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

Time bar (total: 5.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB 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)

sample1.4s (27.9%)

Memory
27.7MiB live, 1 433.3MiB allocated
Samples
461.0ms5 230×0valid
444.0ms2 529×1valid
119.0ms497×2valid
Precisions
Click to see histograms. Total time spent on operations: 755.0ms
ival-pow2: 302.0ms (40% of total)
ival-add: 150.0ms (19.9% of total)
ival-<=: 128.0ms (17% of total)
adjust: 74.0ms (9.8% of total)
ival-sub: 59.0ms (7.8% of total)
ival-and: 21.0ms (2.8% of total)
exact: 17.0ms (2.3% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

explain108.0ms (2.2%)

Memory
2.9MiB live, 131.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
711(5.101587459747441e-136 6.1557661908724555e-189)0-(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
00-0-eps
00-0-(pow.f64 x #s(literal 2 binary64))
00-0-#s(literal 2 binary64)
00-0-(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
00-0-(+.f64 x eps)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))cancellation720
Confusion
Predicted +Predicted -
+710
-1184
Precision
0.9861111111111112
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+7100
-10184
Precision?
0.9861111111111112
Recall?
1.0
Freqs
test
numberfreq
0184
172
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
30.0ms338×0valid
17.0ms146×1valid
5.0ms28×2valid
Compiler

Compiled 82 to 32 computations (61% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-add: 14.0ms (39.3% of total)
ival-pow2: 14.0ms (39.3% of total)
adjust: 3.0ms (8.4% of total)
ival-sub: 3.0ms (8.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess369.0ms (7.3%)

Memory
-32.9MiB live, 186.0MiB 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
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.7MiB live, 0.7MiB 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)

simplify428.0ms (8.5%)

Memory
8.7MiB live, 170.9MiB 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)

localize29.0ms (0.6%)

Memory
-5.9MiB live, 31.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(pow.f64 x #s(literal 2 binary64))
accuracy0.0
(+.f64 x eps)
accuracy0.0078125
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy15.238396498045391
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Samples
10.0ms73×1valid
10.0ms169×0valid
2.0ms14×2valid
Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-pow2: 7.0ms (55.3% of total)
adjust: 2.0ms (15.8% of total)
ival-add: 2.0ms (15.8% of total)
ival-sub: 2.0ms (15.8% 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
5.7MiB live, 5.7MiB 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))

simplify158.0ms (3.1%)

Memory
15.1MiB live, 96.1MiB 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)

rewrite216.0ms (4.3%)

Memory
-23.6MiB live, 167.5MiB 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))))
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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)))

eval42.0ms (0.8%)

Memory
30.9MiB live, 66.8MiB allocated
Compiler

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

prune31.0ms (0.6%)

Memory
-22.8MiB live, 26.7MiB allocated
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3743377
Fresh000
Picked101
Done000
Total3753378
Accuracy
100.0%
Counts
378 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶58.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
▶75.8%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify224.0ms (4.5%)

Memory
-1.4MiB live, 193.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
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: 4 (0.0ms)

IterNodesCost
01572
02172
13372
26372
311769
426163
583563
6237663
7455163
8620363
9719363
10761563
11788363
12788963
13788963
0819663
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
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)))
(*.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

localize53.0ms (1.1%)

Memory
-0.9MiB live, 37.2MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
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))
accuracy0.00390625
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
accuracy0.0
(*.f64 eps x)
accuracy0.046875
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
accuracy26.885029572782212
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
accuracy0.0
(*.f64 eps eps)
accuracy15.513889928200426
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Samples
29.0ms169×0valid
13.0ms73×1valid
3.0ms14×2valid
Compiler

Compiled 131 to 31 computations (76.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-mult: 19.0ms (57.1% of total)
ival-pow2: 7.0ms (21% of total)
ival-add: 3.0ms (9% of total)
adjust: 2.0ms (6% of total)
ival-sub: 2.0ms (6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory
13.6MiB live, 13.6MiB allocated
Counts
8 → 15
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)
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* eps x)
eps
(+ eps (* 2 x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* eps (+ eps (* 2 x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
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))
1.0ms
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))
1.0ms
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))
1.0ms
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))
1.0ms
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))

simplify110.0ms (2.2%)

Memory
-8.5MiB live, 71.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03885
112175
228775
374975
4191175
5373775
6549775
7655075
8713275
0828765
Stop Event
1×iter limit
1×node limit
Counts
15 → 14
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* eps x)
eps
(+ eps (* 2 x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* eps (+ eps (* 2 x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* -1 (* eps (- (* -2 (/ 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)
(* 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)
(* -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)
(* eps (+ eps (* 2 x)))
(*.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)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)

rewrite174.0ms (3.5%)

Memory
11.0MiB live, 168.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01565
02165
17965
252465
3675665
0831565
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
8 → 134
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)
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 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) eps) x)
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 #s(literal 2 binary64) eps)))
(*.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 (*.f64 eps (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) eps))
(*.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 (*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) eps) (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(*.f64 (/.f64 (*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) eps) (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (fma.f64 #s(literal 2 binary64) x eps))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) (-.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(*.f64 (*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) eps) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) (*.f64 (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)) eps))
(*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (/.f64 eps (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.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))) (*.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) #s(literal -1 binary64)) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (*.f64 (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x))) eps) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (*.f64 (neg.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x)))) eps) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (*.f64 (neg.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 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(/.f64 (*.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(/.f64 (*.f64 eps (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x)))) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (*.f64 eps (neg.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))))) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (*.f64 eps (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (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 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 binary64)))))
(/.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 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) eps)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(/.f64 (*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))
(/.f64 (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) (fma.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64)))))
(/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 eps 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 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 #s(literal 2 binary64) eps)) (*.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))
(+.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 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(*.f64 (/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (-.f64 (*.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 eps (*.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))) (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) (-.f64 (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(*.f64 (/.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (fma.f64 #s(literal 2 binary64) x eps))
(*.f64 (fma.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 (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)) (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))))
(*.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) #s(literal -1 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(*.f64 (neg.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (/.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 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)))))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)))
(*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.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))) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #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 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps eps)))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64))) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 eps #s(literal 4 binary64)))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) #s(literal -1 binary64))) (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (*.f64 (fma.f64 #s(literal 512 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 eps #s(literal 9 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) #s(literal -1 binary64))) (-.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64))))
(/.f64 (*.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) #s(literal 1 binary64)) (-.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))) #s(literal 1 binary64)) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))) (*.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))) (fma.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (fma.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))))
(/.f64 (neg.f64 (fma.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 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))))) (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 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(/.f64 (*.f64 (fma.f64 #s(literal 512 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 eps #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps))) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (-.f64 (*.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps eps))))
(/.f64 (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x))) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (*.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) (fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.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 64 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(/.f64 (fma.f64 #s(literal 512 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 eps #s(literal 9 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)) (-.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64)))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (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)))) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (fma.f64 eps eps (*.f64 #s(literal -4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(/.f64 (fma.f64 (neg.f64 eps) eps (*.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))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps))))
(neg.f64 (/.f64 (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(neg.f64 (/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal 4 binary64) x) x (*.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x)) eps)))))
(fma.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 (neg.f64 eps) eps (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (fma.f64 #s(literal 2 binary64) x eps) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x) eps)
(fma.f64 (pow.f64 eps #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) x) (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) eps)
(fma.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 #s(literal 2 binary64) x) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 4 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) x) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x (/.f64 (*.f64 #s(literal 4 binary64) x) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 #s(literal 2 binary64) x))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(-.f64 (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (*.f64 #s(literal 2 binary64) x) eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(+.f64 (*.f64 #s(literal 2 binary64) x) eps)
(+.f64 eps (*.f64 #s(literal 2 binary64) x))

eval15.0ms (0.3%)

Memory
17.2MiB live, 17.2MiB allocated
Compiler

Compiled 4 092 to 535 computations (86.9% saved)

prune17.0ms (0.3%)

Memory
-29.8MiB live, 8.2MiB allocated
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1362138
Fresh000
Picked123
Done000
Total1374141
Accuracy
100.0%
Counts
141 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶58.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
✓75.8%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 62 to 43 computations (30.6% saved)

simplify201.0ms (4%)

Memory
25.9MiB live, 144.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 7 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01461
02061
13359
26359
311759
426055
581855
6236755
7457155
8620255
9719455
10761955
11788755
12789355
13789355
0820051
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 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
(*.f64 eps x)
eps
x
#s(literal 2 binary64)
(*.f64 eps eps)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps x)
eps
x
#s(literal 2 binary64)
(*.f64 eps eps)

localize48.0ms (1%)

Memory
6.8MiB live, 44.7MiB allocated
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 eps x)
accuracy0.0
(*.f64 eps eps)
accuracy0.0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
accuracy0.01953125
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
accuracy0.0
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
accuracy0.0
(*.f64 #s(literal 2 binary64) x)
accuracy26.885029572782212
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
Samples
17.0ms169×0valid
14.0ms73×1valid
8.0ms14×2valid
Compiler

Compiled 110 to 30 computations (72.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-add: 8.0ms (28.5% of total)
ival-mult: 8.0ms (28.5% of total)
ival-pow2: 7.0ms (24.9% of total)
adjust: 2.0ms (7.1% of total)
ival-sub: 2.0ms (7.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory
-27.2MiB live, 9.4MiB allocated
Counts
7 → 9
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 #s(literal 2 binary64) x)
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
(*.f64 eps x)
(*.f64 eps eps)
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* 2 x)
(* eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* eps (+ eps (* 2 x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
Calls

6 calls:

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

simplify103.0ms (2%)

Memory
27.7MiB live, 108.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02659
17649
218749
345249
4132349
5243449
6460049
7747349
0806344
Stop Event
1×iter limit
1×node limit
Counts
9 → 9
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* 2 x)
(* eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* eps (+ eps (* 2 x)))
(* (pow eps 2) (+ 1 (* 2 (/ x 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))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* eps x)
(*.f64 eps x)
(* 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)
(* eps (+ eps (* 2 x)))
(*.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)

rewrite180.0ms (3.6%)

Memory
9.2MiB live, 203.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01455
02055
18153
255853
3720553
0887251
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
7 → 122
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 #s(literal 2 binary64) x)
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
(*.f64 eps x)
(*.f64 eps eps)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) eps) x)
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 #s(literal 2 binary64) eps)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.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 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 3 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 3 binary64)) (fma.f64 #s(literal 2 binary64) x eps))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 (pow.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps (*.f64 #s(literal 2 binary64) x))) (-.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps (*.f64 #s(literal 2 binary64) x))) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) eps) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(*.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))))
(*.f64 (pow.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(*.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))))))
(*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(*.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (pow.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64))))
(*.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)))
(*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) (pow.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) #s(literal -1 binary64))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)) #s(literal -1 binary64))
(/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 eps #s(literal 8 binary64))) (pow.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) #s(literal -1 binary64))) (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 eps #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) (pow.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) #s(literal -1 binary64))) (+.f64 (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 eps #s(literal 6 binary64)) (pow.f64 eps #s(literal 8 binary64))) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) (pow.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 18 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 9 binary64))) (pow.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) (*.f64 #s(literal 8 binary64) (pow.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 3 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps))
(/.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))) (*.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))) (fma.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (fma.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))))) (neg.f64 (*.f64 (neg.f64 eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (neg.f64 (neg.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 eps #s(literal 8 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 eps #s(literal 6 binary64)) (pow.f64 eps #s(literal 8 binary64))) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 18 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) (*.f64 #s(literal 8 binary64) (pow.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 3 binary64)))) (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 eps #s(literal 8 binary64))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 eps #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) (+.f64 (fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 eps #s(literal 6 binary64)) (pow.f64 eps #s(literal 8 binary64))) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) (*.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 18 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 9 binary64))) (*.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 eps #s(literal 12 binary64))) (*.f64 #s(literal 8 binary64) (pow.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 3 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64)))) (neg.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x))) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.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))) (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64)))) (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x))))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) (neg.f64 (*.f64 (*.f64 eps eps) (fma.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))))))
(fma.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 3 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 3 binary64)) (fma.f64 #s(literal 2 binary64) x eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 eps eps))
(fma.f64 (/.f64 (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) eps) (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) eps) eps) (/.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 eps x)) eps) (/.f64 (*.f64 eps x) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) eps) (/.f64 (*.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) eps) (/.f64 (*.f64 eps eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 #s(literal 4 binary64) eps) (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 eps x) eps) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 eps x)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) x) eps) (/.f64 (*.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (/.f64 eps eps) (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
(fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 eps x)) (/.f64 (*.f64 eps x) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) eps) (/.f64 eps (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 #s(literal 2 binary64) eps) x (*.f64 eps eps))
(fma.f64 (*.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (/.f64 (*.f64 eps eps) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 #s(literal 2 binary64) eps)) (*.f64 eps eps))
(fma.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) (/.f64 #s(literal 4 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps) #s(literal -1 binary64)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 eps eps) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 eps x) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 eps x)) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
(fma.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 (*.f64 #s(literal 2 binary64) x) eps (*.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 #s(literal 2 binary64) (*.f64 eps x) (*.f64 eps eps))
(fma.f64 eps (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) eps) (*.f64 (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)) eps)) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(fma.f64 eps (*.f64 #s(literal 2 binary64) x) (*.f64 eps eps))
(fma.f64 eps eps (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
(fma.f64 x (*.f64 #s(literal 2 binary64) eps) (*.f64 eps eps))
(-.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))) (/.f64 (pow.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))
(+.f64 (*.f64 (/.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (neg.f64 (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(+.f64 (*.f64 (*.f64 eps x) #s(literal 2 binary64)) (*.f64 eps eps))
(+.f64 (*.f64 eps eps) (*.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))
(*.f64 (*.f64 eps (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) eps))
(*.f64 eps x)
(*.f64 x 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)))

eval272.0ms (5.4%)

Memory
-15.0MiB live, 23.6MiB allocated
Compiler

Compiled 4 228 to 452 computations (89.3% saved)

prune4.0ms (0.1%)

Memory
9.8MiB live, 9.8MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1260126
Fresh000
Picked022
Done022
Total1264130
Accuracy
100.0%
Counts
130 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓58.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
✓75.8%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 148 to 68 computations (54.1% saved)

regimes13.0ms (0.3%)

Memory
-22.5MiB live, 14.0MiB allocated
Counts
6 → 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 #s(literal 2 binary64) x) 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 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps)))
(-.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:

9.0ms
x
2.0ms
eps
2.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 11 to 11 computations (0% saved)

regimes5.0ms (0.1%)

Memory
12.8MiB live, 12.8MiB allocated
Counts
3 → 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 #s(literal 2 binary64) x) eps))
#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 #s(literal 2 binary64) x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Calls

3 calls:

2.0ms
eps
2.0ms
x
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
92.6%3x
88.4%3eps
99.3%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)

regimes3.0ms (0.1%)

Memory
8.2MiB live, 8.2MiB allocated
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
x
1.0ms
eps
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
75.8%1eps
75.8%1x
75.8%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
0.5MiB live, 0.5MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
5e-324
Compiler

Compiled 12 to 12 computations (0% saved)

simplify63.0ms (1.3%)

Memory
-17.6MiB live, 26.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02269
12969
25169
310969
429361
587761
6242561
7465661
8645661
9792661
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 #s(literal 2 binary64) x) eps)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Outputs
#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 #s(literal 2 binary64) x) eps)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

soundness707.0ms (14.1%)

Memory
-12.9MiB live, 274.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01565
02165
17965
252465
3675665
0831565
069161
1214151
2572151
31829143
44154143
57321143
08166124
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 95 to 47 computations (50.5% saved)

preprocess26.0ms (0.5%)

Memory
-1.8MiB live, 41.4MiB allocated
Compiler

Compiled 156 to 60 computations (61.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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