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

Time bar (total: 5.9s)

analyze0.0ms (0%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25.7%74.3%0%0%0%0
100%25.7%0%74.3%0%0%0%1
Compiler

Compiled 26 to 18 computations (30.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-sub: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-and: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)
ival-<=: 0.0ms (0% of total)
ival-pow: 0.0ms (0% of total)

sample1.7s (28.3%)

Results
549.0ms5119×0valid
509.0ms2573×1valid
186.0ms564×2valid
Precisions
Click to see histograms. Total time spent on operations: 822.0ms
ival-pow: 336.0ms (40.9% of total)
ival-<=: 210.0ms (25.6% of total)
ival-add: 93.0ms (11.3% of total)
backward-pass: 73.0ms (8.9% of total)
ival-sub: 60.0ms (7.3% of total)
ival-and: 26.0ms (3.2% of total)
const: 23.0ms (2.8% of total)
Bogosity

preprocess265.0ms (4.5%)

Algorithm
egg-herbie
Rules
1988×+-lowering-+.f64
1988×+-lowering-+.f32
1748×fmsub-define
1742×fma-lowering-fma.f32
1742×fma-lowering-fma.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02264
15156
217250
369840
4412636
5793436
079
1129
2348
31128
45116
516346
635346
082846
Stop Event
iter limit
node limit
node limit
Calls
Call 1
Inputs
(- (pow (+ x eps) 2) (pow x 2))
Outputs
(- (pow (+ x eps) 2) (pow x 2))
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
Call 2
Inputs
(- (pow (+ x eps) 2) (pow x 2))
(- (pow (+ (neg x) eps) 2) (pow (neg x) 2))
(- (pow (+ x (neg eps)) 2) (pow x 2))
(neg (- (pow (+ (neg x) eps) 2) (pow (neg x) 2)))
(neg (- (pow (+ x (neg eps)) 2) (pow x 2)))
(- (pow (+ eps x) 2) (pow eps 2))
Outputs
(- (pow (+ x eps) 2) (pow x 2))
(* eps (sum3 x eps x))
(- (pow (+ (neg x) eps) 2) (pow (neg x) 2))
(* eps (fma x -2 eps))
(- (pow (+ x (neg eps)) 2) (pow x 2))
(* eps (fma x -2 eps))
(neg (- (pow (+ (neg x) eps) 2) (pow (neg x) 2)))
(* eps (fnmsub x -2 eps))
(neg (- (pow (+ x (neg eps)) 2) (pow x 2)))
(* eps (fnmsub x -2 eps))
(- (pow (+ eps x) 2) (pow eps 2))
(* x (sum3 x eps eps))

explain125.0ms (2.1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
770-0-(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
00-0-x
077(4.704267569903432e-307 1.5194414476616803e-42)0-(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
00-0-(+.f64 x eps)
00-0-#s(literal 2 binary64)
00-0-(pow.f64 x #s(literal 2 binary64))
00-0-eps
Results
54.0ms180×1valid
29.0ms298×0valid
8.0ms34×2valid
Compiler

Compiled 63 to 23 computations (63.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-pow: 17.0ms (51.7% of total)
backward-pass: 6.0ms (18.2% of total)
ival-add: 5.0ms (15.2% of total)
ival-sub: 4.0ms (12.2% of total)
const: 1.0ms (3% of total)

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
cost-diff0
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
Rules
30×*-lowering-*.f32
30×*-lowering-*.f64
20×fma-define
18×*-commutative
18×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0618
11416
22816
34016
04016
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(* eps (+ eps (* x 2)))
eps
(+ eps (* x 2))
(* x 2)
x
2
Outputs
(* eps (+ eps (* x 2)))
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
eps
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)

localize23.0ms (0.4%)

Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
Results
15.0ms256×0valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-mult: 4.0ms (67.5% of total)
ival-add: 1.0ms (16.9% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts
3 → 60
Calls
Call 1
Inputs
#<alt (* eps (+ eps (* x 2)))>
#<alt (+ eps (* x 2))>
#<alt (* x 2)>
Outputs
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
Calls

15 calls:

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

rewrite293.0ms (4.9%)

Algorithm
batch-egg-rewrite
Rules
3084×*-lowering-*.f32
3084×*-lowering-*.f64
2746×/-lowering-/.f32
2746×/-lowering-/.f64
1486×sum5-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0615
12513
221313
3225713
0904613
Stop Event
iter limit
node limit
Counts
3 → 195
Calls
Call 1
Inputs
(* eps (+ eps (* x 2)))
(+ eps (* x 2))
(* x 2)
Outputs
(+.f64 (*.f64 eps eps) (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(+.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
(-.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (/.f64 (*.f64 (*.f64 (*.f64 eps eps) x) (*.f64 x #s(literal 4 binary64))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) x) (*.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))
(fma.f64 eps eps (*.f64 eps (*.f64 x #s(literal 2 binary64))))
(fma.f64 eps (*.f64 x #s(literal 2 binary64)) (*.f64 eps eps))
(fma.f64 x (*.f64 eps #s(literal 2 binary64)) (*.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (*.f64 eps x) (*.f64 eps eps))
(fma.f64 (*.f64 x #s(literal 2 binary64)) eps (*.f64 eps eps))
(fma.f64 (*.f64 eps x) #s(literal 2 binary64) (*.f64 eps eps))
(fma.f64 (*.f64 eps #s(literal 2 binary64)) x (*.f64 eps eps))
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))) (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))))
(/.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) x) (*.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))) (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))))))
(/.f64 (*.f64 (*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(/.f64 (*.f64 eps (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))) (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))))))
(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))))) (neg.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))))
(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))))) (neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps eps) x) (*.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))
(/.f64 (neg.f64 (*.f64 eps (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps eps) x) (*.f64 x #s(literal 4 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))
(/.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))
(/.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 eps (-.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (*.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) eps) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))) eps) (-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (*.f64 eps eps)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (*.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) x) (*.f64 x #s(literal 4 binary64))))) (*.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))))) (neg.f64 (neg.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 eps eps)))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (neg.f64 (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
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(/.f64 (neg.f64 (-.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (+.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 512 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))) (neg.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 eps (*.f64 eps eps)))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))) (neg.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 64 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4 binary64))))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 16 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4 binary64))))))
(/.f64 (+.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) (pow.f64 (neg.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (-.f64 (*.f64 (neg.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (-.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (*.f64 eps eps))) #s(literal -1 binary64))
(*.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(*.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) (/.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) (*.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))))
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(*.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))) #s(literal -1 binary64)))
(*.f64 (-.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 (/.f64 (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))) (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))) (-.f64 (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))) (*.f64 eps eps)))))
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (-.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal -2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(*.f64 (/.f64 (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 512 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 eps (*.f64 eps eps)))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 64 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 64 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4 binary64))))))))
(*.f64 (pow.f64 (/.f64 (-.f64 eps (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 16 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4 binary64))))))
(exp.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 x)))

simplify146.0ms (2.5%)

Algorithm
egg-herbie
Rules
1886×fnmsub-define
1856×sum4-define
1704×fma-lowering-fma.f32
1704×fmm-def
1704×fma-lowering-fma.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038288
1128252
2331252
3870252
42492252
56116252
08495252
Stop Event
iter limit
node limit
Counts
60 → 60
Calls
Call 1
Inputs
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
Outputs
(* 2 (* eps x))
(*.f64 #s(literal 2 binary64) (*.f64 eps x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* eps (+ eps (* 2 x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* eps (+ eps (* 2 x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* 2 (* eps x))
(*.f64 #s(literal 2 binary64) (*.f64 eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* 2 (* eps x))
(*.f64 #s(literal 2 binary64) (*.f64 eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ 1 (* 2 (/ x eps))))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ 1 (* 2 (/ x eps))))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
eps
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ eps x)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ 2 (/ eps x)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ 2 (/ eps x)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)

eval31.0ms (0.5%)

Compiler

Compiled 7360 to 677 computations (90.8% saved)

prune27.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2514255
Fresh000
Picked011
Done000
Total2515256
Accuracy
100.0%
Counts
256 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.7%
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
99.8%
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
100.0%
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
63.9%
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
71.0%
(*.f64 eps eps)
Compiler

Compiled 51 to 34 computations (33.3% saved)

simplify133.0ms (2.2%)

Algorithm
egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
cost-diff128
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
cost-diff0
(*.f64 (*.f64 x x) #s(literal -4 binary64))
cost-diff0
(*.f64 eps eps)
cost-diff0
(+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))
cost-diff0
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
cost-diff0
(*.f64 #s(literal 2 binary64) x)
cost-diff0
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
cost-diff0
(*.f64 eps eps)
Rules
1792×*-lowering-*.f32
1792×*-lowering-*.f64
1712×sum4-define
1526×fma-define
1368×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01895
14291
28488
316988
427088
557988
6178388
7445988
8744188
0804988
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* eps eps)
eps
(* eps (* 2 x))
eps
(* 2 x)
2
x
(* (+ (* eps eps) (* (* x x) -4)) (/ eps (- eps (* x 2))))
(+ (* eps eps) (* (* x x) -4))
(* eps eps)
eps
(* (* x x) -4)
(* x x)
x
-4
(/ eps (- eps (* x 2)))
(- eps (* x 2))
(* x 2)
2
(/ eps (/ 1 (+ eps (* x 2))))
eps
(/ 1 (+ eps (* x 2)))
1
(+ eps (* x 2))
(* x 2)
x
2
Outputs
(* eps eps)
(*.f64 eps eps)
eps
(* eps (* 2 x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
eps
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(* (+ (* eps eps) (* (* x x) -4)) (/ eps (- eps (* x 2))))
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))))
(+ (* eps eps) (* (* x x) -4))
(+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))
(* eps eps)
(*.f64 eps eps)
eps
(* (* x x) -4)
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* x x)
(*.f64 x x)
x
-4
#s(literal -4 binary64)
(/ eps (- eps (* x 2)))
(/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64))))
(- eps (* x 2))
(+.f64 eps (*.f64 x #s(literal -2 binary64)))
(* x 2)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
(/ eps (/ 1 (+ eps (* x 2))))
(*.f64 eps (-.f64 eps (*.f64 x #s(literal -2 binary64))))
eps
(/ 1 (+ eps (* x 2)))
(/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal -2 binary64))))
1
#s(literal 1 binary64)
(+ eps (* x 2))
(-.f64 eps (*.f64 x #s(literal -2 binary64)))
(* x 2)
(*.f64 #s(literal 2 binary64) x)
x
2
#s(literal 2 binary64)

localize109.0ms (1.8%)

Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy99.9%
(/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
accuracy99.7%
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
accuracy100.0%
(+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64)))
accuracy100.0%
(*.f64 (*.f64 x x) #s(literal -4 binary64))
accuracy99.9%
(/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))
accuracy99.8%
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
accuracy100.0%
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
accuracy100.0%
(*.f64 #s(literal 2 binary64) x)
accuracy100.0%
(*.f64 eps eps)
Results
76.0ms256×0valid
Compiler

Compiled 102 to 19 computations (81.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-mult: 12.0ms (48.9% of total)
ival-div: 8.0ms (32.6% of total)
ival-add: 2.0ms (8.2% of total)
ival-sub: 1.0ms (4.1% of total)
const: 1.0ms (4.1% of total)
backward-pass: 0.0ms (0% of total)

series18.0ms (0.3%)

Counts
11 → 216
Calls
Call 1
Inputs
#<alt (* eps eps)>
#<alt (* eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* (+ (* eps eps) (* (* x x) -4)) (/ eps (- eps (* x 2))))>
#<alt (+ (* eps eps) (* (* x x) -4))>
#<alt (* (* x x) -4)>
#<alt (/ eps (/ 1 (+ eps (* x 2))))>
#<alt (/ 1 (+ eps (* x 2)))>
#<alt (+ eps (* x 2))>
#<alt (* x 2)>
#<alt (/ eps (- eps (* x 2)))>
Outputs
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -4 (pow x 2))>
#<alt (+ (* -4 (pow x 2)) (pow eps 2))>
#<alt (+ (* -4 (pow x 2)) (pow eps 2))>
#<alt (+ (* -4 (pow x 2)) (pow eps 2))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (+ (* -4 (pow x 2)) (pow eps 2))>
#<alt (+ (* -4 (pow x 2)) (pow eps 2))>
#<alt (+ (* -4 (pow x 2)) (pow eps 2))>
#<alt (* -4 (pow x 2))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))>
#<alt (* -4 (pow x 2))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (/ 1/2 x)>
#<alt (+ (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (- (* 1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (- (* eps (+ (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))>
#<alt (/ 1 eps)>
#<alt (/ (+ 1 (* -2 (/ x eps))) eps)>
#<alt (/ (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* 2 (/ x eps))) eps)>
#<alt (/ (- (+ 1 (* -8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* 2 (/ x eps)))) eps)>
#<alt (/ 1 eps)>
#<alt (* -1 (/ (- (* 2 (/ x eps)) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow x 2) eps)) (* 2 x)) eps)) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* 4 (pow x 2))) eps)) (* 2 x)) eps)) 1) eps))>
#<alt (/ 1 eps)>
#<alt (+ (* -2 (/ x (pow eps 2))) (/ 1 eps))>
#<alt (+ (* x (- (* 4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))>
#<alt (+ (* x (- (* x (+ (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* -1/4 (/ eps x))) x)>
#<alt (/ (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* 1/4 (/ eps x))) x)>
#<alt (/ (- (+ 1/2 (* -1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ eps x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* 1/4 eps)) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* 1/4 eps)) x)) 1/2) x))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 2 (/ x eps)))>
#<alt (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* -2 (/ x eps)))>
#<alt (- (+ 1 (* 8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* -2 (/ x eps))))>
#<alt 1>
#<alt (+ 1 (* 2 (/ x eps)))>
#<alt (+ 1 (* -1 (/ (- (* -4 (/ (pow x 2) eps)) (* 2 x)) eps)))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -4 (pow x 2))) eps)) (* 2 x)) eps)))>
#<alt 1>
#<alt (+ 1 (* 2 (/ x eps)))>
#<alt (+ 1 (* x (+ (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))))>
#<alt (+ 1 (* x (+ (* x (+ (* 8 (/ x (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x)>
#<alt (/ (- (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 2)))) (* 1/4 (/ (pow eps 2) x))) x)>
#<alt (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 4) (pow x 3)))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (/ (pow eps 2) x)))) x)>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (pow eps 2) x)) (* 1/2 eps)) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 4) x)) (* -1/8 (pow eps 3))) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))>
Calls

54 calls:

TimeVariablePointExpression
4.0ms
eps
@inf
(/ eps (- eps (* x 2)))
2.0ms
eps
@inf
(* (+ (* eps eps) (* (* x x) -4)) (/ eps (- eps (* x 2))))
1.0ms
eps
@0
(* (+ (* eps eps) (* (* x x) -4)) (/ eps (- eps (* x 2))))
1.0ms
eps
@0
(* eps eps)
1.0ms
x
@inf
(* (+ (* eps eps) (* (* x x) -4)) (/ eps (- eps (* x 2))))

rewrite325.0ms (5.5%)

Algorithm
batch-egg-rewrite
Rules
4680×*-lowering-*.f32
4680×*-lowering-*.f64
3084×/-lowering-/.f32
3084×/-lowering-/.f64
1708×frac-times
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01877
19275
274754
0919254
Stop Event
iter limit
node limit
Counts
11 → 911
Calls
Call 1
Inputs
(* eps eps)
(* eps (* 2 x))
(* 2 x)
(* (+ (* eps eps) (* (* x x) -4)) (/ eps (- eps (* x 2))))
(+ (* eps eps) (* (* x x) -4))
(* (* x x) -4)
(/ eps (/ 1 (+ eps (* x 2))))
(/ 1 (+ eps (* x 2)))
(+ eps (* x 2))
(* x 2)
(/ eps (- eps (* x 2)))
Outputs
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 eps)))
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
(/.f64 eps (*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(/.f64 (*.f64 eps eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) eps)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(*.f64 eps eps)
(*.f64 (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(/.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 1 binary64) eps))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) (*.f64 x eps))
(*.f64 x (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) x) eps)
(*.f64 (*.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
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(/.f64 (*.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) (*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (+.f64 eps (*.f64 x #s(literal -2 binary64)))))
(/.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (+.f64 (*.f64 eps eps) (*.f64 x (-.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 eps #s(literal 2 binary64)))))))
(/.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (+.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))))))
(/.f64 (/.f64 #s(literal -1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))))
(/.f64 (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))
(/.f64 (*.f64 eps (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) (*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) #s(literal -1 binary64)))
(/.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (-.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 eps #s(literal 2 binary64))))))))
(/.f64 (*.f64 eps (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (*.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 eps (*.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)))
(/.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x))) (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) (+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x))) (*.f64 eps eps))))))
(/.f64 (*.f64 eps (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal -2 binary64)) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))
(pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps)) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal -1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(*.f64 (/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)) eps)
(*.f64 (/.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(*.f64 (/.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))))
(*.f64 (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(*.f64 (/.f64 eps (/.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (-.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 eps #s(literal 2 binary64)))))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps)) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))))) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(*.f64 (*.f64 (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) #s(literal 1 binary64)) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(*.f64 (*.f64 (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) #s(literal -1 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(*.f64 (*.f64 (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 x (-.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 eps #s(literal 2 binary64)))))))
(*.f64 (*.f64 (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) (/.f64 #s(literal -1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(*.f64 (*.f64 (/.f64 eps (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64))))) (/.f64 (+.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))))) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))

simplify245.0ms (4.1%)

Algorithm
egg-herbie
Rules
5088×*-lowering-*.f32
5088×*-lowering-*.f64
1930×/-lowering-/.f32
1930×/-lowering-/.f64
1754×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02641746
18971662
225261608
083761608
Stop Event
iter limit
node limit
Counts
216 → 216
Calls
Call 1
Inputs
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -4 (pow x 2))
(+ (* -4 (pow x 2)) (pow eps 2))
(+ (* -4 (pow x 2)) (pow eps 2))
(+ (* -4 (pow x 2)) (pow eps 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(pow eps 2)
(+ (* -4 (pow x 2)) (pow eps 2))
(+ (* -4 (pow x 2)) (pow eps 2))
(+ (* -4 (pow x 2)) (pow eps 2))
(* -4 (pow x 2))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(* -4 (pow x 2))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(/ 1/2 x)
(+ (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x)))
(+ (* eps (- (* 1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(+ (* eps (- (* eps (+ (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(/ 1 eps)
(/ (+ 1 (* -2 (/ x eps))) eps)
(/ (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* 2 (/ x eps))) eps)
(/ (- (+ 1 (* -8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* 2 (/ x eps)))) eps)
(/ 1 eps)
(* -1 (/ (- (* 2 (/ x eps)) 1) eps))
(* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow x 2) eps)) (* 2 x)) eps)) 1) eps))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* 4 (pow x 2))) eps)) (* 2 x)) eps)) 1) eps))
(/ 1 eps)
(+ (* -2 (/ x (pow eps 2))) (/ 1 eps))
(+ (* x (- (* 4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(+ (* x (- (* x (+ (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(/ 1/2 x)
(/ (+ 1/2 (* -1/4 (/ eps x))) x)
(/ (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* 1/4 (/ eps x))) x)
(/ (- (+ 1/2 (* -1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ eps x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* 1/4 eps)) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* 1/4 eps)) x)) 1/2) x))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* -1/2 (/ eps x))
(* eps (- (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))
(* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))
1
(+ 1 (* 2 (/ x eps)))
(- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* -2 (/ x eps)))
(- (+ 1 (* 8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* -2 (/ x eps))))
1
(+ 1 (* 2 (/ x eps)))
(+ 1 (* -1 (/ (- (* -4 (/ (pow x 2) eps)) (* 2 x)) eps)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -4 (pow x 2))) eps)) (* 2 x)) eps)))
1
(+ 1 (* 2 (/ x eps)))
(+ 1 (* x (+ (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))))
(+ 1 (* x (+ (* x (+ (* 8 (/ x (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x)
(/ (- (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 2)))) (* 1/4 (/ (pow eps 2) x))) x)
(/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 4) (pow x 3)))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (/ (pow eps 2) x)))) x)
(* -1/2 (/ eps x))
(* -1 (/ (+ (* 1/4 (/ (pow eps 2) x)) (* 1/2 eps)) x))
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 4) x)) (* -1/8 (pow eps 3))) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
Outputs
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
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(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) eps)) eps))
(- (+ 1 (* 8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* -2 (/ x eps))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (*.f64 x (+.f64 (/.f64 (*.f64 x (/.f64 (/.f64 #s(literal 8 binary64) eps) eps)) eps) (/.f64 #s(literal 4 binary64) (*.f64 eps eps)))))))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(+ 1 (* -1 (/ (- (* -4 (/ (pow x 2) eps)) (* 2 x)) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) eps)) eps))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -4 (pow x 2))) eps)) (* 2 x)) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (*.f64 x (*.f64 (/.f64 (*.f64 x x) eps) #s(literal 8 binary64))) (*.f64 x (*.f64 x #s(literal 4 binary64)))) eps)) eps))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(+ 1 (* x (+ (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) eps)) eps))
(+ 1 (* x (+ (* x (+ (* 8 (/ x (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (*.f64 x (+.f64 (/.f64 (*.f64 x (/.f64 (/.f64 #s(literal 8 binary64) eps) eps)) eps) (/.f64 #s(literal 4 binary64) (*.f64 eps eps)))))))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x)) x)
(/ (- (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 2)))) (* 1/4 (/ (pow eps 2) x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) x) (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64))) x)) x)
(/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 4) (pow x 3)))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (/ (pow eps 2) x)))) x)
(/.f64 (+.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 4 binary64))) (*.f64 x (*.f64 x x)))) (/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) x) (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64))) x)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1 (/ (+ (* 1/4 (/ (pow eps 2) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x)) x)
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 (*.f64 eps eps) x)))) (-.f64 #s(literal 0 binary64) x))) x)
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 4) x)) (* -1/8 (pow eps 3))) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 4 binary64)) x)) (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))))) x)) x)) x)

eval139.0ms (2.3%)

Compiler

Compiled 35097 to 2209 computations (93.7% saved)

prune111.0ms (1.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New117331176
Fresh000
Picked134
Done011
Total117471181
Accuracy
100.0%
Counts
1181 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.7%
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
70.8%
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
64.2%
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
99.8%
(*.f64 x (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
100.0%
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
63.9%
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
71.0%
(*.f64 eps eps)
Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify153.0ms (2.6%)

Algorithm
egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1 binary64) eps)
cost-diff128
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
cost-diff0
(/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))
cost-diff0
(*.f64 x #s(literal -4 binary64))
cost-diff0
(*.f64 x (*.f64 x #s(literal -4 binary64)))
cost-diff128
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
cost-diff0
(/.f64 eps x)
cost-diff0
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
cost-diff0
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
cost-diff128
(*.f64 x (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
Rules
3332×*-lowering-*.f32
3332×*-lowering-*.f64
1940×sum3-define
1744×/-lowering-/.f32
1744×/-lowering-/.f64
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01775
14874
212171
323871
433470
574268
6229667
7404867
0883167
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* x (* eps (+ 2 (/ eps x))))
x
(* eps (+ 2 (/ eps x)))
eps
(+ 2 (/ eps x))
2
(/ eps x)
(* (* x (* x -4)) (/ eps (- eps (* x 2))))
(* x (* x -4))
x
(* x -4)
-4
(/ eps (- eps (* x 2)))
eps
(- eps (* x 2))
(* x 2)
2
(/ eps (/ 1 eps))
eps
(/ 1 eps)
1
Outputs
(* x (* eps (+ 2 (/ eps x))))
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
x
(* eps (+ 2 (/ eps x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
eps
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
2
#s(literal 2 binary64)
(/ eps x)
(/.f64 eps x)
(* (* x (* x -4)) (/ eps (- eps (* x 2))))
(*.f64 x (*.f64 eps (/.f64 #s(literal -4 binary64) (+.f64 (/.f64 eps x) #s(literal -2 binary64)))))
(* x (* x -4))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
x
(* x -4)
(*.f64 x #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ eps (- eps (* x 2)))
(/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))
eps
(- eps (* x 2))
(-.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ eps (/ 1 eps))
(*.f64 eps eps)
eps
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
1
#s(literal 1 binary64)

localize71.0ms (1.2%)

Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(/.f64 #s(literal 1 binary64) eps)
accuracy99.8%
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(*.f64 x #s(literal -4 binary64))
accuracy99.9%
(/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))
accuracy99.8%
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
accuracy100.0%
(/.f64 eps x)
accuracy100.0%
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
accuracy99.9%
(*.f64 x (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
accuracy99.8%
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
Results
45.0ms256×0valid
Compiler

Compiled 80 to 18 computations (77.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-div: 10.0ms (43.4% of total)
ival-mult: 9.0ms (39.1% of total)
ival-sub: 1.0ms (4.3% of total)
ival-add: 1.0ms (4.3% of total)
const: 1.0ms (4.3% of total)
backward-pass: 0.0ms (0% of total)

series11.0ms (0.2%)

Counts
11 → 204
Calls
Call 1
Inputs
#<alt (* x (* eps (+ 2 (/ eps x))))>
#<alt (* eps (+ 2 (/ eps x)))>
#<alt (+ 2 (/ eps x))>
#<alt (/ eps x)>
#<alt (* (* x (* x -4)) (/ eps (- eps (* x 2))))>
#<alt (* x (* x -4))>
#<alt (* x -4)>
#<alt (/ eps (- eps (* x 2)))>
#<alt (/ eps (/ 1 eps))>
#<alt (/ 1 eps)>
#<alt (* x 2)>
Outputs
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* 2 eps)>
#<alt (* eps (+ 2 (/ eps x)))>
#<alt (* eps (+ 2 (/ eps x)))>
#<alt (* eps (+ 2 (/ eps x)))>
#<alt (/ (pow eps 2) x)>
#<alt (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (/ (pow eps 2) x)>
#<alt (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (/ (pow eps 2) x)>
#<alt (/ (+ (* 2 (* eps x)) (pow eps 2)) x)>
#<alt (/ (+ (* 2 (* eps x)) (pow eps 2)) x)>
#<alt (/ (+ (* 2 (* eps x)) (pow eps 2)) x)>
#<alt (* 2 eps)>
#<alt (+ (* 2 eps) (/ (pow eps 2) x))>
#<alt (+ (* 2 eps) (/ (pow eps 2) x))>
#<alt (+ (* 2 eps) (/ (pow eps 2) x))>
#<alt (* 2 eps)>
#<alt (+ (* 2 eps) (/ (pow eps 2) x))>
#<alt (+ (* 2 eps) (/ (pow eps 2) x))>
#<alt (+ (* 2 eps) (/ (pow eps 2) x))>
#<alt 2>
#<alt (+ 2 (/ eps x))>
#<alt (+ 2 (/ eps x))>
#<alt (+ 2 (/ eps x))>
#<alt (/ eps x)>
#<alt (* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (/ eps x)>
#<alt (* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))>
#<alt (/ eps x)>
#<alt (/ (+ eps (* 2 x)) x)>
#<alt (/ (+ eps (* 2 x)) x)>
#<alt (/ (+ eps (* 2 x)) x)>
#<alt 2>
#<alt (+ 2 (/ eps x))>
#<alt (+ 2 (/ eps x))>
#<alt (+ 2 (/ eps x))>
#<alt 2>
#<alt (+ 2 (/ eps x))>
#<alt (+ 2 (/ eps x))>
#<alt (+ 2 (/ eps x))>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (* -4 (pow x 2))>
#<alt (* (pow x 2) (- (* -8 (/ x eps)) 4))>
#<alt (* (pow x 2) (- (* x (- (* -16 (/ x (pow eps 2))) (* 8 (/ 1 eps)))) 4))>
#<alt (* (pow x 2) (- (* x (- (* x (- (* -32 (/ x (pow eps 3))) (* 16 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps)))) 4))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (+ (* 2 eps) (/ (pow eps 2) x))))>
#<alt (* x (+ (* 1/4 (/ (pow eps 4) (pow x 3))) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (+ (* 2 eps) (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2)) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (pow eps 3)) (* -1/4 (/ (pow eps 4) x))) x)) (pow eps 2)) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ (* 2 x) (* eps (+ 1 (* 1/2 (/ eps x))))))>
#<alt (* eps (+ (* 2 x) (* eps (+ 1 (* eps (+ (* 1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))))))>
#<alt (* -4 (pow x 2))>
#<alt (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))>
#<alt (+ (* -16 (/ (pow x 4) (pow eps 2))) (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2))))>
#<alt (+ (* -32 (/ (pow x 5) (pow eps 3))) (+ (* -16 (/ (pow x 4) (pow eps 2))) (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))))>
#<alt (* -4 (pow x 2))>
#<alt (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))>
#<alt (+ (* -4 (pow x 2)) (* -1 (/ (+ (* 8 (pow x 3)) (* 16 (/ (pow x 4) eps))) eps)))>
#<alt (+ (* -4 (pow x 2)) (* -1 (/ (+ (* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* -16 (pow x 4))) eps)) (* 8 (pow x 3))) eps)))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 2 (/ x eps)))>
#<alt (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* -2 (/ x eps)))>
#<alt (- (+ 1 (* 8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* -2 (/ x eps))))>
#<alt 1>
#<alt (+ 1 (* 2 (/ x eps)))>
#<alt (+ 1 (* -1 (/ (- (* -4 (/ (pow x 2) eps)) (* 2 x)) eps)))>
#<alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -4 (pow x 2))) eps)) (* 2 x)) eps)))>
#<alt 1>
#<alt (+ 1 (* 2 (/ x eps)))>
#<alt (+ 1 (* x (+ (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))))>
#<alt (+ 1 (* x (+ (* x (+ (* 8 (/ x (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x)>
#<alt (/ (- (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 2)))) (* 1/4 (/ (pow eps 2) x))) x)>
#<alt (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 4) (pow x 3)))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (/ (pow eps 2) x)))) x)>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (pow eps 2) x)) (* 1/2 eps)) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 4) x)) (* -1/8 (pow eps 3))) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
Calls

51 calls:

TimeVariablePointExpression
2.0ms
eps
@0
(* x (* eps (+ 2 (/ eps x))))
1.0ms
x
@-inf
(* x (* eps (+ 2 (/ eps x))))
0.0ms
x
@0
(* x (* eps (+ 2 (/ eps x))))
0.0ms
eps
@-inf
(* x (* eps (+ 2 (/ eps x))))
0.0ms
eps
@inf
(* x (* eps (+ 2 (/ eps x))))

rewrite262.0ms (4.4%)

Algorithm
batch-egg-rewrite
Rules
4318×*-lowering-*.f32
4318×*-lowering-*.f64
3124×/-lowering-/.f32
3124×/-lowering-/.f64
1238×sum5-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01761
19960
269358
3712258
0839358
Stop Event
iter limit
node limit
Counts
11 → 424
Calls
Call 1
Inputs
(* x (* eps (+ 2 (/ eps x))))
(* eps (+ 2 (/ eps x)))
(+ 2 (/ eps x))
(/ eps x)
(* (* x (* x -4)) (/ eps (- eps (* x 2))))
(* x (* x -4))
(* x -4)
(/ eps (- eps (* x 2)))
(/ eps (/ 1 eps))
(/ 1 eps)
(* x 2)
Outputs
(+.f64 (*.f64 x (*.f64 eps #s(literal 2 binary64))) (/.f64 (*.f64 x (*.f64 eps eps)) x))
(+.f64 (/.f64 (*.f64 x (*.f64 eps eps)) x) (*.f64 x (*.f64 eps #s(literal 2 binary64))))
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(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal -1/2 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) eps) (pow.f64 eps #s(literal -1/2 binary64))))
(*.f64 (/.f64 eps (pow.f64 eps #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1/2 binary64))) (/.f64 eps (pow.f64 eps #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 eps)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) eps))
(neg.f64 (/.f64 #s(literal -1 binary64) eps))
(/.f64 #s(literal 1 binary64) eps)
(/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal -1 binary64))
(pow.f64 eps #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(pow.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 eps #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps))
(*.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal -1 binary64))
(*.f64 (pow.f64 eps #s(literal -1/2 binary64)) (pow.f64 eps #s(literal -1/2 binary64)))
(*.f64 (pow.f64 eps #s(literal -1/2 binary64)) (/.f64 (pow.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 eps #s(literal -1/2 binary64)) (*.f64 (pow.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1/2 binary64))) (pow.f64 eps #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -2 binary64)))
(neg.f64 (*.f64 x #s(literal -2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) x))

simplify242.0ms (4.1%)

Algorithm
egg-herbie
Rules
4844×*-lowering-*.f32
4844×*-lowering-*.f64
1770×fma-define
1750×fma-lowering-fma.f32
1750×fma-lowering-fma.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02461422
18101345
224091320
376201320
081401320
Stop Event
iter limit
node limit
Counts
204 → 204
Calls
Call 1
Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 eps)
(* eps (+ 2 (/ eps x)))
(* eps (+ 2 (/ eps x)))
(* eps (+ 2 (/ eps x)))
(/ (pow eps 2) x)
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(/ (pow eps 2) x)
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(/ (pow eps 2) x)
(/ (+ (* 2 (* eps x)) (pow eps 2)) x)
(/ (+ (* 2 (* eps x)) (pow eps 2)) x)
(/ (+ (* 2 (* eps x)) (pow eps 2)) x)
(* 2 eps)
(+ (* 2 eps) (/ (pow eps 2) x))
(+ (* 2 eps) (/ (pow eps 2) x))
(+ (* 2 eps) (/ (pow eps 2) x))
(* 2 eps)
(+ (* 2 eps) (/ (pow eps 2) x))
(+ (* 2 eps) (/ (pow eps 2) x))
(+ (* 2 eps) (/ (pow eps 2) x))
2
(+ 2 (/ eps x))
(+ 2 (/ eps x))
(+ 2 (/ eps x))
(/ eps x)
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(/ eps x)
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(/ eps x)
(/ (+ eps (* 2 x)) x)
(/ (+ eps (* 2 x)) x)
(/ (+ eps (* 2 x)) x)
2
(+ 2 (/ eps x))
(+ 2 (/ eps x))
(+ 2 (/ eps x))
2
(+ 2 (/ eps x))
(+ 2 (/ eps x))
(+ 2 (/ eps x))
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(* -4 (pow x 2))
(* (pow x 2) (- (* -8 (/ x eps)) 4))
(* (pow x 2) (- (* x (- (* -16 (/ x (pow eps 2))) (* 8 (/ 1 eps)))) 4))
(* (pow x 2) (- (* x (- (* x (- (* -32 (/ x (pow eps 3))) (* 16 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps)))) 4))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (+ (* 2 eps) (/ (pow eps 2) x))))
(* x (+ (* 1/4 (/ (pow eps 4) (pow x 3))) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (+ (* 2 eps) (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2)) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (pow eps 3)) (* -1/4 (/ (pow eps 4) x))) x)) (pow eps 2)) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ (* 2 x) (* eps (+ 1 (* 1/2 (/ eps x))))))
(* eps (+ (* 2 x) (* eps (+ 1 (* eps (+ (* 1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))))))
(* -4 (pow x 2))
(+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))
(+ (* -16 (/ (pow x 4) (pow eps 2))) (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2))))
(+ (* -32 (/ (pow x 5) (pow eps 3))) (+ (* -16 (/ (pow x 4) (pow eps 2))) (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))))
(* -4 (pow x 2))
(+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))
(+ (* -4 (pow x 2)) (* -1 (/ (+ (* 8 (pow x 3)) (* 16 (/ (pow x 4) eps))) eps)))
(+ (* -4 (pow x 2)) (* -1 (/ (+ (* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* -16 (pow x 4))) eps)) (* 8 (pow x 3))) eps)))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -1/2 (/ eps x))
(* eps (- (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))
(* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))
1
(+ 1 (* 2 (/ x eps)))
(- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* -2 (/ x eps)))
(- (+ 1 (* 8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* -2 (/ x eps))))
1
(+ 1 (* 2 (/ x eps)))
(+ 1 (* -1 (/ (- (* -4 (/ (pow x 2) eps)) (* 2 x)) eps)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -4 (pow x 2))) eps)) (* 2 x)) eps)))
1
(+ 1 (* 2 (/ x eps)))
(+ 1 (* x (+ (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))))
(+ 1 (* x (+ (* x (+ (* 8 (/ x (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x)
(/ (- (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 2)))) (* 1/4 (/ (pow eps 2) x))) x)
(/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 4) (pow x 3)))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (/ (pow eps 2) x)))) x)
(* -1/2 (/ eps x))
(* -1 (/ (+ (* 1/4 (/ (pow eps 2) x)) (* 1/2 eps)) x))
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 4) x)) (* -1/8 (pow eps 3))) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* eps (+ eps (* 2 x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* eps (+ eps (* 2 x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* eps (+ 2 (/ eps x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* eps (+ 2 (/ eps x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* eps (+ 2 (/ eps x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* (pow eps 2) (+ (* 2 (/ 1 eps)) (/ 1 x)))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (+ (* 2 (* eps x)) (pow eps 2)) x)
(/.f64 (*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) x)
(/ (+ (* 2 (* eps x)) (pow eps 2)) x)
(/.f64 (*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) x)
(/ (+ (* 2 (* eps x)) (pow eps 2)) x)
(/.f64 (*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) x)
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(+ (* 2 eps) (/ (pow eps 2) x))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(+ (* 2 eps) (/ (pow eps 2) x))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(+ (* 2 eps) (/ (pow eps 2) x))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(+ (* 2 eps) (/ (pow eps 2) x))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(+ (* 2 eps) (/ (pow eps 2) x))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(+ (* 2 eps) (/ (pow eps 2) x))
(*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
2
#s(literal 2 binary64)
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(/ eps x)
(/.f64 eps x)
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(/ eps x)
(/.f64 eps x)
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(* eps (+ (* 2 (/ 1 eps)) (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(/ eps x)
(/.f64 eps x)
(/ (+ eps (* 2 x)) x)
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) x)
(/ (+ eps (* 2 x)) x)
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) x)
(/ (+ eps (* 2 x)) x)
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) x)
2
#s(literal 2 binary64)
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
2
#s(literal 2 binary64)
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(+ 2 (/ eps x))
(+.f64 #s(literal 2 binary64) (/.f64 eps x))
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(/ eps x)
(/.f64 eps x)
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* (pow x 2) (- (* -8 (/ x eps)) 4))
(*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (/.f64 (*.f64 x #s(literal -8 binary64)) eps)))
(* (pow x 2) (- (* x (- (* -16 (/ x (pow eps 2))) (* 8 (/ 1 eps)))) 4))
(*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (*.f64 x (+.f64 (*.f64 x (/.f64 #s(literal -16 binary64) (*.f64 eps eps))) (/.f64 #s(literal -8 binary64) eps)))))
(* (pow x 2) (- (* x (- (* x (- (* -32 (/ x (pow eps 3))) (* 16 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps)))) 4))
(*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal -32 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal -16 binary64) (*.f64 eps eps)))) (/.f64 #s(literal -8 binary64) eps)))))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* x (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (+ (* 2 eps) (/ (pow eps 2) x))))
(*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))) (/.f64 (*.f64 eps (*.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x)))
(* x (+ (* 1/4 (/ (pow eps 4) (pow x 3))) (+ (* 1/2 (/ (pow eps 3) (pow x 2))) (+ (* 2 eps) (/ (pow eps 2) x)))))
(*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))) (+.f64 (/.f64 (*.f64 eps (*.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64))) x) (/.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 eps #s(literal 4 binary64))) (*.f64 x (*.f64 x x))))))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 eps x)) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2)) x)))))
(*.f64 (-.f64 (*.f64 eps #s(literal -2 binary64)) (/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (pow eps 3)) (* -1/4 (/ (pow eps 4) x))) x)) (pow eps 2)) x)))))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 (*.f64 eps #s(literal -2 binary64)) (/.f64 (+.f64 (*.f64 eps eps) (/.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 eps #s(literal 4 binary64))) x)) x)) x))))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(* eps (+ (* 2 x) (* eps (+ 1 (* 1/2 (/ eps x))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))))
(* eps (+ (* 2 x) (* eps (+ 1 (* eps (+ (* 1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/4 binary64)) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) x)))))))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))
(*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (/.f64 (*.f64 x #s(literal -8 binary64)) eps)))
(+ (* -16 (/ (pow x 4) (pow eps 2))) (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (/.f64 (*.f64 x #s(literal -8 binary64)) eps))) (/.f64 (*.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps eps)))
(+ (* -32 (/ (pow x 5) (pow eps 3))) (+ (* -16 (/ (pow x 4) (pow eps 2))) (+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (/.f64 (*.f64 x #s(literal -8 binary64)) eps))) (+.f64 (/.f64 (*.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps eps)) (/.f64 (*.f64 #s(literal -32 binary64) (/.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) eps) eps)) eps)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(+ (* -8 (/ (pow x 3) eps)) (* -4 (pow x 2)))
(*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (/.f64 (*.f64 x #s(literal -8 binary64)) eps)))
(+ (* -4 (pow x 2)) (* -1 (/ (+ (* 8 (pow x 3)) (* 16 (/ (pow x 4) eps))) eps)))
(+.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) eps)) eps))
(+ (* -4 (pow x 2)) (* -1 (/ (+ (* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* -16 (pow x 4))) eps)) (* 8 (pow x 3))) eps)))
(-.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 (-.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 8 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -32 binary64) (pow.f64 x #s(literal 5 binary64))) eps) (*.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64)))) eps)) eps))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) x) eps) x) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* -2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) eps))) eps))
(- (+ 1 (* 8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* -2 (/ x eps))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal 8 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 4 binary64) (*.f64 eps eps)))))))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(+ 1 (* -1 (/ (- (* -4 (/ (pow x 2) eps)) (* 2 x)) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) eps))) eps))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -4 (pow x 2))) eps)) (* 2 x)) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -4 binary64) (/.f64 (*.f64 x #s(literal -8 binary64)) eps))) eps) (*.f64 x #s(literal -2 binary64))) eps))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(+ 1 (* x (+ (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) eps))) eps))
(+ 1 (* x (+ (* x (+ (* 8 (/ x (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal 8 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 4 binary64) (*.f64 eps eps)))))))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (/.f64 (*.f64 eps eps) x) #s(literal -1/4 binary64))) x)
(/ (- (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 2)))) (* 1/4 (/ (pow eps 2) x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) x) (*.f64 eps (*.f64 eps #s(literal -1/4 binary64)))) x)) x)
(/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 4) (pow x 3)))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (/ (pow eps 2) x)))) x)
(/.f64 (+.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x x)))) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) x) (*.f64 eps (*.f64 eps #s(literal -1/4 binary64)))) x)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1 (/ (+ (* 1/4 (/ (pow eps 2) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (/.f64 (*.f64 eps eps) x) #s(literal -1/4 binary64))) x)
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/4 binary64))) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) x) #s(literal 1/8 binary64))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 4) x)) (* -1/8 (pow eps 3))) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/16 binary64)) x) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)))) x)) x)) x)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)

eval66.0ms (1.1%)

Compiler

Compiled 11710 to 1403 computations (88% saved)

prune58.0ms (1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New6271628
Fresh000
Picked123
Done044
Total6287635
Accuracy
100.0%
Counts
635 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.7%
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
70.8%
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
63.8%
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
99.8%
(*.f64 x (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
100.0%
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
63.9%
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
71.0%
(*.f64 eps eps)
Compiler

Compiled 63 to 43 computations (31.7% saved)

simplify235.0ms (4%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
cost-diff0
(*.f64 x #s(literal -4 binary64))
cost-diff0
(*.f64 x (*.f64 x #s(literal -4 binary64)))
cost-diff384
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
Rules
4954×*-lowering-*.f32
4954×*-lowering-*.f64
3048×/-lowering-/.f32
3048×/-lowering-/.f64
2358×associate-/l/
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0931
12131
25629
317829
438625
550425
682125
7285025
8382825
9388325
10390325
11392925
12396125
13400525
14548025
15578325
16629425
17705225
18798325
0810725
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* x (* x -4)) (/ (* eps -1/2) x))
(* x (* x -4))
x
(* x -4)
-4
(/ (* eps -1/2) x)
(* eps -1/2)
eps
-1/2
Outputs
(* (* x (* x -4)) (/ (* eps -1/2) x))
(*.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x (* x -4))
(*.f64 #s(literal -4 binary64) (*.f64 x x))
x
(* x -4)
(*.f64 x #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ (* eps -1/2) x)
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)

localize33.0ms (0.5%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 x (*.f64 x #s(literal -4 binary64)))
accuracy100.0%
(*.f64 x #s(literal -4 binary64))
accuracy100.0%
(*.f64 eps #s(literal -1/2 binary64))
accuracy88.9%
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
Results
23.0ms256×0valid
Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-mult: 7.0ms (74% of total)
ival-div: 2.0ms (21.1% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts
5 → 84
Calls
Call 1
Inputs
#<alt (* (* x (* x -4)) (/ (* eps -1/2) x))>
#<alt (* x (* x -4))>
#<alt (* x -4)>
#<alt (/ (* eps -1/2) x)>
#<alt (* eps -1/2)>
Outputs
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 (pow x 2))>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -4 x)>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
Calls

21 calls:

TimeVariablePointExpression
0.0ms
eps
@-inf
(/ (* eps -1/2) x)
0.0ms
eps
@inf
(/ (* eps -1/2) x)
0.0ms
eps
@inf
(* eps -1/2)
0.0ms
eps
@-inf
(* eps -1/2)
0.0ms
x
@inf
(/ (* eps -1/2) x)

rewrite196.0ms (3.3%)

Algorithm
batch-egg-rewrite
Rules
2264×*-lowering-*.f32
2264×*-lowering-*.f64
2116×/-lowering-/.f32
2116×/-lowering-/.f64
792×frac-times
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0927
12927
214125
386021
0501121
Stop Event
iter limit
iter limit
node limit
Counts
5 → 334
Calls
Call 1
Inputs
(* (* x (* x -4)) (/ (* eps -1/2) x))
(* x (* x -4))
(* x -4)
(/ (* eps -1/2) x)
(* eps -1/2)
Outputs
(+.f64 (*.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (*.f64 x (*.f64 eps #s(literal 2 binary64))))
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 x #s(literal 4 binary64))) (*.f64 x (*.f64 eps #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps))
(neg.f64 (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps))
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 eps (*.f64 x (/.f64 x #s(literal 1/2 binary64))))))
(neg.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 x (*.f64 (*.f64 x #s(literal -4 binary64)) eps))))
(neg.f64 (*.f64 (/.f64 (*.f64 #s(literal -2 binary64) eps) x) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(neg.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (/.f64 x (/.f64 eps #s(literal -2 binary64)))))
(/.f64 x (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) eps)))
(/.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal -4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -2 binary64) eps)))
(/.f64 #s(literal -4 binary64) (*.f64 (/.f64 #s(literal -2 binary64) eps) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 x #s(literal -4 binary64)) (/.f64 #s(literal -2 binary64) eps))
(/.f64 (*.f64 x #s(literal -4 binary64)) (*.f64 (/.f64 x (/.f64 eps #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 x #s(literal -4 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 eps #s(literal -2 binary64)))))
(/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 x (/.f64 eps #s(literal -2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) eps))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) x))
(/.f64 (*.f64 eps (*.f64 x (/.f64 x #s(literal 1/2 binary64)))) x)
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) x) eps))
(/.f64 (*.f64 x (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 x (*.f64 (*.f64 x #s(literal -4 binary64)) eps)) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (*.f64 x (/.f64 x #s(literal 1/2 binary64))) (/.f64 x eps))
(/.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) eps) #s(literal -2 binary64))
(/.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) eps) (*.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) eps) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal -1/2 binary64))))
(/.f64 (*.f64 x (*.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 eps #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps) #s(literal -1 binary64))
(/.f64 (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (/.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (*.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 2 binary64) eps))
(/.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 x (*.f64 eps #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal -2 binary64) eps) #s(literal -1 binary64)))
(/.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 4 binary64)))) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x #s(literal 4 binary64))) (/.f64 x (/.f64 eps #s(literal -2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) (*.f64 x (*.f64 x #s(literal -4 binary64)))) (*.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (*.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) eps) (-.f64 #s(literal 0 binary64) x)) (*.f64 (/.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (*.f64 (*.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) x)) (/.f64 x (/.f64 eps #s(literal -2 binary64))))
(/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) (*.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (*.f64 x (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (*.f64 x (*.f64 (*.f64 x #s(literal -4 binary64)) eps)) #s(literal -1 binary64)) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 (*.f64 (*.f64 x (/.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 x eps))
(/.f64 (*.f64 (*.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))))) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))
(/.f64 (*.f64 (*.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) (/.f64 eps #s(literal -2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) (*.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) (*.f64 x #s(literal 4 binary64))) (/.f64 eps #s(literal -2 binary64)))
(/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 x eps)))
(/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 #s(literal -1 binary64) eps)) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) #s(literal -2 binary64)) (/.f64 x eps))
(/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) eps)) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 #s(literal 2 binary64) eps)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #s(literal -1 binary64))
(*.f64 x (*.f64 eps #s(literal 2 binary64)))
(*.f64 #s(literal -4 binary64) (/.f64 x (/.f64 #s(literal -2 binary64) eps)))
(*.f64 (*.f64 x #s(literal -4 binary64)) (/.f64 eps #s(literal -2 binary64)))
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))
(*.f64 eps (/.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x #s(literal -4 binary64)) eps))
(*.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 x #s(literal -4 binary64)))
(*.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x (*.f64 x #s(literal -4 binary64))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 4 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal -2 binary64) eps))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 eps #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 eps (*.f64 x (/.f64 x #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) x) #s(literal -1 binary64)))
(*.f64 (*.f64 x x) (/.f64 #s(literal 2 binary64) (/.f64 x eps)))
(*.f64 (*.f64 eps (*.f64 x (/.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 x (*.f64 (*.f64 x #s(literal -4 binary64)) eps)))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps))
(*.f64 (*.f64 x (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (*.f64 (*.f64 x #s(literal -4 binary64)) eps)) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) eps))
(*.f64 (/.f64 #s(literal -1 binary64) x) (*.f64 x (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 (*.f64 x (/.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 eps (/.f64 x #s(literal 1/2 binary64))) (*.f64 x (*.f64 x #s(literal 4 binary64))))
(*.f64 (*.f64 x (*.f64 (*.f64 x #s(literal -4 binary64)) eps)) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (*.f64 x (/.f64 x #s(literal 1/2 binary64))) (/.f64 eps x))
(*.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 x (*.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 x eps)) (*.f64 x x))
(*.f64 (/.f64 x (/.f64 #s(literal -2 binary64) eps)) #s(literal -4 binary64))
(*.f64 (*.f64 eps #s(literal 2 binary64)) x)
(*.f64 (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps) #s(literal -1 binary64))
(*.f64 (/.f64 eps x) (*.f64 x (/.f64 x #s(literal 1/2 binary64))))
(*.f64 (/.f64 x #s(literal 1/2 binary64)) eps)
(*.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))
(*.f64 (*.f64 x #s(literal 4 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -4 binary64) x) (/.f64 (*.f64 x x) (/.f64 #s(literal -2 binary64) eps)))
(*.f64 (/.f64 (*.f64 x x) (/.f64 #s(literal -2 binary64) eps)) (/.f64 #s(literal -4 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 (*.f64 #s(literal -2 binary64) eps) x))
(*.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) eps))
(*.f64 (*.f64 #s(literal -2 binary64) eps) (-.f64 #s(literal 0 binary64) x))
(*.f64 (*.f64 x (*.f64 eps #s(literal 1/2 binary64))) #s(literal 4 binary64))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)) (/.f64 #s(literal -4 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (*.f64 x (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 eps x)))
(*.f64 #s(literal 4 binary64) (*.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) eps)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) #s(literal 1/2 binary64))) eps)
(*.f64 (neg.f64 (neg.f64 (*.f64 (*.f64 x #s(literal -4 binary64)) eps))) #s(literal -1/2 binary64))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) #s(literal -2 binary64)) (/.f64 eps x))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 #s(literal 2 binary64) eps)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) eps))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) #s(literal 1/2 binary64))
(*.f64 (/.f64 (*.f64 x (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x x))
(*.f64 (/.f64 (*.f64 x (*.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 x x))) x)
(*.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x #s(literal -4 binary64)) eps)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) eps))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (/.f64 x eps)) #s(literal 1/2 binary64))
(neg.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 x #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -4 binary64)))))
(/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(*.f64 #s(literal -4 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal -4 binary64)) x)
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -4 binary64))))
(*.f64 (*.f64 x x) #s(literal -4 binary64))
(neg.f64 (*.f64 x #s(literal 4 binary64)))
(/.f64 #s(literal -4 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal -4 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) x))
(/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))
(*.f64 x #s(literal -4 binary64))
(*.f64 #s(literal -4 binary64) x)
(*.f64 (*.f64 x #s(literal -4 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal -4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x (*.f64 x #s(literal -4 binary64))))
(*.f64 (*.f64 x x) (/.f64 #s(literal -4 binary64) x))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal 4 binary64)))
(*.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -4 binary64) x) (*.f64 x x))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x x))
(*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) x)
(+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64)) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 x (/.f64 eps #s(literal -2 binary64))))))
(-.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))
(neg.f64 (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))
(/.f64 eps (/.f64 x #s(literal -1/2 binary64)))
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
(/.f64 (/.f64 eps #s(literal -2 binary64)) x)
(/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps #s(literal -2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -2 binary64) eps))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))
(/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps)))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 2 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 x #s(literal 1/2 binary64)))
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simplify11.0ms (0.2%)

Algorithm
egg-herbie
Rules
50×*-lowering-*.f32
50×*-lowering-*.f64
20×*-commutative
associate-*r*
associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
013372
123372
234372
337372
037372
Stop Event
iter limit
saturated
Counts
84 → 84
Calls
Call 1
Inputs
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 (pow x 2))
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -4 x)
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
Outputs
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 (pow x 2))
(*.f64 x (*.f64 x #s(literal -4 binary64)))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -4 x)
(*.f64 x #s(literal -4 binary64))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))

eval72.0ms (1.2%)

Compiler

Compiled 5614 to 897 computations (84% saved)

prune70.0ms (1.2%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New4171418
Fresh000
Picked101
Done066
Total4187425
Accuracy
100.0%
Counts
425 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.8%
(/.f64 (*.f64 x (/.f64 x #s(literal 1/2 binary64))) (/.f64 x eps))
99.7%
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
70.8%
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
99.8%
(*.f64 x (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
100.0%
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
63.9%
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
71.0%
(*.f64 eps eps)
Compiler

Compiled 160 to 82 computations (48.8% saved)

regimes13.0ms (0.2%)

Counts
11 → 1
Calls
Call 1
Inputs
(*.f64 eps eps)
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
(*.f64 x (*.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 x (/.f64 x #s(literal 1/2 binary64))) (/.f64 x eps))
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (*.f64 x (*.f64 x #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal -4 binary64))) (/.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Outputs
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
Calls

3 calls:

5.0ms
eps
4.0ms
x
3.0ms
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes4.0ms (0.1%)

Counts
3 → 3
Calls
Call 1
Inputs
(*.f64 eps eps)
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
Outputs
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
(*.f64 eps eps)
(*.f64 eps (*.f64 #s(literal 2 binary64) x))
Calls

2 calls:

2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
89.9%3x
87.4%3eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 eps eps)
Outputs
(*.f64 eps eps)
Calls

2 calls:

1.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
71.0%1eps
71.0%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch42.0ms (0.7%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
18.0ms
5.2030855038981945e-124
8.303418710657207e-121
21.0ms
-2.354944505017353e-93
-4.834560060264842e-100
Results
22.0ms160×1valid
8.0ms112×0valid
Compiler

Compiled 254 to 181 computations (28.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-pow: 9.0ms (49.5% of total)
ival-sub: 4.0ms (22% of total)
ival-add: 3.0ms (16.5% of total)
backward-pass: 2.0ms (11% of total)
const: 0.0ms (0% of total)

simplify9.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
if-if-or-not_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01527
12227
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
(if (<=.f64 x #s(literal -5110428660115861/300613450595050653169853516389035139504087366260264943450533244356122755214669880763353471793250393988087676928 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 1162941958872971/1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043212532355867069203257229312 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal 2 binary64) x))))
(*.f64 eps eps)
Outputs
(*.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))
(if (<=.f64 x #s(literal -5110428660115861/300613450595050653169853516389035139504087366260264943450533244356122755214669880763353471793250393988087676928 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 1162941958872971/1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043212532355867069203257229312 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -5110428660115861/300613450595050653169853516389035139504087366260264943450533244356122755214669880763353471793250393988087676928 binary64)) (*.f64 eps (*.f64 x #s(literal 2 binary64))) (if (<=.f64 x #s(literal 1162941958872971/1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043212532355867069203257229312 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 eps eps)

soundness666.0ms (11.2%)

Rules
1988×+-lowering-+.f64
1988×+-lowering-+.f32
1886×fnmsub-define
1856×sum4-define
1748×fmsub-define
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
038288
1128252
2331252
3870252
42492252
56116252
08495252
079
1129
2348
31128
45116
516346
635346
082846
Stop Event
fuel
iter limit
node limit
iter limit
node limit
Compiler

Compiled 86 to 49 computations (43% saved)

preprocess30.0ms (0.5%)

Compiler

Compiled 88 to 42 computations (52.3% saved)

end0.0ms (0%)

Profiling

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