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

Time bar (total: 1.7s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
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)

sample1.1s (61.9%)

Memory
10.6MiB live, 1 682.0MiB allocated; 182ms collecting garbage
Samples
405.0ms5 104×0valid
331.0ms2 481×1valid
92.0ms671×2valid
Precisions
Click to see histograms. Total time spent on operations: 462.0ms
ival-pow2: 292.0ms (63.2% of total)
ival-sub!: 67.0ms (14.5% of total)
adjust: 65.0ms (14.1% of total)
ival-add!: 37.0ms (8% of total)
Bogosity

explain149.0ms (8.6%)

Memory
-25.7MiB live, 220.8MiB allocated; 18ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
770-1(2.1421238929989093e-66 2.0654079104831564e-68)(-.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)))cancellation762
Confusion
Predicted +Predicted -
+761
-0179
Precision
1.0
Recall
0.987012987012987
Confusion?
Predicted +Predicted MaybePredicted -
+7610
-01178
Precision?
0.9871794871794872
Recall?
1.0
Freqs
test
numberfreq
0180
176
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
61.0ms312×0valid
19.0ms164×1valid
5.0ms36×2valid
Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 67.0ms
ival-pow2: 59.0ms (87.9% of total)
adjust: 4.0ms (6% of total)
ival-add!: 2.0ms (3% of total)
ival-sub!: 2.0ms (3% of total)

preprocess39.0ms (2.2%)

Memory
-21.3MiB live, 29.1MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02264
13460
211860
355358
4177144
5531444
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
73.5%
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 18 to 14 computations (22.2% saved)

series6.0ms (0.4%)

Memory
13.5MiB live, 13.5MiB allocated; 0ms collecting garbage
Counts
7 → 29
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
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) x eps 2 (pow x 2))
1.0ms
eps
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) x eps 2 (pow x 2))
1.0ms
x
@inf
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) x eps 2 (pow x 2))
1.0ms
x
@0
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) x eps 2 (pow x 2))
1.0ms
eps
@inf
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) x eps 2 (pow x 2))

rewrite162.0ms (9.3%)

Memory
24.7MiB live, 212.8MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105456
0110446
1557431
05462412
Stop Event
iter-limit
iter-limit
node-limit
iter-limit
Counts
36 → 120
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))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (+.f64 eps x) x))
(/.f64 (neg.f64 (*.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (+.f64 eps x) x)))) (neg.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(/.f64 (*.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (+.f64 eps x) x))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x))) (fma.f64 (*.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))
(fma.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (+.f64 eps x)) (*.f64 (neg.f64 x) x))
(fma.f64 (fabs.f64 (+.f64 eps x)) (fabs.f64 (+.f64 eps x)) (*.f64 (neg.f64 x) x))
(fma.f64 (exp.f64 (log.f64 (+.f64 eps x))) (exp.f64 (log.f64 (+.f64 eps x))) (*.f64 (neg.f64 x) x))
(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (fma.f64 (*.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x))
(+.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (+.f64 eps x)))
(*.f64 (fabs.f64 (+.f64 eps x)) (fabs.f64 (+.f64 eps x)))
(*.f64 (exp.f64 (log.f64 (+.f64 eps x))) (exp.f64 (log.f64 (+.f64 eps x))))
(*.f64 (+.f64 eps x) (+.f64 eps x))
(pow.f64 (exp.f64 (log.f64 (+.f64 eps x))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) #s(literal 1 binary64))
(pow.f64 (+.f64 eps x) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (+.f64 eps x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (+.f64 eps x)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (*.f64 (+.f64 eps x) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (*.f64 (+.f64 eps x) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (*.f64 (+.f64 eps x) (-.f64 x eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (*.f64 (+.f64 eps x) (-.f64 eps x))) (*.f64 (-.f64 x eps) (-.f64 eps x)))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (-.f64 x eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (-.f64 x eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (*.f64 (+.f64 eps x) (-.f64 x eps))) (*.f64 (-.f64 eps x) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (*.f64 (+.f64 eps x) (-.f64 eps x))) (*.f64 (-.f64 eps x) (-.f64 eps x)))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (-.f64 eps x) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (-.f64 eps x) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (*.f64 (+.f64 eps x) (-.f64 x eps))) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (-.f64 x eps)))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (*.f64 (+.f64 eps x) (-.f64 x eps))) (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (-.f64 x eps)))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (*.f64 (+.f64 eps x) (-.f64 eps x))) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (-.f64 eps x)))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (*.f64 (+.f64 eps x) (-.f64 eps x))) (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (-.f64 eps x)))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(fma.f64 (+.f64 eps x) eps (*.f64 (+.f64 eps x) x))
(fma.f64 (+.f64 eps x) x (*.f64 (+.f64 eps x) eps))
(fma.f64 eps (+.f64 eps x) (*.f64 x (+.f64 eps x)))
(fma.f64 x (+.f64 eps x) (*.f64 eps (+.f64 eps x)))
(exp.f64 (*.f64 (log.f64 (+.f64 eps x)) #s(literal 2 binary64)))
(+.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x)))
(+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (+.f64 eps x)))
(+.f64 (*.f64 (+.f64 eps x) eps) (*.f64 (+.f64 eps x) x))
(+.f64 (*.f64 (+.f64 eps x) x) (*.f64 (+.f64 eps x) eps))
(+.f64 (cosh.f64 (*.f64 (log.f64 (+.f64 eps x)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (+.f64 eps x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 eps x) #s(literal 1/2 binary64)))
(pow.f64 (+.f64 eps x) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(exp.f64 (*.f64 (log.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(+.f64 eps x)
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (pow (+ x eps) 2) (*.f64 eps eps))
#s(approx (pow (+ x eps) 2) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (pow (+ x eps) 2) (fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (pow x 2) (*.f64 x x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) x))
#s(approx (pow (+ x eps) 2) (*.f64 x x))
#s(approx (pow (+ x eps) 2) (*.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal 2 binary64) #s(literal 1 binary64)) x) x))
#s(approx (pow (+ x eps) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) eps) (/.f64 (*.f64 eps eps) x)) x)) x) x))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (neg.f64 (*.f64 #s(literal -2 binary64) eps))) x))
#s(approx (pow (+ x eps) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) eps) (/.f64 (*.f64 eps eps) x)) x)) x) x))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (pow (+ x eps) 2) (*.f64 (fma.f64 #s(literal 2 binary64) eps x) x))
#s(approx (pow (+ x eps) 2) (fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps)))
#s(approx eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (pow (+ x eps) 2) (*.f64 (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (pow (+ x eps) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 x (/.f64 x eps))) eps)) eps) eps))
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (pow (+ x eps) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 x (/.f64 x eps))) eps)) eps) eps))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval13.0ms (0.7%)

Memory
-13.2MiB live, 33.8MiB allocated; 3ms collecting garbage
Compiler

Compiled 2 313 to 393 computations (83% saved)

prune5.0ms (0.3%)

Memory
13.3MiB live, 13.3MiB allocated; 0ms collecting garbage
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1145119
Fresh000
Picked101
Done000
Total1155120
Accuracy
100.0%
Counts
120 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
73.5%
(-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x))
99.8%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) x))
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
63.6%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
71.2%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 150 to 96 computations (36% saved)

series17.0ms (1%)

Memory
-5.7MiB live, 41.7MiB allocated; 1ms collecting garbage
Counts
20 → 68
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
(*.f64 (+.f64 x x) eps)
(+.f64 x x)
(-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x))
(*.f64 (+.f64 eps x) (+.f64 eps x))
(+.f64 eps x)
(*.f64 x x)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) x))
(*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) x)
(fma.f64 eps (/.f64 eps x) (+.f64 eps eps))
(/.f64 eps x)
(+.f64 eps eps)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ x x) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (pow eps 2)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (/ (pow eps 2) x)))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (/ (+ (* 2 (* eps x)) (pow eps 2)) x)))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (pow x 2)))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (* 2 eps)))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (+ (* 2 eps) (/ (pow eps 2) x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (* eps (+ 2 (/ eps x)))))
#s(approx (+ eps eps) #s(hole binary64 (* 2 eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
3.0ms
x
@inf
((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
3.0ms
eps
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
2.0ms
eps
@inf
((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
2.0ms
x
@0
((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))

rewrite48.0ms (2.8%)

Memory
6.9MiB live, 53.8MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01861209
02021112
08321087
Stop Event
iter-limit
iter-limit
node-limit
iter-limit
Counts
88 → 163
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
(*.f64 (+.f64 x x) eps)
(+.f64 x x)
(-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x))
(*.f64 (+.f64 eps x) (+.f64 eps x))
(+.f64 eps x)
(*.f64 x x)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) x))
(*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) x)
(fma.f64 eps (/.f64 eps x) (+.f64 eps eps))
(/.f64 eps x)
(+.f64 eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ x x) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (pow eps 2)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (/ (pow eps 2) x)))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (/ (+ (* 2 (* eps x)) (pow eps 2)) x)))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (pow x 2)))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (* 2 eps)))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (+ (* 2 eps) (/ (pow eps 2) x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (* eps (+ 2 (/ eps x)))))
#s(approx (+ eps eps) #s(hole binary64 (* 2 eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) #s(hole binary64 (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ eps x) (+ eps x)) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 x x) eps))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 (+.f64 x x) eps))
(fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 (+.f64 x x) eps))
(fma.f64 eps eps (*.f64 (+.f64 x x) eps))
(+.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) eps))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (+.f64 x x) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 (+.f64 x x) eps))))
(/.f64 (+.f64 (pow.f64 (+.f64 x x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) eps))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (+.f64 x x) eps)
(+.f64 eps (+.f64 x x))
#s(literal 2 binary64)
x
eps
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 eps eps))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 eps eps)
(pow.f64 eps #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (+.f64 x x) eps))
(*.f64 (+.f64 x x) eps)
(*.f64 eps (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x))))
(+.f64 x x)
(*.f64 (+.f64 (+.f64 eps x) x) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 x x) #s(literal 3 binary64))) (fma.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 (*.f64 x x) (*.f64 x x) (*.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)))))
(fma.f64 (pow.f64 (+.f64 eps x) #s(literal 1 binary64)) (pow.f64 (+.f64 eps x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) x))
(fma.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (+.f64 eps x)) (*.f64 (neg.f64 x) x))
(fma.f64 (fabs.f64 (+.f64 eps x)) (fabs.f64 (+.f64 eps x)) (*.f64 (neg.f64 x) x))
(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
(-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x))
(+.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 (neg.f64 x) x))
(*.f64 (pow.f64 (+.f64 eps x) #s(literal 1 binary64)) (pow.f64 (+.f64 eps x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (+.f64 eps x)))
(*.f64 (fabs.f64 (+.f64 eps x)) (fabs.f64 (+.f64 eps x)))
(*.f64 (+.f64 eps x) (+.f64 eps x))
(pow.f64 (+.f64 eps x) #s(literal 2 binary64))
(fma.f64 (+.f64 eps x) eps (*.f64 (+.f64 eps x) x))
(fma.f64 eps (+.f64 eps x) (*.f64 x (+.f64 eps x)))
(exp.f64 (*.f64 (log.f64 (+.f64 eps x)) #s(literal 2 binary64)))
(+.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x)))
(+.f64 (*.f64 (+.f64 eps x) eps) (*.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 eps x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))
(+.f64 eps x)
(+.f64 x eps)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) x))
(*.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) x)
(*.f64 x (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps))
(fma.f64 (+.f64 eps eps) x (*.f64 (*.f64 (/.f64 eps x) eps) x))
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 eps x) eps) x))
(fma.f64 #s(literal 2 binary64) (*.f64 eps x) (*.f64 (*.f64 (/.f64 eps x) eps) x))
(fma.f64 x (+.f64 eps eps) (*.f64 x (*.f64 (/.f64 eps x) eps)))
(+.f64 (*.f64 x (+.f64 eps eps)) (*.f64 x (*.f64 (/.f64 eps x) eps)))
(+.f64 (*.f64 (+.f64 eps eps) x) (*.f64 (*.f64 (/.f64 eps x) eps) x))
(*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps)
(*.f64 eps (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 eps x) eps) (*.f64 (/.f64 eps x) eps)) (*.f64 (+.f64 eps eps) (+.f64 eps eps))) (-.f64 (*.f64 (/.f64 eps x) eps) (+.f64 eps eps)))
(/.f64 (-.f64 (*.f64 (+.f64 eps eps) (+.f64 eps eps)) (*.f64 (*.f64 (/.f64 eps x) eps) (*.f64 (/.f64 eps x) eps))) (-.f64 (+.f64 eps eps) (*.f64 (/.f64 eps x) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 (+.f64 eps eps) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 eps x) eps) (*.f64 (/.f64 eps x) eps) (-.f64 (*.f64 (+.f64 eps eps) (+.f64 eps eps)) (*.f64 (*.f64 (/.f64 eps x) eps) (+.f64 eps eps)))))
(/.f64 (+.f64 (pow.f64 (+.f64 eps eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 eps x) eps) #s(literal 3 binary64))) (fma.f64 (+.f64 eps eps) (+.f64 eps eps) (-.f64 (*.f64 (*.f64 (/.f64 eps x) eps) (*.f64 (/.f64 eps x) eps)) (*.f64 (+.f64 eps eps) (*.f64 (/.f64 eps x) eps)))))
(fma.f64 (/.f64 eps x) eps (+.f64 eps eps))
(fma.f64 #s(literal 2 binary64) eps (*.f64 (/.f64 eps x) eps))
(fma.f64 eps (/.f64 eps x) (+.f64 eps eps))
(fma.f64 eps #s(literal 2 binary64) (*.f64 (/.f64 eps x) eps))
(+.f64 (fma.f64 (/.f64 eps x) eps eps) eps)
(+.f64 (*.f64 (/.f64 eps x) eps) (+.f64 eps eps))
(+.f64 (+.f64 eps eps) (*.f64 (/.f64 eps x) eps))
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps x)
(*.f64 #s(literal 2 binary64) eps)
(*.f64 eps #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 eps eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 eps eps) (*.f64 eps eps))))
(+.f64 eps eps)
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 eps eps))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
#s(approx (* (+ (* 2 x) eps) eps) (*.f64 eps eps))
#s(approx (* (+ (* 2 x) eps) eps) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
#s(approx (+ (* 2 x) eps) eps)
#s(approx (+ (* 2 x) eps) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx x x)
#s(approx (* (+ x x) eps) (*.f64 (+.f64 eps eps) x))
#s(approx (+ x x) (+.f64 x x))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 eps eps))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 eps eps))
#s(approx (* (+ eps x) (+ eps x)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
#s(approx (* (+ eps x) (+ eps x)) (fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps)))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* x x) (*.f64 x x))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) (*.f64 eps eps))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) (*.f64 (/.f64 eps x) eps))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) (/.f64 (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)) x))
#s(approx (/ eps x) (/.f64 eps x))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (+.f64 eps eps) x))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) x))
#s(approx (* (+ (* 2 x) eps) eps) (*.f64 (+.f64 eps eps) x))
#s(approx (* (+ (* 2 x) eps) eps) (*.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) x))
#s(approx (+ (* 2 x) eps) (+.f64 x x))
#s(approx (+ (* 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (+.f64 eps eps) x))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) x))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 x x))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 (+.f64 (fma.f64 (/.f64 eps x) #s(literal 2 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x))) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) (*.f64 (+.f64 eps eps) x))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) (*.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) x))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) (+.f64 eps eps))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (neg.f64 (*.f64 (fma.f64 #s(literal -2 binary64) eps (neg.f64 (*.f64 (/.f64 eps x) eps))) x)))
#s(approx (* (+ (* 2 x) eps) eps) (neg.f64 (*.f64 (fma.f64 #s(literal -2 binary64) eps (neg.f64 (*.f64 (/.f64 eps x) eps))) x)))
#s(approx (+ (* 2 x) eps) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 eps x)) #s(literal 2 binary64)) x)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (neg.f64 (*.f64 (fma.f64 #s(literal -2 binary64) eps (neg.f64 (*.f64 (/.f64 eps x) eps))) x)))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) eps (neg.f64 (*.f64 (/.f64 eps x) eps))) x)) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (+ eps x) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 eps x)) #s(literal 1 binary64)) x)))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) (neg.f64 (*.f64 (fma.f64 #s(literal -2 binary64) eps (neg.f64 (*.f64 (/.f64 eps x) eps))) x)))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (* (+ (* 2 x) eps) eps) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx eps eps)
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 (fma.f64 #s(literal 2 binary64) eps x) x))
#s(approx (* (+ eps x) (+ eps x)) (fma.f64 (fma.f64 #s(literal 2 binary64) x eps) eps (*.f64 x x)))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps))
#s(approx (+ eps eps) (+.f64 eps eps))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (* (+ (* 2 x) eps) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (+ (* 2 x) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (- (* (+ eps x) (+ eps x)) (* x x)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* eps (/ eps x)) (+ eps eps)) x) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (+ (* eps (/ eps x)) (+ eps eps)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) (*.f64 eps eps)))
#s(approx (+ (* 2 x) eps) (neg.f64 (*.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64)) eps)))
#s(approx (* (+ eps x) (+ eps x)) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (neg.f64 (/.f64 (*.f64 x x) eps))) eps)) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (+ eps x) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 x eps)) #s(literal 1 binary64)) eps)))

eval30.0ms (1.7%)

Memory
-8.2MiB live, 43.5MiB allocated; 3ms collecting garbage
Compiler

Compiled 4 026 to 587 computations (85.4% saved)

prune28.0ms (1.6%)

Memory
-26.8MiB live, 20.8MiB allocated; 1ms collecting garbage
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2001201
Fresh000
Picked235
Done000
Total2024206
Accuracy
100.0%
Counts
206 → 4
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 (+.f64 x x) eps)))
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
63.6%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
71.2%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 62 to 41 computations (33.9% saved)

series6.0ms (0.3%)

Memory
12.6MiB live, 12.6MiB allocated; 0ms collecting garbage
Counts
6 → 18
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
(fma.f64 eps eps (*.f64 (+.f64 x x) eps))
eps
(*.f64 (+.f64 x x) eps)
(+.f64 x x)
x
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ x x) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
Calls

6 calls:

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

rewrite33.0ms (1.9%)

Memory
4.6MiB live, 52.1MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056315
061302
0258283
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
24 → 41
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
(fma.f64 eps eps (*.f64 (+.f64 x x) eps))
eps
(*.f64 (+.f64 x x) eps)
(+.f64 x x)
x
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ x x) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* eps eps) (* (+ x x) eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 (+.f64 x x) eps) (*.f64 (+.f64 x x) eps))) (-.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 x x) eps) #s(literal 3 binary64))) (fma.f64 (*.f64 eps eps) (*.f64 eps eps) (-.f64 (*.f64 (*.f64 (+.f64 x x) eps) (*.f64 (+.f64 x x) eps)) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) eps)))))
(fma.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)) (*.f64 (+.f64 x x) eps))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 (+.f64 x x) eps))
(fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 (+.f64 x x) eps))
(fma.f64 (+.f64 x x) eps (*.f64 eps eps))
(fma.f64 eps (+.f64 x x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 (+.f64 x x) eps))
(-.f64 (*.f64 eps eps) (*.f64 (neg.f64 (+.f64 x x)) eps))
(+.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) eps))
(+.f64 (*.f64 (+.f64 x x) eps) (*.f64 eps eps))
eps
(*.f64 (+.f64 x x) eps)
(*.f64 eps (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x))))
(+.f64 x x)
x
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
#s(approx (+ (* eps eps) (* (+ x x) eps)) (*.f64 eps eps))
#s(approx (+ (* eps eps) (* (+ x x) eps)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
#s(approx (* (+ x x) eps) (*.f64 (+.f64 eps eps) x))
#s(approx (+ x x) (+.f64 x x))
#s(approx x x)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) eps (/.f64 (*.f64 eps eps) x)) x))
#s(approx (+ (* eps eps) (* (+ x x) eps)) (*.f64 (+.f64 eps eps) x))
#s(approx (+ (* eps eps) (* (+ x x) eps)) (*.f64 (fma.f64 #s(literal 2 binary64) eps (/.f64 (*.f64 eps eps) x)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (neg.f64 (*.f64 (fma.f64 #s(literal -2 binary64) eps (neg.f64 (/.f64 (*.f64 eps eps) x))) x)))
#s(approx (+ (* eps eps) (* (+ x x) eps)) (neg.f64 (*.f64 (fma.f64 #s(literal -2 binary64) eps (neg.f64 (/.f64 (*.f64 eps eps) x))) x)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (+ (* eps eps) (* (+ x x) eps)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 eps eps)))
#s(approx (+ (* eps eps) (* (+ x x) eps)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 eps eps)))

eval4.0ms (0.2%)

Memory
11.2MiB live, 11.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 000 to 142 computations (85.8% saved)

prune4.0ms (0.2%)

Memory
8.7MiB live, 8.7MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New46046
Fresh000
Picked011
Done033
Total46450
Accuracy
100.0%
Counts
50 → 4
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 (+.f64 x x) eps)))
100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
63.6%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
71.2%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 164 to 72 computations (56.1% saved)

regimes11.0ms (0.6%)

Memory
-26.4MiB live, 20.0MiB allocated; 4ms collecting garbage
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
(-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) 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 (+.f64 x x) eps)))
Calls

3 calls:

6.0ms
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%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
100.0%1x
100.0%1eps
Compiler

Compiled 11 to 11 computations (0% saved)

regimes5.0ms (0.3%)

Memory
13.2MiB live, 13.2MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
Calls

3 calls:

2.0ms
eps
1.0ms
x
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
100.0%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
100.0%1x
100.0%1eps
Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.2%)

Memory
10.4MiB live, 10.4MiB allocated; 0ms collecting garbage
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Calls

3 calls:

1.0ms
eps
1.0ms
x
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
97.2%2(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
92.2%3x
87.6%3eps
Compiler

Compiled 11 to 11 computations (0% saved)

regimes3.0ms (0.2%)

Memory
9.8MiB live, 9.8MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#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
eps
1.0ms
x
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
71.2%1eps
71.2%1x
71.2%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
1.23535e-318
Compiler

Compiled 12 to 12 computations (0% saved)

derivations67.0ms (3.9%)

Memory
-46.3MiB live, 53.4MiB allocated; 12ms collecting garbage
Stop Event
done
Compiler

Compiled 87 to 25 computations (71.3% saved)

preprocess27.0ms (1.6%)

Memory
45.2MiB live, 92.2MiB allocated; 2ms collecting garbage
Compiler

Compiled 192 to 64 computations (66.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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