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

Time bar (total: 8.9s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze10.0ms (0.1%)

Memory
-45.0MiB live, 1.6MiB allocated
Algorithm
1×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)

sample3.9s (43.3%)

Memory
77.4MiB live, 1 824.8MiB allocated
Samples
1.3s2 527×1valid
1.1s5 207×0valid
550.0ms522×2valid
Precisions
Click to see histograms. Total time spent on operations: 2.1s
ival-pow2: 1.1s (55.2% of total)
ival-add: 594.0ms (28.6% of total)
ival-<=: 118.0ms (5.7% of total)
ival-sub: 103.0ms (5% of total)
adjust: 72.0ms (3.5% of total)
ival-and: 23.0ms (1.1% of total)
exact: 19.0ms (0.9% of total)
ival-assert: 3.0ms (0.1% of total)
Bogosity

explain124.0ms (1.4%)

Memory
-29.4MiB live, 159.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
721(-3.570962740972272e-65 -1.4590687607990471e-67)1(-8.653610253627795e-49 -5.556994354757436e-51)(-.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)))cancellation721
Confusion
Predicted +Predicted -
+711
-1183
Precision
0.9861111111111112
Recall
0.9861111111111112
Confusion?
Predicted +Predicted MaybePredicted -
+7110
-10183
Precision?
0.9863013698630136
Recall?
1.0
Freqs
test
numberfreq
0184
172
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
26.0ms330×0valid
18.0ms154×1valid
5.0ms28×2valid
Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-pow2: 14.0ms (54.2% of total)
ival-add: 4.0ms (15.5% of total)
adjust: 3.0ms (11.6% of total)
ival-sub: 3.0ms (11.6% of total)
ival-true: 1.0ms (3.9% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess513.0ms (5.7%)

Memory
-17.6MiB live, 393.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01955
14547
214945
354935
4172135
5397235
6546635
7618035
8640835
9651435
10653535
11653535
12653535
13653535
14662635
15695435
16774835
079
0119
1169
2369
3919
42717
58557
624247
746307
862907
972777
1077037
1179717
1279777
1379777
082846
Stop Event
1×iter limit
1×node limit
1×iter limit
1×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 (fma.f64 #s(literal 2 binary64) x eps) eps)
Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶76.2%
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify261.0ms (2.9%)

Memory
10.3MiB live, 194.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0723
01123
11623
23623
39123
427121
585521
6242421
7463021
8629021
9727721
10770321
11797121
12797721
13797721
0828420
Stop Event
1×iter limit
1×node limit
1×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 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(pow.f64 (+.f64 eps x) #s(literal 2 binary64))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)

localize32.0ms (0.4%)

Memory
4.7MiB live, 47.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(pow.f64 x #s(literal 2 binary64))
accuracy0.0
(+.f64 x eps)
accuracy0.03125
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy15.213221022348916
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Samples
14.0ms77×1valid
10.0ms165×0valid
2.0ms14×2valid
Compiler

Compiled 25 to 9 computations (64% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-pow2: 12.0ms (68.2% of total)
adjust: 2.0ms (11.4% of total)
ival-add: 2.0ms (11.4% of total)
ival-sub: 2.0ms (11.4% 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
6.9MiB live, 6.9MiB allocated
Counts
4 → 23
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)
(pow.f64 x #s(literal 2 binary64))
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
eps
(+ eps x)
(pow x 2)
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* eps (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* -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) (pow x 2))
1.0ms
x
@inf
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms
x
@0
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms
eps
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms
eps
@inf
((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))

simplify138.0ms (1.5%)

Memory
-12.9MiB live, 132.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069161
1214151
2572151
31829143
44154143
57321143
08166124
Stop Event
1×iter limit
1×node limit
Counts
23 → 21
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
eps
(+ eps x)
(pow x 2)
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* eps (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps))
eps
(+ eps x)
(+.f64 eps x)
(pow x 2)
(*.f64 x x)
(* 2 (* eps x))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(*.f64 (fma.f64 #s(literal 2 binary64) eps x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps))
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow x 2))
(*.f64 (fma.f64 #s(literal 2 binary64) eps x) x)
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

rewrite144.0ms (1.6%)

Memory
28.9MiB live, 165.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
01120
15220
237120
3513420
0815420
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 370
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)
(pow.f64 x #s(literal 2 binary64))
Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (+.f64 eps x) #s(literal 12 binary64)))) (fma.f64 (+.f64 (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (pow.f64 (+.f64 eps x) #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))
(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
(*.f64 (+.f64 (+.f64 eps x) x) (-.f64 (+.f64 eps x) x))
(*.f64 (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (neg.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(*.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))))
(*.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(*.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (+.f64 eps x) #s(literal 8 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))) (+.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 6 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))))
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(*.f64 (pow.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (+.f64 eps x)) (sqrt.f64 (+.f64 eps x)))
(*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (-.f64 x eps) (+.f64 eps x)))
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (*.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 (+.f64 eps x) (*.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)))
(pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (+.f64 eps x) #s(literal 1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (*.f64 x x)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (exp.f64 (log.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (exp.f64 (log.f64 (-.f64 x eps))))
(/.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (exp.f64 (log.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (+.f64 eps x) eps (*.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) eps)
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 eps x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 eps x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (+.f64 eps x)))
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(*.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 x))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 x))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 x x)
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval132.0ms (1.5%)

Memory
-23.4MiB live, 81.1MiB allocated
Compiler

Compiled 9 295 to 1 147 computations (87.7% saved)

prune8.0ms (0.1%)

Memory
-26.6MiB live, 19.1MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3734377
Fresh000
Picked101
Done000
Total3744378
Accuracy
100.0%
Counts
378 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶66.3%
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
▶100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶62.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
▶73.3%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 58 to 38 computations (34.5% saved)

simplify167.0ms (1.9%)

Memory
29.8MiB live, 125.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (neg.f64 x) x)
cost-diff0
(+.f64 eps x)
cost-diff2
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
cost-diff6
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
cost-diff0
(fma.f64 #s(literal 2 binary64) x eps)
cost-diff0
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
cost-diff0
(*.f64 eps x)
cost-diff0
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
cost-diff0
(*.f64 eps eps)
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
020106
03392
16092
29992
323283
464783
5231583
6540783
7735983
0811083
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#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 (*.f64 eps x) #s(literal 2 binary64)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 eps x)
eps
x
#s(literal 2 binary64)
#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
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(+.f64 eps x)
eps
x
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
Outputs
#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 (*.f64 eps x) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 eps x)
eps
x
#s(literal 2 binary64)
#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
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+.f64 eps x)
eps
x
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
(*.f64 eps x)
(*.f64 (neg.f64 x) x)
(neg.f64 x)

localize68.0ms (0.8%)

Memory
5.3MiB live, 93.4MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 (neg.f64 x) x)
accuracy0.0
(neg.f64 x)
accuracy0.0234375
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
accuracy21.58441212559896
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
accuracy0.0
(fma.f64 #s(literal 2 binary64) x eps)
accuracy0.0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy0.0078125
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
accuracy0.0
(*.f64 eps x)
accuracy0.015625
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
accuracy24.074832982553524
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
accuracy0.0
(*.f64 eps eps)
accuracy17.095284037659976
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Samples
26.0ms165×0valid
21.0ms77×1valid
5.0ms14×2valid
Compiler

Compiled 96 to 22 computations (77.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 38.0ms
ival-mult: 13.0ms (34.2% of total)
ival-add: 10.0ms (26.3% of total)
ival-pow2: 7.0ms (18.4% of total)
adjust: 4.0ms (10.5% of total)
ival-sub: 2.0ms (5.3% of total)
ival-neg: 1.0ms (2.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory
-24.0MiB live, 20.8MiB allocated
Counts
13 → 31
Calls
Call 1
Inputs
#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 eps x) #s(literal 2 binary64)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 eps x)
#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)
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(+.f64 eps x)
(*.f64 (neg.f64 x) x)
(neg.f64 x)
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* eps x)
eps
(+ eps (* 2 x))
(+ eps x)
(* -1 (pow x 2))
(* -1 x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

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

simplify160.0ms (1.8%)

Memory
29.9MiB live, 133.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082153
1267133
2786133
32466133
46347133
08049120
Stop Event
1×iter limit
1×node limit
Counts
31 → 29
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* eps x)
eps
(+ eps (* 2 x))
(+ eps x)
(* -1 (pow x 2))
(* -1 x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(* eps x)
(*.f64 eps x)
eps
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps x)
(+.f64 eps x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(*.f64 eps x)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

rewrite186.0ms (2.1%)

Memory
-2.5MiB live, 181.6MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02097
03395
114090
2112290
0830690
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
13 → 502
Calls
Call 1
Inputs
#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 eps x) #s(literal 2 binary64)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 eps x)
#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)
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(+.f64 eps x)
(*.f64 (neg.f64 x) x)
(neg.f64 x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(*.f64 eps eps)
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 #s(literal 2 binary64) eps) x)
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(*.f64 x (*.f64 eps #s(literal 2 binary64)))
(*.f64 eps x)
(*.f64 x eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) eps) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps) (pow.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)))
(*.f64 (*.f64 eps (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)))
(*.f64 (*.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps)))
(/.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps)))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (*.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) eps)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps)) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (neg.f64 (*.f64 eps (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)))) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (neg.f64 (*.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))
(/.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (*.f64 eps (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))
(/.f64 (*.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))) (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (*.f64 eps (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (*.f64 #s(literal 2 binary64) eps) x (*.f64 eps eps))
(fma.f64 (*.f64 eps #s(literal 2 binary64)) x (*.f64 eps eps))
(fma.f64 (*.f64 #s(literal 2 binary64) x) eps (*.f64 eps eps))
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (*.f64 eps x) (*.f64 eps eps))
(fma.f64 eps (*.f64 #s(literal 2 binary64) x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 x (*.f64 #s(literal 2 binary64) eps) (*.f64 eps eps))
(fma.f64 x (*.f64 eps #s(literal 2 binary64)) (*.f64 eps eps))
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps))
(+.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (-.f64 (*.f64 eps eps) (*.f64 #s(literal 4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(*.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(*.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))) (+.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (*.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (neg.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))))
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(fma.f64 (*.f64 eps eps) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(exp.f64 (log.f64 (+.f64 eps x)))
(+.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))
(+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(+.f64 (+.f64 eps x) #s(literal 0 binary64))
(+.f64 eps x)
(+.f64 x eps)
(*.f64 #s(literal -1 binary64) (*.f64 x x))
(*.f64 (neg.f64 x) x)
(*.f64 x (neg.f64 x))
(/.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 x x)))))
(neg.f64 (*.f64 x x))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal -1 binary64))
(/.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (neg.f64 x) x)))
(/.f64 (*.f64 (neg.f64 x) x) x)
(/.f64 (*.f64 x x) (neg.f64 x))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 x x) x))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))

eval69.0ms (0.8%)

Memory
14.7MiB live, 104.2MiB allocated
Compiler

Compiled 20 720 to 1 754 computations (91.5% saved)

prune86.0ms (1%)

Memory
-33.2MiB live, 68.3MiB allocated
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New5863589
Fresh000
Picked134
Done000
Total5876593
Accuracy
100.0%
Counts
593 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
▶76.4%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓62.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
▶62.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
✓73.3%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 95 to 64 computations (32.6% saved)

simplify186.0ms (2.1%)

Memory
24.4MiB live, 170.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 eps x)
cost-diff0
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
cost-diff0
(+.f64 eps x)
cost-diff0
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
cost-diff0
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
cost-diff0
(+.f64 eps x)
cost-diff0
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
cost-diff0
(*.f64 eps #s(literal 2 binary64))
cost-diff0
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022102
02994
15290
28390
320772
456772
5232072
6571372
7766472
0813671
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
eps
#s(literal 2 binary64)
x
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
#s(literal 0 binary64)
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 eps #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) eps)
eps
#s(literal 2 binary64)
x
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
#s(literal 0 binary64)
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)

localize67.0ms (0.8%)

Memory
7.4MiB live, 54.7MiB allocated
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 eps x)
accuracy0.0
(*.f64 eps x)
accuracy0.0
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
accuracy0.0234375
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
accuracy0.0
(+.f64 eps x)
accuracy0.0234375
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
accuracy31.758720965818156
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
accuracy0.0
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
accuracy0.0
(*.f64 eps #s(literal 2 binary64))
accuracy24.074832982553524
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
Samples
33.0ms165×0valid
19.0ms77×1valid
4.0ms14×2valid
Compiler

Compiled 88 to 20 computations (77.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-mult: 23.0ms (53.2% of total)
ival-pow2: 7.0ms (16.2% of total)
ival-add: 6.0ms (13.9% of total)
adjust: 4.0ms (9.2% of total)
ival-sub: 2.0ms (4.6% of total)
ival-neg: 1.0ms (2.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
-33.3MiB live, 12.6MiB allocated
Counts
9 → 24
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
eps
(+ eps x)
(* eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(* 2 eps)
(+ (* -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 x) (pow x 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))))))
(* eps (+ 1 (/ x eps)))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
Calls

6 calls:

TimeVariablePointExpression
4.0ms
eps
@0
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
2.0ms
x
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
1.0ms
eps
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
1.0ms
eps
@inf
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
1.0ms
x
@0
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))

simplify207.0ms (2.3%)

Memory
21.4MiB live, 115.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072122
1234102
2707102
32247102
46016102
0839894
Stop Event
1×iter limit
1×node limit
Counts
24 → 22
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
eps
(+ eps x)
(* eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(* 2 eps)
(+ (* -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 x) (pow x 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))))))
(* eps (+ 1 (/ x eps)))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
eps
(+ eps x)
(+.f64 eps x)
(* eps x)
(*.f64 eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 eps)
(*.f64 #s(literal 2 binary64) eps)
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(*.f64 eps x)

rewrite192.0ms (2.2%)

Memory
-11.4MiB live, 226.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02291
02983
113279
2100271
0895567
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
9 → 222
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) eps) x))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) eps) x)
(*.f64 #s(literal 2 binary64) (*.f64 eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(*.f64 #s(literal 2 binary64) eps)
(*.f64 eps #s(literal 2 binary64))
(*.f64 (-.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) (*.f64 (+.f64 eps x) eps))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))))
(*.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))))))
(*.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
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(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) (*.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)))) (*.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (-.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))) (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64))) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64))) (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)))) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64))) (neg.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(neg.f64 (/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))))))
(fma.f64 (*.f64 eps (sqrt.f64 (+.f64 eps x))) (sqrt.f64 (+.f64 eps x)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)) (fma.f64 eps x #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 (*.f64 (fma.f64 eps eps (*.f64 (neg.f64 x) x)) eps) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (pow.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (pow.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 eps (fma.f64 eps eps (*.f64 (neg.f64 x) x))) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 x eps)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 eps (+.f64 eps x) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 eps eps (fma.f64 eps x #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 eps x (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 x eps (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(-.f64 (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps))) (/.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps))))
(-.f64 (/.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(+.f64 (+.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 eps eps)) (*.f64 eps x))
(+.f64 (+.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 eps x)) (*.f64 eps eps))
(+.f64 (/.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) (neg.f64 (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(+.f64 (*.f64 eps eps) (fma.f64 eps x #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(+.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(+.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps))
(+.f64 (*.f64 eps x) (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 (*.f64 eps (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 eps x)
(*.f64 x eps)

eval35.0ms (0.4%)

Memory
25.2MiB live, 70.6MiB allocated
Compiler

Compiled 11 549 to 713 computations (93.8% saved)

prune7.0ms (0.1%)

Memory
-25.1MiB live, 21.5MiB allocated
Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New3251326
Fresh000
Picked033
Done033
Total3257332
Accuracy
100.0%
Counts
332 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
✓76.4%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓62.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
✓62.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
✓73.3%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶38.0%
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Compiler

Compiled 113 to 75 computations (33.6% saved)

simplify260.0ms (2.9%)

Memory
15.6MiB live, 209.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
01117
12614
26214
321010
453010
5191310
6422710
7655610
8770510
080949
Stop Event
1×iter limit
1×node limit
1×saturated
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(literal 0 binary64)
Outputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(literal 0 binary64)

localize70.0ms (0.8%)

Memory
-22.9MiB live, 28.6MiB allocated
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
accuracy39.68810882653397
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Samples
11.0ms90×1valid
10.0ms166×0valid
Compiler

Compiled 19 to 12 computations (36.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-mult: 6.0ms (42.1% of total)
ival-add: 5.0ms (35.1% of total)
adjust: 2.0ms (14% of total)
ival-neg: 1.0ms (7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Counts
1 → 11
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (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)))
(* (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 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
Calls

6 calls:

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

simplify163.0ms (1.8%)

Memory
42.3MiB live, 84.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04781
114263
242263
3130563
4349463
5774563
0853856
Stop Event
1×iter limit
1×node limit
Counts
11 → 11
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (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)))
(* (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 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(*.f64 (*.f64 x eps) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(*.f64 (*.f64 x eps) #s(literal 2 binary64))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

rewrite269.0ms (3%)

Memory
5.1MiB live, 147.1MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01118
01116
16213
259311
0856211
Stop Event
1×iter limit
1×node limit
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Outputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))

eval1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Compiler

Compiled 83 to 20 computations (75.9% saved)

prune45.0ms (0.5%)

Memory
-38.5MiB live, 6.6MiB allocated
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New404
Fresh000
Picked011
Done066
Total4711
Accuracy
100.0%
Counts
11 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
✓76.4%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓62.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
✓62.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
✓73.3%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓38.0%
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Compiler

Compiled 249 to 116 computations (53.4% saved)

regimes10.0ms (0.1%)

Memory
19.9MiB live, 19.9MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.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)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
Calls

3 calls:

3.0ms
x
3.0ms
eps
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 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory
13.1MiB live, 13.1MiB allocated
Counts
5 → 2
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
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
92.2%3x
87.8%3eps
96.5%2(-.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)

regimes11.0ms (0.1%)

Memory
-34.8MiB live, 10.9MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
Outputs
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
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
76.4%1eps
76.4%1x
76.4%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)

regimes4.0ms (0%)

Memory
10.0MiB live, 10.0MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #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
73.3%1eps
73.3%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
73.3%1x
Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0%)

Memory
8.4MiB live, 8.4MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Outputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
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
38.0%1x
38.0%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
38.0%1eps
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
2.5996418890443415e-308
Compiler

Compiled 12 to 12 computations (0% saved)

simplify57.0ms (0.6%)

Memory
-3.6MiB live, 41.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033102
15595
29595
327079
467279
5220779
6524879
7708779
Stop Event
1×node limit
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (*.f64 eps #s(literal 2 binary64)) x)) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (*.f64 eps #s(literal 2 binary64)) x)) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
(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 (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (*.f64 (*.f64 eps #s(literal 2 binary64)) x)) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))

soundness1.3s (14.1%)

Memory
-30.1MiB live, 575.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072122
1234102
2707102
32247102
46016102
0839894
02097
03395
114090
2112290
0830690
069161
1214151
2572151
31829143
44154143
57321143
08166124
0720
01120
15220
237120
3513420
0815420
082153
1267133
2786133
32466133
46347133
08049120
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 240 to 104 computations (56.7% saved)

preprocess83.0ms (0.9%)

Memory
-7.4MiB live, 92.8MiB allocated
Compiler

Compiled 276 to 72 computations (73.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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