ENA, Section 1.4, Exercise 4b, n=2

Time bar (total: 7.7s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25.7%74.3%0%0%0%0
100%25.7%0%74.3%0%0%0%1
Compiler

Compiled 25 to 18 computations (28% saved)

sample1.5s (19.3%)

Memory
34.2MiB live, 1 937.8MiB allocated
Samples
540.0ms5 190×0valid
479.0ms2 512×1valid
142.0ms554×2valid
Precisions
Click to see histograms. Total time spent on operations: 732.0ms
ival-pow2: 343.0ms (46.9% of total)
ival-add: 107.0ms (14.6% of total)
adjust: 101.0ms (13.8% of total)
ival-<=: 87.0ms (11.9% of total)
ival-sub: 54.0ms (7.4% of total)
ival-and: 20.0ms (2.7% of total)
exact: 16.0ms (2.2% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

explain139.0ms (1.8%)

Memory
-31.5MiB live, 70.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
650-0-(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
00-0-eps
00-0-(pow.f64 x #s(literal 2 binary64))
00-0-#s(literal 2 binary64)
00-0-(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
00-0-(+.f64 x eps)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))cancellation651
Confusion
Predicted +Predicted -
+650
-0191
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+6500
-01190
Precision?
0.9848484848484849
Recall?
1.0
Freqs
test
numberfreq
0191
165
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
50.0ms336×0valid
17.0ms150×1valid
4.0ms26×2valid
Compiler

Compiled 61 to 25 computations (59% saved)

Precisions
Click to see histograms. Total time spent on operations: 55.0ms
ival-pow2: 44.0ms (79.5% of total)
ival-add: 4.0ms (7.2% of total)
adjust: 3.0ms (5.4% of total)
ival-sub: 3.0ms (5.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess683.0ms (8.9%)

Memory
18.0MiB live, 408.6MiB allocated
Algorithm
egg-herbie
Rules
18 770×lower-fma.f64
18 770×lower-fma.f32
2 836×lower-*.f64
2 836×lower-*.f32
2 498×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01955
14547
214945
354235
4166035
5380035
6526935
7598935
8621635
9632235
10634335
11634335
12634335
13634335
14643435
15676235
16756035
17799635
079
0119
1169
2369
3969
42767
58617
623747
742777
859217
969137
1073387
1176067
1276127
1376127
080476
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Outputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 eps (+.f64 eps (+.f64 x x)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.6%
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify414.0ms (5.4%)

Memory
-19.4MiB live, 573.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x eps)
cost-diff512
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
cost-diff5952
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff6144
(pow.f64 x #s(literal 2 binary64))
Rules
18 770×lower-fma.f64
18 770×lower-fma.f32
2 836×lower-*.f64
2 836×lower-*.f32
2 498×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0723
01123
11623
23623
39623
427621
586121
6237421
7427721
8592121
9691321
10733821
11760621
12761221
13761221
0804720
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
Outputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 eps (+.f64 eps (+.f64 x x)))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(*.f64 (+.f64 x eps) (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)

localize28.0ms (0.4%)

Memory
5.8MiB live, 45.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(pow.f64 x #s(literal 2 binary64))
accuracy0
(+.f64 x eps)
accuracy0.01953125
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy14.333604029977964
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Samples
9.0ms75×1valid
9.0ms168×0valid
2.0ms13×2valid
Compiler

Compiled 25 to 9 computations (64% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-pow2: 6.0ms (50.2% of total)
ival-add: 2.0ms (16.7% of total)
ival-sub: 2.0ms (16.7% of total)
adjust: 1.0ms (8.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
8.5MiB live, 8.5MiB allocated
Counts
4 → 84
Calls
Call 1
Inputs
#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
Outputs
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* 2 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* 2 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* 2 x))) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* 2 x))) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
Calls

21 calls:

TimeVariablePointExpression
0.0ms
eps
@inf
(pow (+ x eps) 2)
0.0ms
x
@inf
(pow x 2)
0.0ms
x
@0
(pow x 2)
0.0ms
eps
@0
(- (pow (+ x eps) 2) (pow x 2))
0.0ms
x
@0
(pow (+ x eps) 2)

simplify233.0ms (3%)

Memory
-26.5MiB live, 337.5MiB allocated
Algorithm
egg-herbie
Rules
9 222×lower-fma.f64
9 222×lower-fma.f32
3 242×lower-*.f64
3 242×lower-*.f32
1 646×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069492
1214450
2574450
31825438
44173438
57244438
08097390
Stop Event
iter limit
node limit
Counts
84 → 78
Calls
Call 1
Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(pow x 2)
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 2 binary64) eps x))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 2 binary64) eps x))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow x 2)
(*.f64 x x)
(+ (* 2 (* eps x)) (pow x 2))
(*.f64 x (fma.f64 #s(literal 2 binary64) eps x))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* 2 (* eps x))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* 2 (* eps x))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* 2 (* eps x))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)

rewrite300.0ms (3.9%)

Memory
44.3MiB live, 395.0MiB allocated
Rules
5 048×lower-fma.f64
5 048×lower-fma.f32
4 066×lower-*.f64
4 066×lower-*.f32
2 090×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
01120
15220
237120
3510720
0821920
Stop Event
iter limit
node limit
iter limit
Counts
4 → 371
Calls
Call 1
Inputs
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(+.f64 x eps)
Outputs
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(*.f64 x x)
(*.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 x)))
(*.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(+.f64 (*.f64 x (+.f64 x eps)) (*.f64 eps (+.f64 x eps)))
(+.f64 (*.f64 eps (+.f64 x eps)) (*.f64 x (+.f64 x eps)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (+.f64 x eps))))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (+.f64 x eps))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x eps))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (+.f64 x eps))))
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 x eps)) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (+.f64 x eps))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (+.f64 x eps) (*.f64 eps (+.f64 x eps)))
(fma.f64 eps (+.f64 x eps) (*.f64 x (+.f64 x eps)))
(fma.f64 (+.f64 x eps) x (*.f64 eps (+.f64 x eps)))
(fma.f64 (+.f64 x eps) eps (*.f64 x (+.f64 x eps)))
(fma.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) eps) (*.f64 x (+.f64 x eps)))
(fma.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) x) (*.f64 eps (+.f64 x eps)))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) eps) (*.f64 x (+.f64 x eps)))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) (*.f64 eps (+.f64 x eps)))
(fma.f64 (sqrt.f64 x) (*.f64 (+.f64 x eps) (sqrt.f64 x)) (*.f64 eps (+.f64 x eps)))
(fma.f64 (sqrt.f64 (+.f64 x eps)) (*.f64 x (sqrt.f64 (+.f64 x eps))) (*.f64 eps (+.f64 x eps)))
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eval60.0ms (0.8%)

Memory
-44.1MiB live, 125.4MiB allocated
Compiler

Compiled 14 368 to 1 131 computations (92.1% saved)

prune66.0ms (0.9%)

Memory
25.8MiB live, 104.2MiB allocated
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New4445449
Fresh000
Picked101
Done000
Total4455450
Accuracy
100.0%
Counts
450 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
67.5%
(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
67.3%
(fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps)))
66.7%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
75.3%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 104 to 52 computations (50% saved)

simplify435.0ms (5.7%)

Memory
25.5MiB live, 454.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(neg.f64 (*.f64 x x))
cost-diff0
(+.f64 x eps)
cost-diff128
(fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))
cost-diff768
(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
cost-diff0
(+.f64 x eps)
cost-diff0
(*.f64 (+.f64 x eps) (+.f64 x eps))
cost-diff0
(neg.f64 x)
cost-diff512
(fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps)))
cost-diff0
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
cost-diff128
(*.f64 #s(literal 2 binary64) eps)
cost-diff0
(*.f64 eps eps)
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
cost-diff0
(fma.f64 x #s(literal 2 binary64) eps)
cost-diff0
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
Rules
17 644×lower-fma.f32
17 636×lower-fma.f64
2 624×lower-+.f32
2 622×lower-+.f64
2 384×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023132
040126
174126
2124126
3275108
4734108
52456108
63891108
74949108
85468108
95702108
105796108
115836108
126056108
136376108
146440108
156536108
166568108
176568108
187947108
08029107
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
eps
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
x
(*.f64 #s(literal 2 binary64) eps)
#s(literal 2 binary64)
eps
(fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps)))
(neg.f64 x)
x
(*.f64 (+.f64 x eps) (+.f64 x eps))
(+.f64 x eps)
eps
(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
(+.f64 x eps)
x
eps
(fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))
(neg.f64 (*.f64 x x))
(*.f64 x x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (+.f64 x (+.f64 x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 eps (+.f64 x (+.f64 x eps)))
eps
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 x (+.f64 x eps))
x
#s(literal 2 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (+.f64 eps eps)))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(*.f64 x (+.f64 eps eps))
x
(*.f64 #s(literal 2 binary64) eps)
(+.f64 eps eps)
#s(literal 2 binary64)
eps
(fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps)))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(neg.f64 x)
x
(*.f64 (+.f64 x eps) (+.f64 x eps))
(+.f64 x eps)
eps
(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(+.f64 x eps)
x
eps
(fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))
(fma.f64 x (-.f64 eps x) (*.f64 eps eps))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(*.f64 x x)

localize97.0ms (1.3%)

Memory
-29.2MiB live, 130.6MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0
(neg.f64 (*.f64 x x))
accuracy0.01171875
(fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))
accuracy20.766115561361506
(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
accuracy0
(+.f64 x eps)
accuracy0
(neg.f64 x)
accuracy0.01953125
(*.f64 (+.f64 x eps) (+.f64 x eps))
accuracy20.898107906709566
(fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps)))
accuracy0
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
accuracy0
(*.f64 #s(literal 2 binary64) eps)
accuracy21.305348917980293
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
accuracy0
(*.f64 eps eps)
accuracy15.778342268794304
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
accuracy0
(fma.f64 x #s(literal 2 binary64) eps)
accuracy0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
accuracy0.0078125
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
Samples
40.0ms168×0valid
23.0ms75×1valid
6.0ms13×2valid
Compiler

Compiled 123 to 25 computations (79.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-mult: 24.0ms (51.5% of total)
ival-add: 7.0ms (15% of total)
ival-pow2: 6.0ms (12.9% of total)
adjust: 4.0ms (8.6% of total)
ival-sub: 2.0ms (4.3% of total)
ival-neg: 2.0ms (4.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series20.0ms (0.3%)

Memory
-7.4MiB live, 30.5MiB allocated
Counts
16 → 324
Calls
Call 1
Inputs
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())
#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)) #<representation binary64>) () ())
#s(alt (*.f64 eps eps) (patch (*.f64 eps eps) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal 2 binary64) eps) (patch (*.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())
#s(alt (*.f64 x (*.f64 #s(literal 2 binary64) eps)) (patch (*.f64 x (*.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps))) (patch (fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps))) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (*.f64 (+.f64 x eps) (+.f64 x eps)) (patch (*.f64 (+.f64 x eps) (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt (fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))) (patch (fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))) #<representation binary64>) () ())
#s(alt (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))) (patch (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))) #<representation binary64>) () ())
#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt (pow eps 2) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (pow x 2)) (taylor 0 x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (neg.f64 (*.f64 x x)) (patch (neg.f64 (*.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 (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

81 calls:

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

simplify397.0ms (5.2%)

Memory
44.3MiB live, 439.3MiB allocated
Algorithm
egg-herbie
Rules
18 304×lower-fma.f64
18 304×lower-fma.f32
3 066×lower-*.f64
3 066×lower-*.f32
2 382×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221961
13881731
210611731
334141707
085241540
Stop Event
iter limit
node limit
Counts
324 → 315
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(pow x 2)
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* -1 (pow x 2))
(- (* eps x) (pow x 2))
(- (* eps (+ eps x)) (pow x 2))
(- (* eps (+ eps x)) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 x) (/ (pow x 2) eps)) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 x) (/ (pow x 2) eps)) eps))))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* x (+ eps (* -1 x))) (pow eps 2))
(+ (* x (+ eps (* -1 x))) (pow eps 2))
(* -1 (pow x 2))
(* (pow x 2) (- (/ eps x) 1))
(* (pow x 2) (- (+ (/ eps x) (/ (pow eps 2) (pow x 2))) 1))
(* (pow x 2) (- (+ (/ eps x) (/ (pow eps 2) (pow x 2))) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ eps x) 1))
(* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1))
(* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
eps
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
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(* (pow x 2) (- (/ eps x) 1))
(*.f64 x (-.f64 eps x))
(* (pow x 2) (- (+ (/ eps x) (/ (pow eps 2) (pow x 2))) 1))
(fma.f64 x (-.f64 eps x) (*.f64 eps eps))
(* (pow x 2) (- (+ (/ eps x) (/ (pow eps 2) (pow x 2))) 1))
(fma.f64 x (-.f64 eps x) (*.f64 eps eps))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* (pow x 2) (- (/ eps x) 1))
(*.f64 x (-.f64 eps x))
(* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1))
(fma.f64 x (-.f64 eps x) (*.f64 eps eps))
(* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1))
(fma.f64 x (-.f64 eps x) (*.f64 eps eps))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite464.0ms (6%)

Memory
16.6MiB live, 593.2MiB allocated
Rules
11 822×lower-fma.f32
11 814×lower-fma.f64
3 882×lower-*.f32
3 870×lower-*.f64
3 854×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023118
040109
1157109
21161109
08669109
Stop Event
iter limit
node limit
iter limit
Counts
16 → 897
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(fma.f64 x #s(literal 2 binary64) eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
(*.f64 #s(literal 2 binary64) eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps)))
(neg.f64 x)
(*.f64 (+.f64 x eps) (+.f64 x eps))
(+.f64 x eps)
(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
(fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))
(neg.f64 (*.f64 x x))
(*.f64 x x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(+.f64 (*.f64 eps eps) (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(+.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
(-.f64 (/.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))
(fma.f64 x (*.f64 eps #s(literal 2 binary64)) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(fma.f64 eps (*.f64 x #s(literal 2 binary64)) (*.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (*.f64 x eps) (*.f64 eps eps))
(fma.f64 (*.f64 eps #s(literal 2 binary64)) x (*.f64 eps eps))
(fma.f64 (*.f64 x #s(literal 2 binary64)) eps (*.f64 eps eps))
(fma.f64 (*.f64 x eps) #s(literal 2 binary64) (*.f64 eps eps))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)) (*.f64 (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (*.f64 eps (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))) (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) eps)))
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (fma.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))))
(/.f64 (*.f64 (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))
(/.f64 (*.f64 (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 eps (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (*.f64 eps (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) eps) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))
(/.f64 (neg.f64 (*.f64 eps (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 eps (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) eps)) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) eps)) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (fma.f64 (*.f64 eps eps) (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))
(*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(*.f64 (*.f64 eps (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) eps) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) eps) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(+.f64 (*.f64 x #s(literal 2 binary64)) eps)
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(fma.f64 x #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(fma.f64 (pow.f64 eps #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (fma.f64 eps eps (fma.f64 (*.f64 x x) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) (*.f64 x eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps eps (fma.f64 (*.f64 x x) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) (*.f64 x eps)))) (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64))) (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (neg.f64 (fma.f64 eps eps (fma.f64 (*.f64 x x) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) (*.f64 x eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (*.f64 eps eps))) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (neg.f64 (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x)))) (neg.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal -1 binary64))
(*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))
(*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps (fma.f64 (*.f64 x x) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) (*.f64 x eps))))))
(*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (neg.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))))
(*.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(*.f64 (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(*.f64 eps eps)
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(*.f64 eps #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (*.f64 x #s(literal 2 binary64))))
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(/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal 0 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (neg.f64 (*.f64 x (*.f64 x (*.f64 x x))))))
(/.f64 (neg.f64 (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x x))
(*.f64 x (neg.f64 x))
(*.f64 (neg.f64 x) x)
(*.f64 (*.f64 x x) #s(literal -1 binary64))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 x x))
(*.f64 (neg.f64 (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (neg.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)))
(*.f64 #s(literal 1 binary64) (*.f64 x x))

eval253.0ms (3.3%)

Memory
-33.1MiB live, 335.4MiB allocated
Compiler

Compiled 50 060 to 2 292 computations (95.4% saved)

prune243.0ms (3.2%)

Memory
28.0MiB live, 261.5MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1 40221 404
Fresh000
Picked235
Done000
Total1 40451 409
Accuracy
100.0%
Counts
1 409 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
66.7%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
75.3%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
43.9%
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
Compiler

Compiled 38 to 22 computations (42.1% saved)

simplify453.0ms (5.9%)

Memory
-41.1MiB live, 699.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 eps (*.f64 x #s(literal 2 binary64)))
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
cost-diff128
(*.f64 x #s(literal 2 binary64))
cost-diff192
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
cost-diff0
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
Rules
18 700×lower-fma.f32
18 698×lower-fma.f64
2 844×lower-*.f32
2 840×lower-*.f64
2 520×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01752
02149
14549
28749
316049
442843
5109043
6323643
7517743
8668543
9746943
10780943
0803939
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
eps
(*.f64 eps (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
Outputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) (*.f64 eps (+.f64 x (+.f64 x eps))))
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(*.f64 eps (+.f64 x (+.f64 x eps)))
eps
(*.f64 eps (*.f64 x #s(literal 2 binary64)))
(*.f64 x (+.f64 eps eps))
(*.f64 x #s(literal 2 binary64))
(+.f64 x x)
x
#s(literal 2 binary64)

localize49.0ms (0.6%)

Memory
25.7MiB live, 144.5MiB allocated
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
accuracy0
(*.f64 x #s(literal 2 binary64))
accuracy0
(*.f64 eps (*.f64 x #s(literal 2 binary64)))
accuracy0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
accuracy35.92075204526309
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
Samples
17.0ms168×0valid
16.0ms75×1valid
3.0ms13×2valid
Compiler

Compiled 44 to 18 computations (59.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-mult: 10.0ms (38% of total)
ival-pow2: 6.0ms (22.8% of total)
ival-add: 4.0ms (15.2% of total)
adjust: 3.0ms (11.4% of total)
ival-sub: 2.0ms (7.6% of total)
ival-neg: 1.0ms (3.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory
-43.3MiB live, 12.5MiB allocated
Counts
5 → 108
Calls
Call 1
Inputs
#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
Outputs
#s(alt (pow eps 2) (taylor 0 x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (pow x 2)) (taylor 0 eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2))) (taylor 0 eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2))) (taylor 0 eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2))) (taylor 0 eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))) (taylor inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))) (taylor inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps)))) (taylor -inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps)))) (taylor -inf eps) (#s(alt #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) (patch (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (*.f64 eps (*.f64 x #s(literal 2 binary64))) (patch (*.f64 eps (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
Calls

27 calls:

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

simplify369.0ms (4.8%)

Memory
19.8MiB live, 446.1MiB allocated
Algorithm
egg-herbie
Rules
13 984×lower-fma.f64
13 984×lower-fma.f32
2 374×lower--.f64
2 374×lower--.f32
2 130×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047710
1142600
2423600
31307600
43458600
57620600
08440547
Stop Event
iter limit
node limit
Counts
108 → 108
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))

rewrite403.0ms (5.2%)

Memory
20.6MiB live, 610.2MiB allocated
Rules
10 444×lower-fma.f32
10 442×lower-fma.f64
5 844×lower-*.f32
5 840×lower-*.f64
3 690×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01748
02143
110343
282443
0873741
Stop Event
iter limit
node limit
iter limit
Counts
5 → 69
Calls
Call 1
Inputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(*.f64 x #s(literal 2 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 eps (*.f64 x #s(literal 2 binary64)))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(literal 0 binary64))
(+.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
(+.f64 (*.f64 eps eps) (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(+.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(-.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(-.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(fma.f64 x (*.f64 #s(literal 2 binary64) eps) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(fma.f64 eps (*.f64 x #s(literal 2 binary64)) (*.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (*.f64 x eps) (*.f64 eps eps))
(fma.f64 (*.f64 x #s(literal 2 binary64)) eps (*.f64 eps eps))
(fma.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(fma.f64 (*.f64 x eps) #s(literal 2 binary64) (*.f64 eps eps))
(fma.f64 (*.f64 eps #s(literal 2 binary64)) x (*.f64 eps eps))
(fma.f64 (*.f64 #s(literal 2 binary64) eps) x (*.f64 eps eps))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 eps eps) (/.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(fma.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) eps) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(fma.f64 (*.f64 (*.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 eps eps))
(neg.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))
(neg.f64 (/.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) (*.f64 (neg.f64 eps) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(neg.f64 (/.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))))) (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))
(neg.f64 (/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (fma.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps) (*.f64 (*.f64 eps eps) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps) (*.f64 (*.f64 eps eps) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps) (*.f64 (*.f64 eps eps) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))))) (*.f64 (neg.f64 eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (*.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)))) (*.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) #s(literal 64 binary64)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))) (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))) #s(literal 1 binary64)) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (fma.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 (*.f64 x x) #s(literal 4 binary64)))) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))))) #s(literal 1 binary64)) (*.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 (*.f64 x x) #s(literal 4 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))))) (neg.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)))))) (neg.f64 (*.f64 (neg.f64 eps) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (fma.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (*.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) (*.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))) (+.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps)) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -1 binary64))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))
(*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) eps) (*.f64 (*.f64 eps eps) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))))
(*.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(*.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))
(*.f64 (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 eps) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(*.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(*.f64 (/.f64 (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) eps) (/.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(*.f64 eps (*.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 x eps))
(*.f64 (*.f64 x #s(literal 2 binary64)) eps)
(*.f64 (*.f64 x eps) #s(literal 2 binary64))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 (*.f64 #s(literal 2 binary64) eps) x)
(*.f64 (*.f64 (*.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))

eval16.0ms (0.2%)

Memory
4.5MiB live, 42.6MiB allocated
Compiler

Compiled 2 817 to 203 computations (92.8% saved)

prune35.0ms (0.4%)

Memory
-15.4MiB live, 64.7MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New1770177
Fresh000
Picked022
Done033
Total1775182
Accuracy
100.0%
Counts
182 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
66.7%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
75.3%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
43.9%
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
Compiler

Compiled 102 to 45 computations (55.9% saved)

regimes9.0ms (0.1%)

Memory
21.6MiB live, 21.6MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
(fma.f64 (neg.f64 x) x (*.f64 (+.f64 x eps) (+.f64 x eps)))
(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
Calls

3 calls:

3.0ms
eps
3.0ms
x
3.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes7.0ms (0.1%)

Memory
-21.8MiB live, 16.5MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
Calls

3 calls:

3.0ms
x
2.0ms
eps
2.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes5.0ms (0.1%)

Memory
15.0MiB live, 15.0MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Calls

3 calls:

2.0ms
eps
2.0ms
x
2.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
93.5%3x
87.4%3eps
97.2%2(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes5.0ms (0.1%)

Memory
13.1MiB live, 13.1MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Calls

3 calls:

1.0ms
x
1.0ms
eps
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
75.3%1eps
75.3%1x
75.3%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes4.0ms (0.1%)

Memory
-28.3MiB live, 11.4MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
Outputs
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
Calls

3 calls:

1.0ms
x
1.0ms
eps
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
43.9%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
43.9%1x
43.9%1eps
Compiler

Compiled 17 to 11 computations (35.3% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
1.039326e-318
Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify7.0ms (0.1%)

Memory
16.7MiB live, 16.7MiB allocated
Algorithm
egg-herbie
Rules
12×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031101
139101
243101
345101
446101
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps))) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps))) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 eps #s(literal 2 binary64)))) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (neg x) x) (* (+ x eps) (+ x eps))) #s(literal 0 binary64))

soundness928.0ms (12.1%)

Memory
13.4MiB live, 537.0MiB allocated
Rules
18 304×lower-fma.f64
18 304×lower-fma.f32
11 822×lower-fma.f32
11 814×lower-fma.f64
9 222×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069492
1214450
2574450
31825438
44173438
57244438
08097390
023118
040109
1157109
21161109
08669109
01221961
13881731
210611731
334141707
085241540
0720
01120
15220
237120
3510720
0821920
Stop Event
done
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 110 to 52 computations (52.7% saved)

preprocess68.0ms (0.9%)

Memory
1.6MiB live, 79.0MiB allocated
Compiler

Compiled 114 to 50 computations (56.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...