System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

Time bar (total: 3.4s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample596.0ms (17.6%)

Memory
15.5MiB live, 749.5MiB allocated
Samples
369.0ms8 255×0valid
0.0ms1×2valid
Precisions
Click to see histograms. Total time spent on operations: 205.0ms
ival-mult: 125.0ms (60.9% of total)
ival-sub: 67.0ms (32.6% of total)
ival-true: 6.0ms (2.9% of total)
exact: 5.0ms (2.4% of total)
ival-assert: 3.0ms (1.5% of total)
adjust: 0.0ms (0% of total)
Bogosity

explain268.0ms (7.9%)

Memory
-12.2MiB live, 72.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-y
00-0-(-.f64 (*.f64 x x) y)
00-0-(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
00-0-#s(literal 1/2 binary64)
00-0-(*.f64 x x)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
159.0ms512×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 147.0ms
ival-mult: 143.0ms (97.5% of total)
ival-sub: 2.0ms (1.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess43.0ms (1.3%)

Memory
7.7MiB live, 45.4MiB allocated
Algorithm
1×egg-herbie
Rules
336×lower-fma.f64
336×lower-fma.f32
216×lower-*.f32
212×lower-*.f64
200×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01637
14635
212935
338135
467835
584435
688235
788235
067
097
1127
2237
3457
4717
5997
61697
72667
84107
94667
104967
04967
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
Outputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
(*.f64 (-.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify14.0ms (0.4%)

Memory
17.2MiB live, 17.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) y)
cost-diff0
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
Rules
336×lower-fma.f64
336×lower-fma.f32
216×lower-*.f32
212×lower-*.f64
80×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
0918
11218
22318
34518
47118
59918
616918
726618
841018
946618
1049618
049618
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
#s(literal 1/2 binary64)
(-.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
Outputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
(*.f64 (-.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 (*.f64 x x) y)
(*.f64 x x)
x
y

localize31.0ms (0.9%)

Memory
-14.1MiB live, 23.0MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 (*.f64 x x) y)
accuracy0
(*.f64 x x)
accuracy0
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
Samples
27.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-mult: 5.0ms (75.8% of total)
ival-sub: 1.0ms (15.2% 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
4.4MiB live, 4.4MiB allocated
Counts
3 → 60
Calls
Call 1
Inputs
#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())
#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) 1)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) 1)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) 1)) (taylor inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) y) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) y) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) y) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) y) (patch (-.f64 (*.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify132.0ms (3.9%)

Memory
15.9MiB live, 94.5MiB allocated
Algorithm
1×egg-herbie
Rules
5 028×lower-fma.f64
5 028×lower-fma.f32
3 454×lower-*.f64
3 454×lower-*.f32
1 354×div-sub
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035327
1102327
2299327
3996291
42501291
54979291
67157291
08115291
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
Calls
Call 1
Inputs
(* 1/2 (pow x 2))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(pow x 2)
(+ (* -1 y) (pow x 2))
(+ (* -1 y) (pow x 2))
(+ (* -1 y) (pow x 2))
(* -1/2 y)
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* -1 y)
(* y (- (/ (pow x 2) y) 1))
(* y (- (/ (pow x 2) y) 1))
(* y (- (/ (pow x 2) y) 1))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(* -1/2 y)
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(* -1 y)
(- (pow x 2) y)
(- (pow x 2) y)
(- (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(+ (* -1 y) (pow x 2))
(fma.f64 x x (neg.f64 y))
(+ (* -1 y) (pow x 2))
(fma.f64 x x (neg.f64 y))
(+ (* -1 y) (pow x 2))
(fma.f64 x x (neg.f64 y))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 y)
(neg.f64 y)
(* y (- (/ (pow x 2) y) 1))
(fma.f64 x x (neg.f64 y))
(* y (- (/ (pow x 2) y) 1))
(fma.f64 x x (neg.f64 y))
(* y (- (/ (pow x 2) y) 1))
(fma.f64 x x (neg.f64 y))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(fma.f64 x x (neg.f64 y))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(fma.f64 x x (neg.f64 y))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(fma.f64 x x (neg.f64 y))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 y)
(neg.f64 y)
(- (pow x 2) y)
(fma.f64 x x (neg.f64 y))
(- (pow x 2) y)
(fma.f64 x x (neg.f64 y))
(- (pow x 2) y)
(fma.f64 x x (neg.f64 y))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite299.0ms (8.8%)

Memory
-6.8MiB live, 225.7MiB allocated
Rules
6 946×lower-fma.f64
6 946×lower-fma.f32
4 110×lower-/.f64
4 110×lower-/.f32
3 550×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
0915
12715
217815
3164515
0853215
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 266
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
(-.f64 (*.f64 x x) y)
(*.f64 x x)
Outputs
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eval75.0ms (2.2%)

Memory
12.4MiB live, 49.5MiB allocated
Compiler

Compiled 8 156 to 910 computations (88.8% saved)

prune58.0ms (1.7%)

Memory
-33.6MiB live, 19.7MiB allocated
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3242326
Fresh000
Picked011
Done000
Total3243327
Accuracy
100.0%
Counts
327 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
▶53.5%
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
▶48.7%
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
Compiler

Compiled 17 to 17 computations (0% saved)

simplify15.0ms (0.4%)

Memory
14.3MiB live, 14.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (- (* x x) y) (*.f64 x x))
cost-diff0
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
cost-diff0
(*.f64 y #s(literal -1/2 binary64))
cost-diff0
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
Rules
336×lower-fma.f64
336×lower-fma.f32
220×lower-*.f32
214×lower-*.f64
80×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01241
01541
12041
23141
35241
47741
510541
617541
727441
841541
947141
1050341
050341
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
#s(literal 1/2 binary64)
#s(approx (- (* x x) y) (*.f64 x x))
(*.f64 x x)
x
Outputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) y)
y
#s(literal -1/2 binary64)
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
(*.f64 #s(approx (- (* x x) y) (*.f64 x x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (- (* x x) y) (*.f64 x x))
(*.f64 x x)
x

localize46.0ms (1.4%)

Memory
-8.9MiB live, 27.9MiB allocated
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
accuracy29.7524752781461
#s(approx (- (* x x) y) (*.f64 x x))
accuracy0
(*.f64 y #s(literal -1/2 binary64))
accuracy32.856336445498236
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
Samples
40.0ms256×0valid
Compiler

Compiled 31 to 10 computations (67.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-mult: 31.0ms (93.7% of total)
ival-sub: 1.0ms (3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory
12.0MiB live, 12.0MiB allocated
Counts
5 → 96
Calls
Call 1
Inputs
#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (/ (pow x 2) y)) 1/2)) (taylor inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) 1)) (taylor inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) 1)) (taylor inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) 1)) (taylor inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal -1/2 binary64)) (patch (*.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (pow x 2) y))))) (taylor -inf y) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) y) (taylor 0 x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) y) (taylor 0 x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) y) (taylor 0 x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) (patch (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) y) (*.f64 x x)) (patch #s(approx (- (* x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify101.0ms (3%)

Memory
16.5MiB live, 87.4MiB allocated
Algorithm
1×egg-herbie
Rules
5 028×lower-fma.f64
5 028×lower-fma.f32
3 454×lower-*.f64
3 454×lower-*.f32
1 354×div-sub
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035549
1102549
2299549
3996477
42501477
54979477
67157477
08115477
Stop Event
1×iter limit
1×node limit
Counts
96 → 96
Calls
Call 1
Inputs
(* 1/2 (pow x 2))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* 1/2 (pow x 2))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(pow x 2)
(+ (* -1 y) (pow x 2))
(+ (* -1 y) (pow x 2))
(+ (* -1 y) (pow x 2))
(* -1/2 y)
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(* -1 y)
(* y (- (/ (pow x 2) y) 1))
(* y (- (/ (pow x 2) y) 1))
(* y (- (/ (pow x 2) y) 1))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(* -1/2 y)
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(* -1/2 y)
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(* -1 y)
(- (pow x 2) y)
(- (pow x 2) y)
(- (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(+ (* -1 y) (pow x 2))
(fma.f64 x x (neg.f64 y))
(+ (* -1 y) (pow x 2))
(fma.f64 x x (neg.f64 y))
(+ (* -1 y) (pow x 2))
(fma.f64 x x (neg.f64 y))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* y (- (* 1/2 (/ (pow x 2) y)) 1/2))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 y)
(neg.f64 y)
(* y (- (/ (pow x 2) y) 1))
(fma.f64 x x (neg.f64 y))
(* y (- (/ (pow x 2) y) 1))
(fma.f64 x x (neg.f64 y))
(* y (- (/ (pow x 2) y) 1))
(fma.f64 x x (neg.f64 y))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 (* y (+ 1/2 (* -1/2 (/ (pow x 2) y)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(fma.f64 x x (neg.f64 y))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(fma.f64 x x (neg.f64 y))
(* -1 (* y (+ 1 (* -1 (/ (pow x 2) y)))))
(fma.f64 x x (neg.f64 y))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1/2 y)
(*.f64 y #s(literal -1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(+ (* -1/2 y) (* 1/2 (pow x 2)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* -1 y)
(neg.f64 y)
(- (pow x 2) y)
(fma.f64 x x (neg.f64 y))
(- (pow x 2) y)
(fma.f64 x x (neg.f64 y))
(- (pow x 2) y)
(fma.f64 x x (neg.f64 y))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/2 (/ y (pow x 2)))))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(* (pow x 2) (+ 1 (* -1 (/ y (pow x 2)))))
(fma.f64 x x (neg.f64 y))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite150.0ms (4.4%)

Memory
-24.1MiB live, 221.5MiB allocated
Rules
6 950×lower-fma.f64
6 950×lower-fma.f32
4 110×lower-/.f64
4 110×lower-/.f32
3 558×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01237
01537
13537
218637
3165637
0852037
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
5 → 26
Calls
Call 1
Inputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
#s(approx (- (* x x) y) (*.f64 x x))
(*.f64 x x)
Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval11.0ms (0.3%)

Memory
21.2MiB live, 21.2MiB allocated
Compiler

Compiled 864 to 98 computations (88.7% saved)

prune128.0ms (3.8%)

Memory
-22.4MiB live, 15.2MiB allocated
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1220122
Fresh000
Picked022
Done011
Total1223125
Accuracy
100.0%
Counts
125 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
✓53.5%
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
✓48.7%
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
Compiler

Compiled 34 to 28 computations (17.6% saved)

regimes10.0ms (0.3%)

Memory
23.6MiB live, 23.6MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
Outputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
Calls

5 calls:

2.0ms
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
2.0ms
y
2.0ms
(-.f64 (*.f64 x x) y)
2.0ms
x
2.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
100.0%1(-.f64 (*.f64 x x) y)
100.0%1(*.f64 x x)
Compiler

Compiled 17 to 17 computations (0% saved)

regimes27.0ms (0.8%)

Memory
-11.9MiB live, 25.0MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
Outputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x)))
Calls

5 calls:

21.0ms
(-.f64 (*.f64 x x) y)
2.0ms
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
2.0ms
y
2.0ms
(*.f64 x x)
2.0ms
x
Results
AccuracySegmentsBranch
86.8%2x
69.5%3y
80.9%2(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
80.9%2(-.f64 (*.f64 x x) y)
86.8%2(*.f64 x x)
Compiler

Compiled 17 to 17 computations (0% saved)

regimes319.0ms (9.4%)

Memory
-27.4MiB live, 22.3MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
Outputs
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
Calls

5 calls:

314.0ms
y
1.0ms
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
1.0ms
x
1.0ms
(-.f64 (*.f64 x x) y)
1.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
48.7%1y
48.7%1(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
48.7%1(-.f64 (*.f64 x x) y)
48.7%1x
48.7%1(*.f64 x x)
Compiler

Compiled 17 to 17 computations (0% saved)

bsearch10.0ms (0.3%)

Memory
13.1MiB live, 13.1MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
9.0ms
104802.74247692474
1058262202.7798247
Samples
4.0ms128×0valid
Compiler

Compiled 74 to 107 computations (-44.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-sub: 1.0ms (56.2% of total)
ival-mult: 1.0ms (56.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify293.0ms (8.6%)

Memory
2.4MiB live, 41.9MiB allocated
Algorithm
1×egg-herbie
Rules
8×*-commutative-binary64-*.f64
4×+-commutative-binary64-+.f64
4×sub-neg-binary64-neg.f64-+.f64--.f64
2×neg-sub0-binary64--.f64-neg.f64
2×neg-mul-1-binary64-*.f64-neg.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01746
12246
22746
32946
43046
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
(if (<=.f64 (*.f64 x x) #s(literal 165000 binary64)) #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
Outputs
(*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y))
(*.f64 (-.f64 (*.f64 x x) y) #s(literal 1/2 binary64))
(if (<=.f64 (*.f64 x x) #s(literal 165000 binary64)) #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) (*.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))))
(if (<=.f64 (*.f64 x x) #s(literal 165000 binary64)) #s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y)) (*.f64 #s(approx (- (* x x) y) (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

soundness373.0ms (11%)

Memory
1.6MiB live, 171.1MiB allocated
Rules
5 028×lower-fma.f64
5 028×lower-fma.f32
3 454×lower-*.f64
3 454×lower-*.f32
1 354×div-sub
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035327
1102327
2299327
3996291
42501291
54979291
67157291
08115291
Stop Event
1×done
1×iter limit
1×node limit
Compiler

Compiled 38 to 27 computations (28.9% saved)

preprocess382.0ms (11.3%)

Memory
-14.9MiB live, 63.6MiB allocated
Remove

(abs x)

Compiler

Compiled 110 to 76 computations (30.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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