y))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(fma.f64 (fma.f64 #s(literal 2 binary64) y x) x (*.f64 y y))

rewrite247.0ms (6.4%)

Memory
-0.4MiB live, 273.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0933
01533
15029
242029
3635729
0821926
Stop Event
iter limit
node limit
iter limit
Counts
5 → 210
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y))
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(*.f64 x x)
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 y (*.f64 x x)) #s(literal 2 binary64)) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x)))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) (-.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (/.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) x) (/.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) (-.f64 x (*.f64 y #s(literal 2 binary64)))))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(*.f64 (-.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (pow.f64 (*.f64 (neg.f64 x) (-.f64 x (*.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64))))
(*.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (/.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x)))
(*.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (*.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))))
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
(pow.f64 (/.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (-.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 4 binary64))) (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 6 binary64))) (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))) (+.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 y y)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64))))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))
(/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) (pow.f64 y #s(literal 4 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64)))) (fma.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) (pow.f64 y #s(literal 4 binary64)))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(neg.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64))) (neg.f64 (fma.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 y (*.f64 x x)) #s(literal 2 binary64)) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64))) (*.f64 y y))
(fma.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x)))) (*.f64 y y))
(fma.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) (-.f64 (*.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (*.f64 y (*.f64 #s(literal 2 binary64) x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (*.f64 y y))
(fma.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (*.f64 y y) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x)) (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (*.f64 y y))
(fma.f64 (/.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) x) (/.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) (-.f64 x (*.f64 y #s(literal 2 binary64)))) (*.f64 y y))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 (*.f64 y x) #s(literal 2 binary64) (fma.f64 y y (*.f64 x x)))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (*.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)) #s(literal -1 binary64)) (*.f64 x x))
(fma.f64 (-.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 y y))
(fma.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 y y))
(fma.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 y #s(literal 3 binary64))))) #s(literal -1 binary64)) (*.f64 x x))
(fma.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (pow.f64 (*.f64 (neg.f64 x) (-.f64 x (*.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (*.f64 y #s(literal 2 binary64)) x (fma.f64 y y (*.f64 x x)))
(fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64))) (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (/.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x)) (*.f64 y y))
(fma.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (/.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (*.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) (pow.f64 (*.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))) (*.f64 y y))
(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 y (*.f64 #s(literal 2 binary64) x) (fma.f64 y y (*.f64 x x)))
(fma.f64 (*.f64 #s(literal 2 binary64) x) y (fma.f64 y y (*.f64 x x)))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) (fma.f64 y y (*.f64 x x)))
(fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y))
(fma.f64 x (*.f64 y #s(literal 2 binary64)) (fma.f64 y y (*.f64 x x)))
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(-.f64 (fma.f64 y y (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) x) (-.f64 x (*.f64 y #s(literal 2 binary64))))) (/.f64 (/.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) x) (-.f64 x (*.f64 y #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 y y) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (/.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (-.f64 (*.f64 y y) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))) (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x y) y) #s(literal 2 binary64)) (-.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) x) (-.f64 x (*.f64 y #s(literal 2 binary64)))) (-.f64 (/.f64 (/.f64 (pow.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) x) (-.f64 x (*.f64 y #s(literal 2 binary64)))) (*.f64 y y)))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (fma.f64 y y (*.f64 x x)) (*.f64 y (*.f64 #s(literal 2 binary64) x)))
(+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(+.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x y) y) (*.f64 x x))
(+.f64 (*.f64 y y) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(+.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) (*.f64 y y))
(+.f64 (*.f64 y (*.f64 #s(literal 2 binary64) x)) (fma.f64 y y (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (*.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 y x))
(*.f64 x (*.f64 y #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))

eval24.0ms (0.6%)

Memory
10.0MiB live, 84.5MiB allocated
Compiler

Compiled 6 527 to 649 computations (90.1% saved)

prune4.0ms (0.1%)

Memory
15.4MiB live, 15.4MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2134217
Fresh000
Picked101
Done000
Total2144218
Accuracy
100.0%
Counts
218 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.7%
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
95.7%
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
56.2%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
56.7%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Compiler

Compiled 55 to 36 computations (34.5% saved)

simplify16.0ms (0.4%)

Memory
-58.0MiB live, 7.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 11 expressions of interest:

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01898
02798
14390
25690
35990
05990
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 (fma.f64 #s(literal 2 binary64) x y) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
x
y
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
x
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
y
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
y
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 y #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
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 (fma.f64 #s(literal 2 binary64) x y) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
x
y
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
x
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
y
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
y
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 y #s(literal 2 binary64) x)
#s(literal 2 binary64)
x

localize41.0ms (1.1%)

Memory
27.1MiB live, 65.4MiB allocated
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(fma.f64 y #s(literal 2 binary64) x)
accuracy0.00390625
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
accuracy2.749969723661162
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
accuracy0.0
(fma.f64 #s(literal 2 binary64) x y)
accuracy0.0078125
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy2.749969723661162
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
accuracy0.0
(fma.f64 #s(literal 2 binary64) x y)
accuracy0.0078125
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy28.023030286019466
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
accuracy0.0
(*.f64 y y)
accuracy27.725057144031773
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Samples
31.0ms256×0valid
Compiler

Compiled 197 to 38 computations (80.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-mult: 12.0ms (62.8% of total)
ival-add: 7.0ms (36.6% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series11.0ms (0.3%)

Memory
-18.9MiB live, 19.3MiB allocated
Counts
9 → 33
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 (fma.f64 #s(literal 2 binary64) x y) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) 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
(+ 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 (+ (* 2 y) (/ (pow y 2) x)))
(* 2 x)
(* x (+ 2 (/ y x)))
x
(* x (+ 1 (* 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)))
(* -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 (* 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 (- (* -2 (/ x y)) 1)))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* -1 (* y (- (* -1 (/ x y)) 2)))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
y
@inf
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* x x) (* (+ (* 2 x) y) y)) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x))
1.0ms
y
@-inf
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* x x) (* (+ (* 2 x) y) y)) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x))
1.0ms
x
@-inf
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* x x) (* (+ (* 2 x) y) y)) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x))
1.0ms
x
@inf
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* x x) (* (+ (* 2 x) y) y)) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x))
1.0ms
x
@0
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* x x) (* (+ (* 2 x) y) y)) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x))

simplify128.0ms (3.3%)

Memory
35.9MiB live, 191.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082205
1269205
2745205
32192205
44595205
57551205
08023173
Stop Event
iter limit
node limit
Counts
33 → 31
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 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 (+ (* 2 y) (/ (pow y 2) x)))
(* 2 x)
(* x (+ 2 (/ y x)))
x
(* x (+ 1 (* 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)))
(* -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 (* 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 (- (* -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
(+ 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 (fma.f64 y #s(literal 2 binary64) x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ y x)))
(fma.f64 #s(literal 2 binary64) x y)
x
(* x (+ 1 (* 2 (/ y x))))
(fma.f64 y #s(literal 2 binary64) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 #s(literal 2 binary64) x y)
(* -1 (* x (- (* -2 (/ y x)) 1)))
(fma.f64 y #s(literal 2 binary64) x)
(+ (* 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 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
(* y (+ (* 2 x) (/ (pow x 2) y)))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(* y (+ 2 (/ x y)))
(fma.f64 y #s(literal 2 binary64) x)
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 #s(literal 2 binary64) x y)
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(* -1 (* y (- (* -1 (/ x y)) 2)))
(fma.f64 y #s(literal 2 binary64) x)

rewrite272.0ms (7%)

Memory
-12.2MiB live, 300.4MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01878
02778
111270
298770
0906270
Stop Event
iter limit
node limit
iter limit
Counts
9 → 486
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 (fma.f64 #s(literal 2 binary64) x y) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 y #s(literal 2 binary64) x)
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y)) y) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) y) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)))
(*.f64 (*.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y))) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y) #s(literal -1 binary64)))
(*.f64 (*.f64 y (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y))))
(*.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 y y) (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))))))
(*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y)) (*.f64 (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y) #s(literal -1 binary64)) y))
(*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (*.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
(/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (*.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (*.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (pow.f64 y #s(literal 3 binary64)) (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y)) y)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) y)) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (neg.f64 (*.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y)))) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y)))
(/.f64 (neg.f64 (*.f64 y (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (neg.f64 (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (*.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 y y) (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y)) y) (-.f64 (*.f64 #s(literal 2 binary64) x) y))
(/.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) y) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (*.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y))) (-.f64 (*.f64 #s(literal 2 binary64) x) y))
(/.f64 (*.f64 y (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x))))
(/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (*.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y)) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))) (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y) (*.f64 y (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))) (*.f64 y (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (neg.f64 (pow.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 y y) (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x))))) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (*.f64 y y) (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x))))))
(/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x y)))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 (*.f64 y x) #s(literal 2 binary64)))
(fma.f64 (*.f64 y x) #s(literal 2 binary64) (*.f64 y y))
(fma.f64 (*.f64 x y) #s(literal 2 binary64) (*.f64 y y))
(fma.f64 (*.f64 y #s(literal 2 binary64)) x (*.f64 y y))
(fma.f64 (*.f64 #s(literal 2 binary64) x) y (*.f64 y y))
(fma.f64 y (*.f64 #s(literal 2 binary64) x) (*.f64 y y))
(fma.f64 y y (*.f64 (*.f64 y x) #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) (*.f64 y y))
(fma.f64 #s(literal 2 binary64) (*.f64 x y) (*.f64 y y))
(fma.f64 x (*.f64 y #s(literal 2 binary64)) (*.f64 y y))
(-.f64 (/.f64 (*.f64 (pow.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y))))
(+.f64 (*.f64 y y) (*.f64 (*.f64 y x) #s(literal 2 binary64)))
(+.f64 (*.f64 (*.f64 y x) #s(literal 2 binary64)) (*.f64 y y))
(*.f64 (fma.f64 y y (*.f64 #s(literal -4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 y (*.f64 #s(literal 2 binary64) x))))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x y))
(*.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (neg.f64 y) y))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y))))
(*.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 y (-.f64 y (*.f64 #s(literal 2 binary64) x)))))))
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(/.f64 (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 y y))) (-.f64 x (*.f64 y #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) (fma.f64 x x (*.f64 #s(literal -4 binary64) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (*.f64 (*.f64 y #s(literal 2 binary64)) (-.f64 (*.f64 y #s(literal 2 binary64)) x))) (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 (neg.f64 x) x))) (neg.f64 (-.f64 (*.f64 y #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (*.f64 (*.f64 y #s(literal 2 binary64)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64))) (*.f64 #s(literal 4 binary64) (*.f64 y y)))))
(/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) y) y (*.f64 (neg.f64 x) x)) (-.f64 (*.f64 y #s(literal 2 binary64)) x))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (*.f64 (*.f64 y #s(literal 2 binary64)) (-.f64 (*.f64 y #s(literal 2 binary64)) x))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64))) (*.f64 #s(literal 4 binary64) (*.f64 y y))))
(neg.f64 (fma.f64 #s(literal -2 binary64) y (neg.f64 x)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 y #s(literal 2 binary64)))
(fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (pow.f64 (-.f64 (*.f64 y #s(literal 2 binary64)) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 y #s(literal 2 binary64)) x))))
(fma.f64 y #s(literal 2 binary64) x)
(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 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 y y)) (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (neg.f64 (/.f64 (*.f64 x 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)))

eval82.0ms (2.1%)

Memory
-5.8MiB live, 84.1MiB allocated
Compiler

Compiled 12 159 to 1 138 computations (90.6% saved)

prune11.0ms (0.3%)

Memory
-6.5MiB live, 29.8MiB allocated
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New4334437
Fresh000
Picked134
Done000
Total4347441
Accuracy
100.0%
Counts
441 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
51.9%
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
95.7%
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
53.8%
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
58.1%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
56.2%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
56.7%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
60.7%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Compiler

Compiled 111 to 74 computations (33.3% saved)

simplify5.0ms (0.1%)

Memory
16.4MiB live, 16.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y #s(literal 2 binary64))
cost-diff0
#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
cost-diff0
(*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x)
cost-diff0
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
cost-diff0
(*.f64 #s(literal 2 binary64) x)
cost-diff0
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
cost-diff0
(*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y)
cost-diff0
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
cost-diff0
(fma.f64 y #s(literal 2 binary64) x)
cost-diff0
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
cost-diff0
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) 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
026131
035131
151125
268125
372125
072120
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
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 y #s(literal 2 binary64) x)
y
#s(literal 2 binary64)
x
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
x
(*.f64 #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)
y
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
y
(*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x)
#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
(*.f64 y #s(literal 2 binary64))
#s(literal 2 binary64)
x
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 y #s(literal 2 binary64) x)
y
#s(literal 2 binary64)
x
(fma.f64 x 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))
x
(*.f64 #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)
y
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
(fma.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x (*.f64 y y))
y
(*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x)
#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
(*.f64 y #s(literal 2 binary64))
#s(literal 2 binary64)
x

localize74.0ms (1.9%)

Memory
-29.3MiB live, 94.7MiB allocated
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 y #s(literal 2 binary64))
accuracy0.00390625
(*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x)
accuracy2.749969723661162
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
accuracy32.9069428156289
#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
accuracy0.0
(*.f64 #s(literal 2 binary64) x)
accuracy0.0078125
(*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y)
accuracy2.749969723661162
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
accuracy29.680505683334392
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
accuracy0.0
(fma.f64 y #s(literal 2 binary64) x)
accuracy0.00390625
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
accuracy26.79064085444805
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
accuracy0.0
(*.f64 x x)
accuracy25.172605222566244
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Samples
35.0ms256×0valid
Compiler

Compiled 239 to 46 computations (80.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-mult: 15.0ms (67.9% of total)
ival-add: 6.0ms (27.1% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory
7.8MiB live, 7.8MiB allocated
Counts
13 → 33
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 y #s(literal 2 binary64) x)
(fma.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)
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
(*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x)
#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
(*.f64 y #s(literal 2 binary64))
Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(pow x 2)
(* 2 (* x y))
(* x (+ x (* 2 y)))
(* 2 y)
(+ x (* 2 y))
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)))))
x
(* x (+ 1 (* 2 (/ y x))))
(* 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 x)) 1)))
(* -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 (+ (* 2 x) (/ (pow x 2) y)))
(* y (+ 2 (/ x y)))
(* y (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* -1 (* y (- (* -1 (/ x y)) 2)))
(* -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) (* (* x 2) y)) (* y y)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (* x x) (* (+ (* 2 x) y) y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (* 2 x) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (* y 2))
1.0ms
x
@inf
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (* x x) (* (+ (* 2 x) y) y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (* 2 x) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (* y 2))
1.0ms
y
@-inf
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (* x x) (* (+ (* 2 x) y) y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (* 2 x) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (* y 2))
1.0ms
y
@inf
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (* x x) (* (+ (* 2 x) y) y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (* 2 x) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (* y 2))
1.0ms
x
@0
((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (* x x) (* (+ (* 2 x) y) y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (* 2 x) (+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (* y 2))

simplify179.0ms (4.6%)

Memory
11.0MiB live, 125.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082205
1269205
2745205
32211205
44627205
57595205
08064173
Stop Event
iter limit
node limit
Counts
33 → 31
Calls
Call 1
Inputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(pow x 2)
(* 2 (* x y))
(* x (+ x (* 2 y)))
(* 2 y)
(+ x (* 2 y))
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)))))
x
(* x (+ 1 (* 2 (/ y x))))
(* 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 x)) 1)))
(* -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 (+ (* 2 x) (/ (pow x 2) y)))
(* y (+ 2 (/ x y)))
(* y (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* -1 (* y (- (* -1 (/ x y)) 2)))
(* -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 y #s(literal 2 binary64) x) x (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* 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)
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 (fma.f64 y #s(literal 2 binary64) x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
x
(* x (+ 1 (* 2 (/ y x))))
(fma.f64 y #s(literal 2 binary64) x)
(* x (+ (* 2 y) (/ (pow y 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* x (+ 2 (/ y x)))
(fma.f64 #s(literal 2 binary64) x y)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
(* -1 (* x (- (* -2 (/ y x)) 1)))
(fma.f64 y #s(literal 2 binary64) x)
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 #s(literal 2 binary64) x y)
(+ (* 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 y #s(literal 2 binary64) x) x (*.f64 y y))
(* y (+ y (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(* y (+ 2 (/ x y)))
(fma.f64 y #s(literal 2 binary64) x)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(* -1 (* y (- (* -1 (/ x y)) 2)))
(fma.f64 y #s(literal 2 binary64) x)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 #s(literal 2 binary64) x y)

rewrite246.0ms (6.3%)

Memory
28.6MiB live, 183.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026121
035121
1120115
2941115
08256110
Stop Event
iter limit
node limit
iter limit
Counts
13 → 206
Calls
Call 1
Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 y #s(literal 2 binary64) x)
(fma.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)
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
(*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x)
#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
(*.f64 y #s(literal 2 binary64))
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
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eval66.0ms (1.7%)

Memory
-9.4MiB live, 41.3MiB allocated
Compiler

Compiled 8 297 to 760 computations (90.8% saved)

prune17.0ms (0.4%)

Memory
-21.8MiB live, 16.9MiB allocated
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New2160216
Fresh000
Picked044
Done033
Total2167223
Accuracy
100.0%
Counts
223 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
51.9%
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
95.7%
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
53.8%
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
58.1%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
56.2%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
56.7%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
60.7%
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
Compiler

Compiled 244 to 112 computations (54.1% saved)

regimes10.0ms (0.2%)

Memory
15.5MiB live, 15.5MiB allocated
Counts
9 → 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))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
Outputs
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
Calls

3 calls:

3.0ms
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%2x
100.0%2y
98.2%2(+.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)

regimes77.0ms (2%)

Memory
-29.6MiB live, 10.0MiB allocated
Counts
7 → 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))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
Calls

2 calls:

74.0ms
x
3.0ms
y
Results
AccuracySegmentsBranch
100.0%2x
97.7%2y
Compiler

Compiled 2 to 4 computations (-100% saved)

regimes7.0ms (0.2%)

Memory
8.0MiB live, 8.0MiB allocated
Counts
6 → 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))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 x x (*.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(fma.f64 y y (*.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
Calls

3 calls:

2.0ms
x
2.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
2.0ms
y
Results
AccuracySegmentsBranch
86.0%2y
64.7%2(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
88.7%2x
Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes2.0ms (0%)

Memory
1.7MiB live, 1.7MiB 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

1 calls:

1.0ms
x
Results
AccuracySegmentsBranch
88.5%2x
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes3.0ms (0.1%)

Memory
4.4MiB live, 4.4MiB 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

3 calls:

1.0ms
x
1.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
1.0ms
y
Results
AccuracySegmentsBranch
60.7%1(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
60.7%1y
60.7%1x
Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch8.0ms (0.2%)

Memory
3.0MiB live, 3.0MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
7.0ms
3.029816948849646e+140
6.358150836427054e+140
Samples
4.0ms80×0valid
Compiler

Compiled 146 to 109 computations (25.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 2.0ms (73.3% of total)
ival-add: 1.0ms (36.6% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch12.0ms (0.3%)

Memory
4.1MiB live, 4.1MiB allocated
Algorithm
binary-search
Stop Event
predicate-same
Steps
TimeLeftRight
10.0ms
-1.719386701887236e+191
-9.758405291077438e+185
Samples
6.0ms112×0valid
Compiler

Compiled 198 to 147 computations (25.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-mult: 3.0ms (78.8% of total)
ival-add: 1.0ms (26.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch12.0ms (0.3%)

Memory
4.1MiB live, 4.1MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
10.0ms
-1.2695685507174354e-17
-5.970377052750271e-20
Samples
6.0ms112×0valid
Compiler

Compiled 275 to 196 computations (28.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-mult: 3.0ms (76.5% of total)
ival-add: 1.0ms (25.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
1.0ms
-1.2695685507174354e-17
-5.970377052750271e-20
Compiler

Compiled 254 to 182 computations (28.3% saved)

simplify66.0ms (1.7%)

Memory
-20.7MiB live, 18.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030156
132156
Stop Event
saturated
Calls
Call 1
Inputs
(if (<=.f64 y #s(literal 629999999999999971772042677720707107320085122381498420870810919186200387282225586886692277358428678926886615475192055692798859247824725344256 binary64)) (fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
(if (<=.f64 x #s(literal -999999999999999979617044168753715171107129451866841652067632118957448454785561110036171446110395985078602511391629572118883509758736380261518894779920079058604308854941977225917932503040 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) (fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -3530761863803683/41538374868278621028243970633760768 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -3530761863803683/41538374868278621028243970633760768 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
(if (<=.f64 y #s(literal 629999999999999971772042677720707107320085122381498420870810919186200387282225586886692277358428678926886615475192055692798859247824725344256 binary64)) (fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
(if (<=.f64 x #s(literal -999999999999999979617044168753715171107129451866841652067632118957448454785561110036171446110395985078602511391629572118883509758736380261518894779920079058604308854941977225917932503040 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) (fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -3530761863803683/41538374868278621028243970633760768 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -3530761863803683/41538374868278621028243970633760768 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))

soundness643.0ms (16.6%)

Memory
7.2MiB live, 168.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0933
01533
15029
242029
3635729
0821926
056129
1166129
2468129
31326129
43270129
56410129
08142110
082205
1269205
2745205
32192205
44595205
57551205
08023173
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 242 to 88 computations (63.6% saved)

preprocess70.0ms (1.8%)

Memory
22.8MiB live, 138.8MiB allocated
Compiler

Compiled 424 to 134 computations (68.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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