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

Time bar (total: 6.2s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.4MiB live, 0.4MiB 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)

sample1.5s (24.8%)

Memory
45.9MiB live, 1 542.2MiB allocated
Samples
444.0ms5 267×0valid
361.0ms2 472×1valid
214.0ms517×2valid
Precisions
Click to see histograms. Total time spent on operations: 766.0ms
ival-pow2: 243.0ms (31.7% of total)
ival-add: 193.0ms (25.2% of total)
ival-<=: 159.0ms (20.8% of total)
adjust: 69.0ms (9% of total)
ival-sub: 61.0ms (8% of total)
ival-and: 21.0ms (2.7% of total)
exact: 16.0ms (2.1% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

explain164.0ms (2.6%)

Memory
-22.9MiB live, 262.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
7320(2.0728634934801444e-85 9.120795100282895e-242)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)))cancellation930
Confusion
Predicted +Predicted -
+730
-20163
Precision
0.7849462365591398
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+7300
-200163
Precision?
0.7849462365591398
Recall?
1.0
Freqs
test
numberfreq
0163
193
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
24.0ms160×1valid
21.0ms336×0valid
3.0ms16×2valid
Compiler

Compiled 105 to 45 computations (57.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-pow2: 14.0ms (56.7% of total)
ival-add: 4.0ms (16.2% of total)
adjust: 3.0ms (12.1% of total)
ival-sub: 3.0ms (12.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess374.0ms (6%)

Memory
2.2MiB live, 200.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01955
14547
214945
354235
4166035
5380035
6526935
7598935
8621635
9632235
10634335
11634335
12634335
13634335
14643435
15676235
16756035
17799635
079
0119
1169
2369
3969
42767
58617
623747
742777
859217
969137
1073387
1176067
1276127
1376127
080476
Stop Event
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
0.8MiB live, 0.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶75.1%
(-.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)

simplify257.0ms (4.2%)

Memory
5.5MiB live, 158.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x eps)
cost-diff0
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff6144
(pow.f64 x #s(literal 2 binary64))
cost-diff6464
(-.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
39623
427621
586121
6237421
7427721
8592121
9691321
10733821
11760621
12761221
13761221
0804720
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)

localize53.0ms (0.9%)

Memory
7.7MiB live, 52.9MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(pow.f64 x #s(literal 2 binary64))
accuracy0
(+.f64 x eps)
accuracy0.0234375
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy15.865541124265903
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Samples
17.0ms168×0valid
10.0ms80×1valid
1.0ms8×2valid
Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
ival-pow2: 14.0ms (71.2% of total)
adjust: 2.0ms (10.2% of total)
ival-add: 2.0ms (10.2% of total)
ival-sub: 2.0ms (10.2% 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
7.3MiB live, 7.3MiB 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 x #s(literal 2 binary64))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(pow x 2)
(+ (* x (+ x (* 2 eps))) (pow eps 2))
eps
(+ eps x)
(* 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 2) (pow (+ x eps) 2) (+ x eps))
1.0ms
x
@inf
((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms
x
@0
((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms
eps
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms
eps
@inf
((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))

simplify171.0ms (2.8%)

Memory
-16.0MiB live, 144.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069161
1214151
2570151
31802143
44139143
57201143
08049124
Stop Event
1×iter limit
1×node limit
Counts
23 → 21
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(pow x 2)
(+ (* x (+ x (* 2 eps))) (pow eps 2))
eps
(+ eps x)
(* 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)
(pow x 2)
(*.f64 x x)
(+ (* 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)
(* 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)

rewrite167.0ms (2.7%)

Memory
9.7MiB live, 169.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
01120
15220
237120
3510920
0821920
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 371
Calls
Call 1
Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
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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(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (+.f64 eps x))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 eps x))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(+.f64 (*.f64 (+.f64 eps x) eps) (*.f64 (+.f64 eps x) x))
(+.f64 (*.f64 (+.f64 eps x) x) (*.f64 (+.f64 eps x) eps))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps 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)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)))
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(*.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)))))
(sqrt.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))
(-.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)

eval43.0ms (0.7%)

Memory
-4.9MiB live, 69.3MiB allocated
Compiler

Compiled 9 307 to 1 150 computations (87.6% saved)

prune5.0ms (0.1%)

Memory
19.7MiB live, 19.7MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3744378
Fresh000
Picked101
Done000
Total3754379
Accuracy
100.0%
Counts
379 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶67.4%
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
▶100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶64.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
▶73.1%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 58 to 38 computations (34.5% saved)

simplify190.0ms (3.1%)

Memory
-26.2MiB live, 132.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (neg.f64 x) x)
cost-diff0
(+.f64 eps x)
cost-diff192
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
cost-diff704
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
cost-diff0
(fma.f64 #s(literal 2 binary64) x eps)
cost-diff0
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
cost-diff0
(*.f64 eps x)
cost-diff0
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
cost-diff0
(*.f64 eps eps)
cost-diff0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
020106
03392
16092
29992
323283
466583
5228083
6521983
7704683
0823683
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 eps x)
eps
x
#s(literal 2 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(+.f64 eps x)
eps
x
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 eps x)
eps
x
#s(literal 2 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+.f64 eps x)
eps
x
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
(*.f64 eps x)
(*.f64 (neg.f64 x) x)
(neg.f64 x)

localize92.0ms (1.5%)

Memory
14.6MiB live, 97.2MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 (neg.f64 x) x)
accuracy0
(neg.f64 x)
accuracy0.015625
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
accuracy20.872464357472204
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
accuracy0
(fma.f64 #s(literal 2 binary64) x eps)
accuracy0
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy0.0078125
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
accuracy0
(*.f64 eps x)
accuracy0.015625
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
accuracy22.78437780349461
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
accuracy0
(*.f64 eps eps)
accuracy17.235885626960602
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Samples
32.0ms168×0valid
21.0ms80×1valid
3.0ms8×2valid
Compiler

Compiled 202 to 43 computations (78.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 38.0ms
ival-mult: 13.0ms (34.4% of total)
ival-pow2: 11.0ms (29.1% of total)
ival-add: 7.0ms (18.5% of total)
adjust: 4.0ms (10.6% of total)
ival-sub: 2.0ms (5.3% of total)
ival-neg: 1.0ms (2.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series16.0ms (0.3%)

Memory
-20.7MiB live, 16.3MiB allocated
Counts
13 → 31
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 eps x)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x))
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(+.f64 eps x)
(*.f64 (neg.f64 x) x)
(neg.f64 x)
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* eps x)
eps
(+ eps (* 2 x))
(+ eps x)
(* -1 (pow x 2))
(* -1 x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
eps
@inf
((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (* (neg x) x) (neg x))
3.0ms
eps
@0
((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (* (neg x) x) (neg x))
2.0ms
x
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (* (neg x) x) (neg x))
2.0ms
eps
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (* (neg x) x) (neg x))
2.0ms
x
@0
((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (* (neg x) x) (neg x))

simplify109.0ms (1.8%)

Memory
22.2MiB live, 96.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082153
1267133
2784133
32434133
46295133
08135120
Stop Event
1×iter limit
1×node limit
Counts
31 → 29
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* eps x)
eps
(+ eps (* 2 x))
(+ eps x)
(* -1 (pow x 2))
(* -1 x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(* eps x)
(*.f64 eps x)
eps
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps x)
(+.f64 eps x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(*.f64 eps x)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

rewrite215.0ms (3.5%)

Memory
3.7MiB live, 158.7MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

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

eval94.0ms (1.5%)

Memory
3.1MiB live, 121.6MiB allocated
Compiler

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

prune23.0ms (0.4%)

Memory
-13.0MiB live, 25.9MiB allocated
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New5863589
Fresh000
Picked224
Done000
Total5885593
Accuracy
100.0%
Counts
593 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
▶76.5%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶64.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
✓73.1%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Compiler

Compiled 80 to 53 computations (33.8% saved)

simplify183.0ms (3%)

Memory
7.1MiB live, 159.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 10 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
022102
02994
15290
28390
320772
457772
5226372
6550472
7745272
0848571
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
eps
#s(literal 2 binary64)
x
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
#s(literal 0 binary64)
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 eps #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) eps)
eps
#s(literal 2 binary64)
x
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
#s(literal 0 binary64)
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(+.f64 eps x)
eps
x
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)

localize88.0ms (1.4%)

Memory
22.0MiB live, 111.3MiB allocated
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 eps x)
accuracy0
(*.f64 eps x)
accuracy0
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
accuracy0.015625
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
accuracy0
(+.f64 eps x)
accuracy0.015625
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
accuracy30.744787574843453
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
accuracy0
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
accuracy0
(*.f64 eps #s(literal 2 binary64))
accuracy22.78437780349461
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
Samples
50.0ms168×0valid
19.0ms80×1valid
3.0ms8×2valid
Compiler

Compiled 190 to 43 computations (77.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-mult: 10.0ms (34.1% of total)
ival-add: 6.0ms (20.5% of total)
ival-pow2: 6.0ms (20.5% of total)
adjust: 3.0ms (10.2% of total)
ival-sub: 2.0ms (6.8% of total)
ival-neg: 1.0ms (3.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory
-27.4MiB live, 11.2MiB allocated
Counts
9 → 24
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
eps
(+ eps x)
(* eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(* 2 eps)
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* eps (+ 1 (/ x eps)))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@inf
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
2.0ms
x
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
1.0ms
eps
@-inf
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
1.0ms
eps
@inf
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))
1.0ms
x
@0
((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ eps x) (+ (* (+ eps x) x) (* (neg x) x)) (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) (+ (* (+ eps x) x) (* (neg x) x)) (* eps x))

simplify177.0ms (2.9%)

Memory
11.4MiB live, 90.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072122
1234102
2705102
32212102
45988102
0822594
Stop Event
1×iter limit
1×node limit
Counts
24 → 22
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
eps
(+ eps x)
(* eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
x
(* x (+ 1 (/ eps x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ eps (* 2 x)))
(* 2 eps)
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* eps (+ 1 (/ x eps)))
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
eps
(+ eps x)
(+.f64 eps x)
(* eps x)
(*.f64 eps x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 eps)
(*.f64 #s(literal 2 binary64) eps)
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* -1 (pow x 2)) (+ (* eps x) (pow x 2)))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ x (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(*.f64 eps x)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)))))
(*.f64 eps x)

rewrite225.0ms (3.6%)

Memory
19.9MiB live, 219.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02291
02983
113279
2100271
0886067
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
9 → 222
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
(+.f64 eps x)
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 eps x)
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 #s(literal 2 binary64) eps) x))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 (*.f64 eps x) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) eps) x)
(*.f64 #s(literal 2 binary64) (*.f64 eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(*.f64 x (*.f64 #s(literal 2 binary64) eps))
(*.f64 #s(literal 2 binary64) eps)
(*.f64 eps #s(literal 2 binary64))
(*.f64 (-.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) (*.f64 (+.f64 eps x) eps))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))))
(*.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))))))
(*.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
(*.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)) #s(literal 2 binary64))) (pow.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))) #s(literal -1 binary64)))
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(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) (*.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)))) (*.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (-.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))) (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64))) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64))) (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)))) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64)))) (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64))) (neg.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(neg.f64 (/.f64 (+.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps)) (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64))))))
(fma.f64 (*.f64 eps (sqrt.f64 (+.f64 eps x))) (sqrt.f64 (+.f64 eps x)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)) (fma.f64 eps x #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 (*.f64 (fma.f64 eps eps (*.f64 (neg.f64 x) x)) eps) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (pow.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (pow.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 eps (fma.f64 eps eps (*.f64 (neg.f64 x) x))) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) (-.f64 x eps)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) eps (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) #s(literal -1 binary64)) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (pow.f64 (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 eps (+.f64 eps x) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 eps eps (fma.f64 eps x #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 eps x (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(fma.f64 x eps (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(-.f64 (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps))) (/.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps))))
(-.f64 (/.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))))
(+.f64 (+.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 eps eps)) (*.f64 eps x))
(+.f64 (+.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 eps x)) (*.f64 eps eps))
(+.f64 (/.f64 (pow.f64 (*.f64 (+.f64 eps x) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))) (neg.f64 (/.f64 (pow.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) #s(literal 2 binary64)) (-.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))))
(+.f64 (*.f64 eps eps) (fma.f64 eps x #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
(+.f64 (*.f64 (+.f64 eps x) eps) #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(+.f64 #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)) (*.f64 (+.f64 eps x) eps))
(+.f64 (*.f64 eps x) (fma.f64 eps eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))))
#s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x))
(*.f64 (*.f64 eps (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 eps x)
(*.f64 x eps)

eval37.0ms (0.6%)

Memory
-11.9MiB live, 65.2MiB allocated
Compiler

Compiled 11 549 to 713 computations (93.8% saved)

prune9.0ms (0.1%)

Memory
-28.0MiB live, 19.9MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New3251326
Fresh000
Picked033
Done022
Total3256331
Accuracy
100.0%
Counts
331 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
✓76.5%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓64.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
✓73.1%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶38.9%
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Compiler

Compiled 98 to 64 computations (34.7% saved)

simplify170.0ms (2.7%)

Memory
20.1MiB live, 175.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 1 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
01117
12614
26214
321010
453010
5191710
6413710
7637110
8753010
082209
Stop Event
1×iter limit
1×node limit
1×saturated
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(literal 0 binary64)
Outputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(literal 0 binary64)

localize26.0ms (0.4%)

Memory
21.4MiB live, 21.4MiB allocated
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
accuracy39.10588866610714
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Samples
10.0ms87×1valid
10.0ms169×0valid
Compiler

Compiled 38 to 23 computations (39.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-mult: 6.0ms (44.5% of total)
ival-add: 4.0ms (29.7% of total)
adjust: 2.0ms (14.8% of total)
ival-neg: 1.0ms (7.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series70.0ms (1.1%)

Memory
-33.5MiB live, 3.8MiB allocated
Counts
1 → 11
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
Calls

6 calls:

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

simplify181.0ms (2.9%)

Memory
12.3MiB live, 168.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04781
114263
242363
3130763
4344763
5761863
0841856
Stop Event
1×iter limit
1×node limit
Counts
11 → 11
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(*.f64 (*.f64 x eps) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(*.f64 (*.f64 x eps) #s(literal 2 binary64))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

rewrite263.0ms (4.2%)

Memory
-18.0MiB live, 310.6MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01118
01116
16213
259311
0848911
Stop Event
1×iter limit
1×node limit
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Outputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))

eval1.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Compiler

Compiled 83 to 20 computations (75.9% saved)

prune3.0ms (0.1%)

Memory
5.5MiB live, 5.5MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New404
Fresh000
Picked011
Done055
Total4610
Accuracy
100.0%
Counts
10 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
✓76.5%
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
✓100.0%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓64.4%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
✓73.1%
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓38.9%
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Compiler

Compiled 234 to 105 computations (55.1% saved)

regimes10.0ms (0.2%)

Memory
16.3MiB live, 16.3MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) (*.f64 eps x)))
(fma.f64 (+.f64 eps x) eps (fma.f64 (+.f64 eps x) x (*.f64 (neg.f64 x) x)))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
Calls

3 calls:

4.0ms
eps
3.0ms
x
3.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory
12.3MiB live, 12.3MiB allocated
Counts
5 → 2
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps x) #s(literal 2 binary64)))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
Calls

3 calls:

2.0ms
eps
2.0ms
x
2.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
92.5%3x
88.6%3eps
97.9%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)

regimes19.0ms (0.3%)

Memory
-25.7MiB live, 12.9MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
Outputs
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
Calls

3 calls:

15.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
76.5%1eps
76.5%1x
76.5%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
8.9MiB live, 8.9MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
Calls

3 calls:

2.0ms
x
2.0ms
eps
1.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
73.1%1eps
73.1%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
73.1%1x
Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory
11.3MiB live, 11.3MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

3 calls:

1.0ms
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
38.9%1eps
38.9%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
38.9%1x
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1e-323
Compiler

Compiled 12 to 12 computations (0% saved)

simplify25.0ms (0.4%)

Memory
3.8MiB live, 41.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033108
139108
243108
345108
446108
Stop Event
1×saturated
Calls
Call 1
Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x)) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))
Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (*.f64 eps #s(literal 2 binary64)) x)) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 eps x) #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) eps) x)) (fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64))))
(fma.f64 (+.f64 eps x) eps #s(approx (+ (* (+ eps x) x) (* (neg x) x)) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) eps) (+ (* (+ eps x) x) (* (neg x) x))) #s(literal 0 binary64))

soundness1.1s (18.3%)

Memory
-21.7MiB live, 458.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082153
1267133
2784133
32434133
46295133
08135120
02097
03395
114090
2112290
0830690
0720
01120
15220
237120
3510920
0821920
069161
1214151
2570151
31802143
44139143
57201143
08049124
072122
1234102
2705102
32212102
45988102
0822594
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 219 to 108 computations (50.7% saved)

preprocess27.0ms (0.4%)

Memory
27.1MiB live, 27.1MiB allocated
Compiler

Compiled 234 to 80 computations (65.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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