ENA, Section 1.4, Exercise 4d

Time bar (total: 10.1s)

analyze25.0ms (0.2%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%12.8%87.2%0%0%0%0
0%0%12.8%87.2%0%0%0%1
0%0%12.8%87.2%0%0%0%2
50%6.4%6.4%87.2%0%0%0%3
57.1%6.4%4.8%87.2%0%1.6%0%4
69.2%7.2%3.2%87.2%0%2.4%0%5
75%7.2%2.4%87.2%0%3.2%0%6
82.6%7.6%1.6%87.2%0%3.6%0%7
86.4%7.6%1.2%87.2%0%4%0%8
90.7%7.8%0.8%87.2%0%4.2%0%9
92.6%7.8%0.6%87.2%0%4.4%0%10
95%7.9%0.4%87.2%0%4.5%0%11
96.3%8%0.3%87.2%0%4.5%0%12
Compiler

Compiled 25 to 17 computations (32% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-<=: 6.0ms (49.2% of total)
ival-sub: 2.0ms (16.4% of total)
ival-mult: 2.0ms (16.4% of total)
ival-sqrt: 2.0ms (16.4% of total)
ival-and: 1.0ms (8.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.5s (14.9%)

Results
485.0ms2747×1valid
459.0ms4874×0valid
164.0ms635×2valid
15.0ms174×0invalid
Precisions
Click to see histograms. Total time spent on operations: 774.0ms
ival-sub: 182.0ms (23.5% of total)
ival-mult: 180.0ms (23.3% of total)
ival-<=: 161.0ms (20.8% of total)
ival-sqrt: 119.0ms (15.4% of total)
backward-pass: 87.0ms (11.2% of total)
ival-and: 25.0ms (3.2% of total)
const: 19.0ms (2.5% of total)
Bogosity

preprocess62.0ms (0.6%)

Algorithm
egg-herbie
Rules
598×fnmadd-define
520×fmsub-define
502×fnmsub-define
464×sum3-define
432×fmm-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02148
15746
214943
342643
4113043
5206443
6230843
7233243
067
1127
2207
3347
4577
51337
63447
75397
87217
99457
1011097
1111217
011217
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- x (sqrt (- (* x x) eps)))
Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Call 2
Inputs
(- x (sqrt (- (* x x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- x (sqrt (- (* x x) (neg eps))))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- eps (sqrt (- (* eps eps) x)))
Outputs
(- x (sqrt (- (* x x) eps)))
(- x (sqrt (fmsub x x eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- (neg x) (sqrt (fmsub x x eps)))
(- x (sqrt (- (* x x) (neg eps))))
(- x (sqrt (fma x x eps)))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(+ x (sqrt (fmsub x x eps)))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- (sqrt (fma x x eps)) x)
(- eps (sqrt (- (* eps eps) x)))
(- eps (sqrt (fmsub eps eps x)))

explain126.0ms (1.3%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1100-0-(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
00-0-x
00-0-(*.f64 x x)
00-0-(-.f64 (*.f64 x x) eps)
00-0-(sqrt.f64 (-.f64 (*.f64 x x) eps))
00-0-eps
Results
25.0ms166×1valid
21.0ms300×0valid
9.0ms46×2valid
Compiler

Compiled 64 to 20 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-sqrt: 10.0ms (34.5% of total)
ival-sub: 8.0ms (27.6% of total)
ival-mult: 7.0ms (24.2% of total)
backward-pass: 4.0ms (13.8% of total)
const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
60.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

simplify37.0ms (0.4%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff0
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Rules
324×sum3-define
296×fnmadd-define
214×fma-define
184×fma-lowering-fma.f32
184×fma-lowering-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0621
11221
22021
33421
45721
513321
634421
753921
872121
994521
10110921
11112121
0112121
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- x (sqrt (- (* x x) eps)))
x
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps
Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (- (* x x) eps))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps

localize45.0ms (0.4%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(-.f64 (*.f64 x x) eps)
accuracy100.0%
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy60.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
19.0ms150×0valid
11.0ms83×1valid
5.0ms23×2valid
Compiler

Compiled 27 to 7 computations (74.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-sqrt: 4.0ms (28.1% of total)
ival-mult: 4.0ms (28.1% of total)
ival-sub: 4.0ms (28.1% of total)
backward-pass: 2.0ms (14% of total)
const: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts
4 → 84
Calls
Call 1
Inputs
#<alt (- x (sqrt (- (* x x) eps)))>
#<alt (sqrt (- (* x x) eps))>
#<alt (- (* x x) eps)>
#<alt (* x x)>
Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
Calls

21 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(- x (sqrt (- (* x x) eps)))
1.0ms
eps
@inf
(- x (sqrt (- (* x x) eps)))
1.0ms
eps
@0
(- x (sqrt (- (* x x) eps)))
1.0ms
x
@0
(- x (sqrt (- (* x x) eps)))
1.0ms
eps
@-inf
(- x (sqrt (- (* x x) eps)))

rewrite314.0ms (3.1%)

Algorithm
batch-egg-rewrite
Rules
2262×*-lowering-*.f32
2262×*-lowering-*.f64
1852×fma-lowering-fma.f32
1852×fma-lowering-fma.f64
1702×fmsub-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0619
14019
232419
3405519
0821819
Stop Event
iter limit
node limit
Counts
4 → 209
Calls
Call 1
Inputs
(- x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
Outputs
(+.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x)
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x))
(-.f64 (+.f64 x #s(literal 0 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 x (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 x (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) (+.f64 eps (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
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(*.f64 (*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (-.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (-.f64 eps (*.f64 x x)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify279.0ms (2.8%)

Algorithm
egg-herbie
Rules
4906×*-lowering-*.f32
4906×*-lowering-*.f64
2924×+-lowering-+.f64
2924×+-lowering-+.f32
2068×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02571162
18561135
230301098
080341098
Stop Event
iter limit
node limit
Counts
84 → 84
Calls
Call 1
Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) eps)) (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(*.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 5/128 binary64)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (+.f64 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (/.f64 x eps) (-.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x))))) eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (-.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 (sqrt.f64 eps) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) eps)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval37.0ms (0.4%)

Compiler

Compiled 9912 to 1041 computations (89.5% saved)

prune48.0ms (0.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New27716293
Fresh000
Picked011
Done000
Total27717294
Accuracy
99.7%
Counts
294 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.9%
(fma.f64 (*.f64 x x) (/.f64 x (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
60.2%
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
60.4%
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
60.5%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
43.3%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
45.6%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
60.4%
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
3.5%
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
7.0%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
60.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
56.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
27.2%
(-.f64 x (sqrt.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))))
60.8%
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
4.3%
(-.f64 x x)
3.6%
(*.f64 x #s(literal 2 binary64))
30.6%
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
Compiler

Compiled 640 to 308 computations (51.9% saved)

simplify145.0ms (1.4%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff64
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
cost-diff64
(/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
cost-diff128
(neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
cost-diff13888
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
cost-diff0
(*.f64 x x)
cost-diff384
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
cost-diff384
(sqrt.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
cost-diff384
(-.f64 x (sqrt.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))))
cost-diff0
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))
cost-diff256
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
cost-diff512
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))
cost-diff256
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
cost-diff256
(sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))))
cost-diff256
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
Rules
1762×fnmadd-define
1518×*-lowering-*.f32
1518×*-lowering-*.f64
1504×fmsub-define
1380×fmm-def
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
032243
196230
2237215
3792172
43265172
08339172
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
x
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(* eps (+ -1 (/ (* x x) eps)))
eps
(+ -1 (/ (* x x) eps))
-1
(/ (* x x) eps)
(* x x)
(* x 2)
x
2
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
x
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+ 1 (/ (* eps -1/2) (* x x)))
1
(/ (* eps -1/2) (* x x))
(* eps -1/2)
eps
-1/2
(* x x)
(- x (sqrt (* (* x x) (- 1 (/ eps (* x x))))))
x
(sqrt (* (* x x) (- 1 (/ eps (* x x)))))
(* (* x x) (- 1 (/ eps (* x x))))
(* x x)
(- 1 (/ eps (* x x)))
1
(/ eps (* x x))
eps
(+ (* x (/ x (+ x (pow (- (* x x) eps) 1/2)))) (neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))))
x
(/ x (+ x (pow (- (* x x) eps) 1/2)))
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(* x x)
eps
1/2
(neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2))))
(/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
Outputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(* eps (+ -1 (/ (* x x) eps)))
(-.f64 (*.f64 x x) eps)
eps
(+ -1 (/ (* x x) eps))
(+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))
-1
#s(literal -1 binary64)
(/ (* x x) eps)
(/.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
x
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ 1 (/ (* eps -1/2) (* x x)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))
1
#s(literal 1 binary64)
(/ (* eps -1/2) (* x x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
(- x (sqrt (* (* x x) (- 1 (/ eps (* x x))))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (* (* x x) (- 1 (/ eps (* x x)))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(* (* x x) (- 1 (/ eps (* x x))))
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
(- 1 (/ eps (* x x)))
(-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))
1
#s(literal 1 binary64)
(/ eps (* x x))
(/.f64 eps (*.f64 x x))
eps
(+ (* x (/ x (+ x (pow (- (* x x) eps) 1/2)))) (neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
x
(/ x (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 x (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+ x (pow (- (* x x) eps) 1/2))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow (- (* x x) eps) 1/2)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps
1/2
#s(literal 1/2 binary64)
(neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2))))
(/.f64 (-.f64 eps (*.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

localize479.0ms (4.8%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
accuracy99.8%
(/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
accuracy99.6%
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
accuracy99.6%
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
accuracy100.0%
(sqrt.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
accuracy99.6%
(-.f64 x (sqrt.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))))
accuracy81.6%
(/.f64 eps (*.f64 x x))
accuracy66.9%
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
accuracy100.0%
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))
accuracy99.6%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
accuracy85.3%
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
accuracy81.6%
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))))
accuracy100.0%
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
accuracy99.6%
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
accuracy81.2%
(/.f64 (*.f64 x x) eps)
Results
308.0ms106×5exit
50.0ms150×0valid
Compiler

Compiled 260 to 32 computations (87.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 192.0ms
backward-pass: 64.0ms (33.4% of total)
ival-neg: 31.0ms (16.2% of total)
ival-mult: 23.0ms (12% of total)
ival-div: 17.0ms (8.9% of total)
ival-pow: 16.0ms (8.3% of total)
ival-sub: 12.0ms (6.3% of total)
ival-add: 10.0ms (5.2% of total)
ival-sqrt: 9.0ms (4.7% of total)
compiled-spec: 9.0ms (4.7% of total)
const: 1.0ms (0.5% of total)

series62.0ms (0.6%)

Counts
20 → 456
Calls
Call 1
Inputs
#<alt (- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))>
#<alt (sqrt (* eps (+ -1 (/ (* x x) eps))))>
#<alt (* eps (+ -1 (/ (* x x) eps)))>
#<alt (+ -1 (/ (* x x) eps))>
#<alt (* x 2)>
#<alt (- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))>
#<alt (* x (+ 1 (/ (* eps -1/2) (* x x))))>
#<alt (+ 1 (/ (* eps -1/2) (* x x)))>
#<alt (/ (* eps -1/2) (* x x))>
#<alt (- x (sqrt (* (* x x) (- 1 (/ eps (* x x))))))>
#<alt (sqrt (* (* x x) (- 1 (/ eps (* x x)))))>
#<alt (* (* x x) (- 1 (/ eps (* x x))))>
#<alt (* x x)>
#<alt (+ (* x (/ x (+ x (pow (- (* x x) eps) 1/2)))) (neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))))>
#<alt (neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2))))>
#<alt (/ x (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (/ (* x x) eps)>
#<alt (/ eps (* x x))>
#<alt (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))>
Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (pow (sqrt -1) 3))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (pow (sqrt -1) 3)))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt -1>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (/ (pow x 2) eps)>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (/ (pow x 2) eps)>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))>
#<alt (/ (pow x 2) eps)>
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)>
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)>
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)>
#<alt -1>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt -1>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<alt (- (/ (pow x 2) eps) 1)>
#<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 (* 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) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
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#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
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#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
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#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
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#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
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#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (/ 1 (* eps (pow (sqrt -1) 2)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* -1/2 x)>
#<alt (* x (- (+ (* -1/8 (/ eps (pow x 2))) (* 1/2 (/ eps (pow x 2)))) 1/2))>
#<alt (* x (- (+ (* -1/8 (/ eps (pow x 2))) (+ (* -1/16 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) (+ 1/2 (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (- (+ (* -1/8 (/ eps (pow x 2))) (+ (* -1/16 (/ (pow eps 2) (pow x 4))) (+ (* -1/32 (/ (pow eps 3) (pow x 6))) (+ (* -1/128 (/ (pow eps 3) (pow x 6))) (* 1/2 (/ eps (pow x 2))))))) (+ 1/2 (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -2 (/ (pow x 3) eps))>
#<alt (* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (* 5/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))) (+ (* -1/2 (/ eps (pow x 4))) (* 5/2 (/ 1 (pow x 2)))))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 6)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))))))))>
#<alt (* -1/2 x)>
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#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
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#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ x (pow (sqrt -1) 2))))))>
#<alt (- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (+ (* -1/2 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ x (pow (sqrt -1) 2))))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (- (* -1 (* eps x)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (- (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* eps (pow x 3))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (- (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* eps (pow x 3))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (pow eps 2) (pow x 3))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))) eps))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))>
#<alt (* x (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* x (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* x (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2))))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))))>
#<alt (* 2 (/ (pow x 2) eps))>
#<alt (* (pow x 2) (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (+ 1/2 (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 6))) (* 1/16 (/ 1 (pow x 4))))) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))>
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#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 3) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 4)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ x (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 3) (pow (sqrt -1) 3)))) (/ (pow x 2) (pow (sqrt -1) 2))))) eps)>
#<alt (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))>
#<alt (* -1 (/ (+ (* -1 (pow x 2)) (* (sqrt eps) (* x (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 3) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) (* -1 (* eps (pow x 2)))) eps)) (* (sqrt eps) (* x (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1))))))))) (* -1/2 (* eps (pow x 4)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 2)))) eps)) (* (sqrt eps) (* x (sqrt -1)))) eps))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
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#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (* -1 (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))>
#<alt (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (- (+ 1/2 (* -1/2 (/ eps (pow x 2)))) (* -1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))) (pow x 4))) (* -1/2 (/ eps (pow x 2))))) (* -1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))))))) (pow x 6))) (* -1/2 (/ eps (pow x 2))))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* 2 (/ (pow x 3) eps))>
#<alt (* -1 (* (pow x 3) (- (* 5/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 5/8 eps)) (pow x 4))) (* 5/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2)))) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))>
#<alt (* 1/2 x)>
#<alt (+ (* -3/8 (/ eps x)) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))>
#<alt (+ (* 1/2 x) (* eps (- (* eps (- (* -3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))>
#<alt (* -1 (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2))))>
#<alt (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))>
#<alt (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))>
Calls

114 calls:

TimeVariablePointExpression
11.0ms
x
@0
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
5.0ms
eps
@inf
(+ (* x (/ x (+ x (pow (- (* x x) eps) 1/2)))) (neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))))
4.0ms
eps
@inf
(/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
2.0ms
x
@-inf
(- x (sqrt (* (* x x) (- 1 (/ eps (* x x))))))
1.0ms
x
@-inf
(+ (* x (/ x (+ x (pow (- (* x x) eps) 1/2)))) (neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))))

rewrite378.0ms (3.8%)

Algorithm
batch-egg-rewrite
Rules
2814×fma-lowering-fma.f32
2814×fma-lowering-fma.f64
2614×*-lowering-*.f32
2614×*-lowering-*.f64
1934×prod-diff
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032184
1235174
22312146
08889146
Stop Event
iter limit
node limit
Counts
20 → 668
Calls
Call 1
Inputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(* eps (+ -1 (/ (* x x) eps)))
(+ -1 (/ (* x x) eps))
(* x 2)
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+ 1 (/ (* eps -1/2) (* x x)))
(/ (* eps -1/2) (* x x))
(- x (sqrt (* (* x x) (- 1 (/ eps (* x x))))))
(sqrt (* (* x x) (- 1 (/ eps (* x x)))))
(* (* x x) (- 1 (/ eps (* x x))))
(* x x)
(+ (* x (/ x (+ x (pow (- (* x x) eps) 1/2)))) (neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))))
(neg (/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2))))
(/ x (+ x (pow (- (* x x) eps) 1/2)))
(+ x (pow (- (* x x) eps) 1/2))
(/ (* x x) eps)
(/ eps (* x x))
(/ (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
Outputs
(+.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 x (*.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x)
(+.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (+.f64 (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 (*.f64 x x) eps)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) (sqrt.f64 eps) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal 1 binary64) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))))) (fma.f64 (neg.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))) (fma.f64 (neg.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (*.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(+.f64 (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal 1 binary64) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)))))
(+.f64 (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))))) (fma.f64 (neg.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))))
(+.f64 (fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))) (fma.f64 (neg.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (*.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(+.f64 (fma.f64 (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) x (neg.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal 1 binary64) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
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(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (*.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps)) (pow.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) #s(literal 1 binary64)) (*.f64 (+.f64 eps (*.f64 x x)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 eps (*.f64 x x)))
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))
(*.f64 (pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x x))))

simplify365.0ms (3.6%)

Algorithm
egg-herbie
Rules
5572×*-lowering-*.f32
5572×*-lowering-*.f64
4020×+-lowering-+.f64
4020×+-lowering-+.f32
1096×distribute-rgt-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
09596793
134406497
082856497
Stop Event
iter limit
node limit
Counts
456 → 456
Calls
Call 1
Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (pow (sqrt -1) 3))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (pow (sqrt -1) 3)))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 eps)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(/ (pow x 2) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(* 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))
(* 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) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
x
(+ x (* -1/2 (/ eps x)))
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(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
1
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(+ 1 (* -1/2 (/ eps (pow x 2))))
(* -1/2 (/ eps (pow x 2)))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ eps (pow x 2)))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
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(* -1/2 (/ eps (pow x 2)))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
1
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
1
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(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
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(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
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(* (sqrt eps) (sqrt -1))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
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(+ (* -1 eps) (pow x 2))
(pow x 2)
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(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
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(pow x 2)
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(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
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(* -1 eps)
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(pow x 2)
(pow x 2)
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(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
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(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
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(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
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(* x (- (+ (* -1/8 (/ eps (pow x 2))) (+ (* -1/16 (/ (pow eps 2) (pow x 4))) (+ (* -1/32 (/ (pow eps 3) (pow x 6))) (+ (* -1/128 (/ (pow eps 3) (pow x 6))) (* 1/2 (/ eps (pow x 2))))))) (+ 1/2 (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -2 (/ (pow x 3) eps))
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(* -1 (* (pow x 3) (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 6)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))))))))
(* -1/2 x)
(- (* 3/8 (/ eps x)) (* 1/2 x))
(- (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))) (* 1/2 x))
(- (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))) (* 1/2 x))
(* (sqrt eps) (/ 1 (sqrt -1)))
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(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ x (pow (sqrt -1) 2))))))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (+ (* -1/2 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ x (pow (sqrt -1) 2))))))))
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(- (* -1 (/ (- (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* eps (pow x 3))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (- (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* eps (pow x 3))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (pow eps 2) (pow x 3))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))) eps))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))
(* (sqrt (/ 1 eps)) (/ x (sqrt -1)))
(* x (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* x (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* x (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2))))
(- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))))
(* 2 (/ (pow x 2) eps))
(* (pow x 2) (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))))
(+ 1/2 (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 6))) (* 1/16 (/ 1 (pow x 4))))) (* 1/8 (/ 1 (pow x 2))))))
(* (sqrt (/ 1 eps)) (/ x (sqrt -1)))
(/ (+ (* -1 (/ (pow x 2) (pow (sqrt -1) 2))) (* (sqrt eps) (/ x (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 3) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ x (sqrt -1)))) (/ (pow x 2) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 3) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 4)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ x (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 3) (pow (sqrt -1) 3)))) (/ (pow x 2) (pow (sqrt -1) 2))))) eps)
(* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 2)) (* (sqrt eps) (* x (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 3) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) (* -1 (* eps (pow x 2)))) eps)) (* (sqrt eps) (* x (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1))))))))) (* -1/2 (* eps (pow x 4)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 2)))) eps)) (* (sqrt eps) (* x (sqrt -1)))) eps))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(* 1/2 x)
(* x (- (+ 1/2 (* -1/2 (/ eps (pow x 2)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))) (pow x 4))) (* -1/2 (/ eps (pow x 2))))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))))))) (pow x 6))) (* -1/2 (/ eps (pow x 2))))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4)))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 5/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 5/8 eps)) (pow x 4))) (* 5/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2)))) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 1/2 x)
(+ (* -3/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (- (* eps (- (* -3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(* (sqrt eps) (sqrt -1))
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(*.f64 (-.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 5/128 binary64) eps) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (/.f64 x eps) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))))))
(* (sqrt eps) (pow (sqrt -1) 3))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(*.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(*.f64 (-.f64 (/.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(*.f64 (-.f64 (/.f64 (-.f64 x (/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) eps)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))
(* -1 (* (sqrt eps) (pow (sqrt -1) 3)))
(*.f64 (sqrt.f64 eps) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(*.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))
(*.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))
(*.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))) (-.f64 #s(literal 0 binary64) eps))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/8 binary64)))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))
x
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x)
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(* (sqrt eps) (sqrt -1))
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(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* -1 x)
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(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
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(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
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x
(+ x (* -1/2 (/ eps x)))
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(* (sqrt eps) (sqrt -1))
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(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
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(-.f64 #s(literal 0 binary64) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
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(pow x 2)
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(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
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(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
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(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
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(pow x 2)
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(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
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(* -1 eps)
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(* eps (- (/ (pow x 2) eps) 1))
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(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
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(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
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(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
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(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
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(* -1 (* (sqrt eps) (sqrt -1)))
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(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
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(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
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(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (+ (* -1/8 (/ eps (pow x 2))) (* 1/2 (/ eps (pow x 2)))) 1/2))
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(* x (- (+ (* -1/8 (/ eps (pow x 2))) (+ (* -1/16 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) (+ 1/2 (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* -2 (/ (pow x 3) eps))
(*.f64 #s(literal -2 binary64) (/.f64 (*.f64 x (*.f64 x x)) eps))
(* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (* 5/2 (/ 1 (pow x 2))))))
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(* -1/2 x)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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(* (sqrt eps) (sqrt -1))
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
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(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
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(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.f64 eps x)) eps))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (+.f64 (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.f64 eps x))))) (*.f64 eps x)) eps))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) (+.f64 (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.f64 eps x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))))) (*.f64 (sqrt.f64 eps) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (+.f64 (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.f64 eps x)))))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))))) (*.f64 (sqrt.f64 eps) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (+.f64 (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.f64 eps x)))))) eps)) (*.f64 eps x)) eps))

eval186.0ms (1.9%)

Compiler

Compiled 39895 to 3657 computations (90.8% saved)

prune205.0ms (2%)

Pruning

43 alts after pruning (40 fresh and 3 done)

PrunedKeptTotal
New1327331360
Fresh4711
Picked325
Done011
Total1334431377
Accuracy
100.0%
Counts
1377 → 43
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.2%
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
2.4%
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) x)
60.4%
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
60.4%
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
60.4%
(fma.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x)) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
27.0%
(fma.f64 x (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) x)
5.9%
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
60.5%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
6.9%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (-.f64 x (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
26.1%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) (+.f64 x (*.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))))
43.3%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
45.6%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
45.4%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
5.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
60.4%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
6.9%
(-.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
6.9%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
3.6%
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
7.0%
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
5.1%
(-.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 x x) eps)))) x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
5.5%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
7.0%
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
27.0%
(-.f64 x (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) x))
4.7%
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
3.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
3.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
5.0%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps x) (/.f64 x eps))))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
6.1%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
6.1%
(-.f64 x (*.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
7.0%
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
60.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
56.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
4.3%
(-.f64 x x)
99.5%
(+.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
5.9%
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
45.3%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
3.6%
(*.f64 x #s(literal 2 binary64))
40.0%
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
30.6%
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
Compiler

Compiled 1990 to 923 computations (53.6% saved)

simplify185.0ms (1.8%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff0
(*.f64 x x)
cost-diff512
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
cost-diff512
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
cost-diff128
(-.f64 x x)
cost-diff256
(-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
cost-diff256
(*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
cost-diff1664
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
cost-diff0
(*.f64 eps #s(literal 1/8 binary64))
cost-diff0
(/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)))
cost-diff0
(+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
cost-diff128
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
cost-diff128
(-.f64 x x)
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
cost-diff14336
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
cost-diff14464
(+.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
Rules
3956×*-lowering-*.f32
3956×*-lowering-*.f64
1554×+-lowering-+.f64
1554×+-lowering-+.f32
1446×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031240
196227
2240188
3882188
47698188
08134188
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))
(- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))
(/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))
(* x x)
x
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
eps
1/2
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(- x x)
x
(* eps (+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x)))
eps
(+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x))
(/ (* eps 1/8) (* x (* x x)))
(* eps 1/8)
1/8
(* x (* x x))
x
(* x x)
(/ 1/2 x)
1/2
(* (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))
(* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))
(+ (+ x x) (/ (* eps -1/2) x))
(+ x x)
x
(/ (* eps -1/2) x)
(* eps -1/2)
eps
-1/2
(- (- x x) (/ (* eps -1/2) x))
(- x x)
(/ 1 (+ (+ x x) (/ (* eps -1/2) x)))
1
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
(- (* x x) (- (* x x) eps))
(* x x)
x
(- (* x x) eps)
eps
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
1/2
Outputs
(+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))
#s(literal 0 binary64)
(/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(* x x)
(*.f64 x x)
x
(+ x (pow (- (* x x) eps) 1/2))
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(pow (- (* x x) eps) 1/2)
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
1/2
#s(literal 1/2 binary64)
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(- x x)
#s(literal 0 binary64)
x
(* eps (+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x)))
(*.f64 (/.f64 eps x) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))))
eps
(+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x))
(+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(/ (* eps 1/8) (* x (* x x)))
(/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)))
(* eps 1/8)
(*.f64 eps #s(literal 1/8 binary64))
1/8
#s(literal 1/8 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(* (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))
(/.f64 (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(+ (+ x x) (/ (* eps -1/2) x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x x)
(*.f64 x #s(literal 2 binary64))
x
(/ (* 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)
(- (- x x) (/ (* eps -1/2) x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(- x x)
#s(literal 0 binary64)
(/ 1 (+ (+ x x) (/ (* eps -1/2) x)))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
1
#s(literal 1 binary64)
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(- (* x x) (- (* x x) eps))
eps
(* x x)
(*.f64 x x)
x
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
(+ x (pow (- (* x x) eps) 1/2))
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(pow (- (* x x) eps) 1/2)
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize284.0ms (2.8%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
accuracy99.6%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
accuracy61.4%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
accuracy100.0%
(+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
accuracy99.8%
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
accuracy99.5%
(*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
accuracy91.0%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
accuracy100.0%
(+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
accuracy99.8%
(*.f64 x (*.f64 x x))
accuracy87.2%
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
accuracy84.7%
(/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)))
accuracy100.0%
(-.f64 x x)
accuracy100.0%
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
accuracy99.6%
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
accuracy91.5%
(/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
Results
138.0ms164×1valid
28.0ms25×2valid
23.0ms67×0valid
Compiler

Compiled 331 to 32 computations (90.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 118.0ms
ival-pow: 35.0ms (29.6% of total)
ival-mult: 24.0ms (20.3% of total)
ival-div: 21.0ms (17.8% of total)
backward-pass: 15.0ms (12.7% of total)
ival-sub: 11.0ms (9.3% of total)
ival-add: 11.0ms (9.3% of total)
const: 1.0ms (0.8% of total)

series37.0ms (0.4%)

Counts
21 → 456
Calls
Call 1
Inputs
#<alt (+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))>
#<alt (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))>
#<alt (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (* x x)>
#<alt (- x x)>
#<alt (* eps (+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x)))>
#<alt (+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x))>
#<alt (/ (* eps 1/8) (* x (* x x)))>
#<alt (* eps 1/8)>
#<alt (* (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))>
#<alt (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))>
#<alt (- (- x x) (/ (* eps -1/2) x))>
#<alt (/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (- (* x x) (- (* x x) eps))>
#<alt (- (* x x) eps)>
#<alt (/ eps (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (pow (- (* x x) eps) 1/2)>
#<alt (* x (* x x))>
#<alt (/ 1 (+ (+ x x) (/ (* eps -1/2) x)))>
#<alt (+ (+ x x) (/ (* eps -1/2) x))>
Outputs
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))>
#<alt (* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))>
#<alt (* 2 (/ (pow x 3) eps))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/8 (/ eps x)) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))>
#<alt (+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))>
#<alt (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))>
#<alt (/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)>
#<alt (* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))>
#<alt (* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<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 (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
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#<alt eps>
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#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
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#<alt x>
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#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
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#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (pow x 3)>
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#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
Calls

114 calls:

TimeVariablePointExpression
6.0ms
eps
@0
(* eps (+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x)))
3.0ms
eps
@-inf
(/ 1 (+ (+ x x) (/ (* eps -1/2) x)))
2.0ms
eps
@inf
(/ (* eps 1/8) (* x (* x x)))
1.0ms
eps
@0
(* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))
1.0ms
eps
@-inf
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))

rewrite188.0ms (1.9%)

Algorithm
batch-egg-rewrite
Rules
1586×*-lowering-*.f32
1586×*-lowering-*.f64
1416×/-lowering-/.f32
1416×/-lowering-/.f64
626×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
031174
1263139
03218139
Stop Event
iter limit
iter limit
node limit
Counts
21 → 630
Calls
Call 1
Inputs
(+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))
(- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))
(/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))
(* x x)
(- x x)
(* eps (+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x)))
(+ (/ (* eps 1/8) (* x (* x x))) (/ 1/2 x))
(/ (* eps 1/8) (* x (* x x)))
(* eps 1/8)
(* (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))
(* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))
(- (- x x) (/ (* eps -1/2) x))
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
(- (* x x) (- (* x x) eps))
(- (* x x) eps)
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(* x (* x x))
(/ 1 (+ (+ x x) (/ (* eps -1/2) x)))
(+ (+ x x) (/ (* eps -1/2) x))
Outputs
(+.f64 x (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 x (*.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 0 binary64))
(neg.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64)) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64)) (-.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps))) (+.f64 eps #s(literal 0 binary64))) (*.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (+.f64 eps #s(literal 0 binary64))) (*.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (*.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (*.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.f64 x x)) (-.f64 (*.f64 x x) eps))) (*.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.f64 x x)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) eps))) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps))) (+.f64 eps #s(literal 0 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (*.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (+.f64 eps #s(literal 0 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (neg.f64 (+.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (*.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps))) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps))))
(/.f64 (*.f64 (*.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) eps)
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 eps #s(literal 0 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (+.f64 eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 eps #s(literal 0 binary64))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(*.f64 (/.f64 eps (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 eps (+.f64 eps #s(literal 0 binary64))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
#s(literal 0 binary64)
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.f64 x x)) #s(literal -1 binary64))
(*.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
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(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (/.f64 (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(fma.f64 #s(literal 2 binary64) x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (+.f64 (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))))
(/.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (*.f64 #s(literal 0 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 0 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) x) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (-.f64 #s(literal 0 binary64) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 x (*.f64 x (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))) (*.f64 x (+.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (+.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64)))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))) (*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) (neg.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))) (neg.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) #s(literal 3 binary64))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 eps (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (*.f64 eps eps) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1 binary64))
(*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 eps (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))

simplify337.0ms (3.3%)

Algorithm
egg-herbie
Rules
6530×*-lowering-*.f32
6530×*-lowering-*.f64
3452×+-lowering-+.f64
3452×+-lowering-+.f32
1726×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07105438
124525105
081935105
Stop Event
iter limit
node limit
Counts
456 → 456
Calls
Call 1
Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
0
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0
0
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0
0
0
0
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0
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(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 1/2 x)
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
0
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(* 1/2 (/ eps x))
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(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
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eps
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(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
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(* 1/2 (/ eps x))
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(* -1 (* (sqrt eps) (sqrt -1)))
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(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
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(pow x 2)
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(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
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(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
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(* 2 x)
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(* (sqrt eps) (sqrt -1))
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(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
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(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
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(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -2 (/ x eps))
(* x (- (* -8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps))))
(* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 3))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 4))) (* 32 (/ 1 (pow eps 3))))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/32 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/128 (/ (pow eps 3) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4))))) x)
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/32 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(* -1 (/ (- (* -1/128 (/ (pow eps 3) (pow x 6))) (+ 1/2 (+ (* 1/32 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(* -2 (/ x eps))
(/ (+ (* -8 (/ (pow x 3) eps)) (* -2 x)) eps)
(/ (- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps))) eps)
(/ (- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2))))) eps)
(* -2 (/ x eps))
(* -1 (/ (+ (* 2 x) (* 8 (/ (pow x 3) eps))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 128 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(* -1/2 (/ eps x))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64)))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (-.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x))) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (-.f64 (/.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(*.f64 (-.f64 (/.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))) (+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) eps))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x))))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 5/128 binary64) eps) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (*.f64 eps eps))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (*.f64 (sqrt.f64 eps) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) x))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/2 binary64)) (/.f64 x #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (/.f64 (-.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) eps) (*.f64 eps x)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps x) (/.f64 (+.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/2 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x (sqrt.f64 eps)))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)))) eps))) eps) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (/.f64 x eps) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps))))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps))))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/16 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(*.f64 x (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))))
(* 2 (/ (pow x 3) eps))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) eps)
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal -2 binary64) eps))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(*.f64 (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -2 binary64) eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (*.f64 eps eps)) (+.f64 (*.f64 eps (*.f64 #s(literal -1/4 binary64) (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 eps (*.f64 eps #s(literal 1/16 binary64))))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 2 binary64) eps))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (/.f64 eps x) #s(literal 1/8 binary64)))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/8 binary64) x))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
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(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
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(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
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(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
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(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x))) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
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(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
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(* 2 x)
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(* (sqrt eps) (sqrt -1))
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(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
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(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* -1 x)
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(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
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x
(+ x (* -1/2 (/ eps x)))
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(* (sqrt eps) (sqrt -1))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))))))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(* -2 (/ x eps))
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(* x (- (* -8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps))))
(*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -8 binary64) (*.f64 x x)) (*.f64 eps eps)) (/.f64 #s(literal -2 binary64) eps)))
(* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 3))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal -32 binary64) (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal -8 binary64) (*.f64 eps eps)))) (/.f64 #s(literal -2 binary64) eps)))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 4))) (* 32 (/ 1 (pow eps 3))))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal -128 binary64) (*.f64 x x)) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -32 binary64) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal -8 binary64) (*.f64 eps eps)))) (/.f64 #s(literal -2 binary64) eps)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x)
(/ (- (+ 1/2 (* 1/32 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/32 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))))) x)
(/ (- (+ 1/2 (* 1/128 (/ (pow eps 3) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/128 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))))) (/.f64 (*.f64 #s(literal 1/32 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x)
(* -1 (/ (- (* -1/32 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (* -1/128 (/ (pow eps 3) (pow x 6))) (+ 1/2 (+ (* 1/32 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/128 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/32 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))))) (-.f64 #s(literal 0 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))))
(+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/32 binary64)))))
(+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 1/128 binary64) eps) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/32 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* -2 (/ x eps))
(/.f64 (*.f64 x #s(literal -2 binary64)) eps)
(/ (+ (* -8 (/ (pow x 3) eps)) (* -2 x)) eps)
(/.f64 (+.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) eps)) eps)
(/ (- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps))) eps)
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -32 binary64)) (*.f64 eps eps)) (+.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) eps))) eps)
(/ (- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2))))) eps)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal -128 binary64) (pow.f64 x #s(literal 7 binary64))) (*.f64 eps (*.f64 eps eps))) (-.f64 (+.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) eps)) (/.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 32 binary64)) (*.f64 eps eps)))) eps)
(* -2 (/ x eps))
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(* -1 (/ (+ (* 2 x) (* 8 (/ (pow x 3) eps))) eps))
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (/ (+ (* -1 (/ (- (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal -32 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 128 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal 128 binary64) (pow.f64 x #s(literal 7 binary64))) eps) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 32 binary64))) eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(* 2 x)
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(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
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(* 2 x)
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(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
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(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x))) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* 2 x)
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(+ (* -1/2 (/ eps x)) (* 2 x))
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(+ (* -1/2 (/ eps x)) (* 2 x))
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(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))))

eval473.0ms (4.7%)

Compiler

Compiled 59844 to 3446 computations (94.2% saved)

prune225.0ms (2.2%)

Pruning

40 alts after pruning (37 fresh and 3 done)

PrunedKeptTotal
New1724181742
Fresh161935
Picked415
Done123
Total1745401785
Accuracy
100.0%
Counts
1785 → 40
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.4%
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
5.9%
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
5.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
7.4%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
7.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
45.6%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
99.5%
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
45.4%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
5.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
3.6%
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
7.0%
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
5.5%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
7.0%
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
4.7%
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
3.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
3.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
6.1%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
60.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
56.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
23.4%
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 eps (*.f64 x x))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.9%
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
5.8%
(*.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
45.2%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.2%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
44.7%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))
45.3%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))))
46.1%
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
13.4%
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.1%
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
3.6%
(*.f64 x #s(literal 2 binary64))
43.1%
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
46.1%
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
45.4%
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
45.4%
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/2 binary64) x)))
40.0%
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
4.3%
#s(literal 0 binary64)
Compiler

Compiled 1772 to 905 computations (48.9% saved)

simplify178.0ms (1.8%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff256
(-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
cost-diff256
(*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
cost-diff1536
(/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
cost-diff1664
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
cost-diff0
(/.f64 eps (*.f64 x x))
cost-diff0
(*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))
cost-diff0
(*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64)))
cost-diff128
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
cost-diff0
(/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))
cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x)))
cost-diff0
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x)
cost-diff0
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff64
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
cost-diff64
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
cost-diff64
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
Rules
3548×*-lowering-*.f32
3548×*-lowering-*.f64
1798×fnmadd-define
1250×sum5-define
1172×associate-*r*
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
032275
184217
2212208
3930207
46960207
08350207
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
eps
(+ x (pow (- (* x x) eps) 1/2))
x
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(* x x)
1/2
0
(* eps (/ (+ 1/2 (/ (* eps 1/8) (* x x))) x))
eps
(/ (+ 1/2 (/ (* eps 1/8) (* x x))) x)
(+ 1/2 (/ (* eps 1/8) (* x x)))
1/2
(/ (* eps 1/8) (* x x))
(* eps 1/8)
1/8
(* x x)
x
(* (* eps (* (/ eps (* x x)) -1/4)) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))
(* eps (* (/ eps (* x x)) -1/4))
eps
(* (/ eps (* x x)) -1/4)
(/ eps (* x x))
(* x x)
x
-1/4
(/ 1 (+ (+ x x) (/ (* eps -1/2) x)))
1
(+ (+ x x) (/ (* eps -1/2) x))
(+ x x)
(/ (* eps -1/2) x)
(* eps -1/2)
-1/2
(/ 1 (/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))))
1
(/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))))
(+ (+ x x) (/ (* eps -1/2) x))
(+ x x)
x
(/ (* eps -1/2) x)
(* eps -1/2)
eps
-1/2
(* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))
(- (- x x) (/ (* eps -1/2) x))
(- x x)
Outputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
eps
(+ x (pow (- (* x x) eps) 1/2))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(pow (- (* x x) eps) 1/2)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
1/2
#s(literal 1/2 binary64)
0
#s(literal 0 binary64)
(* eps (/ (+ 1/2 (/ (* eps 1/8) (* x x))) x))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps x)) x)) x))
eps
(/ (+ 1/2 (/ (* eps 1/8) (* x x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps x)) x)) x)
(+ 1/2 (/ (* eps 1/8) (* x x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps x)) x))
1/2
#s(literal 1/2 binary64)
(/ (* eps 1/8) (* x x))
(/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps x)) x)
(* eps 1/8)
(*.f64 eps #s(literal 1/8 binary64))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
x
(* (* eps (* (/ eps (* x x)) -1/4)) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))
(/.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 eps eps)) x) x) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(* eps (* (/ eps (* x x)) -1/4))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 eps eps)) x) x)
eps
(* (/ eps (* x x)) -1/4)
(/.f64 (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x) x)
(/ eps (* x x))
(/.f64 (/.f64 eps x) x)
(* x x)
(*.f64 x x)
x
-1/4
#s(literal -1/4 binary64)
(/ 1 (+ (+ x x) (/ (* eps -1/2) x)))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
1
#s(literal 1 binary64)
(+ (+ x x) (/ (* eps -1/2) x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x x)
(*.f64 x #s(literal 2 binary64))
(/ (* eps -1/2) x)
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ 1 (/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))))
(/.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ (+ x x) (/ (* eps -1/2) x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x x)
(*.f64 x #s(literal 2 binary64))
x
(/ (* 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)
(* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(- (- x x) (/ (* eps -1/2) x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(- x x)
#s(literal 0 binary64)

localize140.0ms (1.4%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
accuracy99.5%
(*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
accuracy91.2%
(/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
accuracy99.8%
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
accuracy93.9%
(*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64)))
accuracy88.1%
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
accuracy81.5%
(/.f64 eps (*.f64 x x))
accuracy100.0%
(*.f64 eps #s(literal 1/8 binary64))
accuracy99.9%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x)
accuracy87.2%
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
accuracy81.4%
(/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))
accuracy100.0%
(-.f64 (*.f64 x x) eps)
accuracy100.0%
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
accuracy99.6%
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
Results
93.0ms256×0valid
Compiler

Compiled 288 to 33 computations (88.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-mult: 18.0ms (34.7% of total)
ival-div: 13.0ms (25.1% of total)
ival-add: 8.0ms (15.4% of total)
ival-pow: 8.0ms (15.4% of total)
ival-sub: 4.0ms (7.7% of total)
const: 1.0ms (1.9% of total)
backward-pass: 0.0ms (0% of total)

series22.0ms (0.2%)

Counts
19 → 444
Calls
Call 1
Inputs
#<alt (/ eps (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (pow (- (* x x) eps) 1/2)>
#<alt (- (* x x) eps)>
#<alt (* eps (/ (+ 1/2 (/ (* eps 1/8) (* x x))) x))>
#<alt (/ (+ 1/2 (/ (* eps 1/8) (* x x))) x)>
#<alt (+ 1/2 (/ (* eps 1/8) (* x x)))>
#<alt (/ (* eps 1/8) (* x x))>
#<alt (* (* eps (* (/ eps (* x x)) -1/4)) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))>
#<alt (* eps (* (/ eps (* x x)) -1/4))>
#<alt (* (/ eps (* x x)) -1/4)>
#<alt (/ eps (* x x))>
#<alt (/ 1 (/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))))>
#<alt (/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))))>
#<alt (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))>
#<alt (- (- x x) (/ (* eps -1/2) x))>
#<alt (* eps 1/8)>
#<alt (/ 1 (+ (+ x x) (/ (* eps -1/2) x)))>
#<alt (+ (+ x x) (/ (* eps -1/2) x))>
Outputs
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
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#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
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#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
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#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (* -1/4 (/ eps (pow x 2)))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<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 (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
#<alt eps>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt eps>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<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 (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* 1/8 eps)>
#<alt (* -2 (/ x eps))>
#<alt (* x (- (* -8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps))))>
#<alt (* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 3))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 4))) (* 32 (/ 1 (pow eps 3))))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (* 1/32 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (* 1/128 (/ (pow eps 3) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4))))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/32 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))>
#<alt (* -1 (/ (- (* -1/128 (/ (pow eps 3) (pow x 6))) (+ 1/2 (+ (* 1/32 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))>
#<alt (* -2 (/ x eps))>
#<alt (/ (+ (* -8 (/ (pow x 3) eps)) (* -2 x)) eps)>
#<alt (/ (- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps))) eps)>
#<alt (/ (- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2))))) eps)>
#<alt (* -2 (/ x eps))>
#<alt (* -1 (/ (+ (* 2 x) (* 8 (/ (pow x 3) eps))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 128 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
Calls

111 calls:

TimeVariablePointExpression
2.0ms
x
@0
(/ (+ 1/2 (/ (* eps 1/8) (* x x))) x)
1.0ms
x
@0
(* eps (* (/ eps (* x x)) -1/4))
1.0ms
eps
@0
(* eps (/ (+ 1/2 (/ (* eps 1/8) (* x x))) x))
1.0ms
eps
@0
(* eps (* (/ eps (* x x)) -1/4))
1.0ms
eps
@inf
(* eps (* (/ eps (* x x)) -1/4))

rewrite130.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
1104×*-lowering-*.f32
1104×*-lowering-*.f64
1002×/-lowering-/.f32
1002×/-lowering-/.f64
382×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
031217
1212151
02005151
Stop Event
iter limit
iter limit
node limit
Counts
19 → 401
Calls
Call 1
Inputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(* eps (/ (+ 1/2 (/ (* eps 1/8) (* x x))) x))
(/ (+ 1/2 (/ (* eps 1/8) (* x x))) x)
(+ 1/2 (/ (* eps 1/8) (* x x)))
(/ (* eps 1/8) (* x x))
(* (* eps (* (/ eps (* x x)) -1/4)) (/ 1 (+ (+ x x) (/ (* eps -1/2) x))))
(* eps (* (/ eps (* x x)) -1/4))
(* (/ eps (* x x)) -1/4)
(/ eps (* x x))
(/ 1 (/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))))
(/ (+ (+ x x) (/ (* eps -1/2) x)) (* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x))))
(* (+ (+ x x) (/ (* eps -1/2) x)) (- (- x x) (/ (* eps -1/2) x)))
(- (- x x) (/ (* eps -1/2) x))
(* eps 1/8)
(/ 1 (+ (+ x x) (/ (* eps -1/2) x)))
(+ (+ x x) (/ (* eps -1/2) x))
Outputs
(neg.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) eps)
(*.f64 (/.f64 eps (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (/.f64 eps (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(*.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 eps (*.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (sqrt.f64 (+.f64 eps (*.f64 x x))))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(+.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps))
(+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x x))
(exp.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))) (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 (*.f64 x x) eps)
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 eps (*.f64 x x))))) (/.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 eps (*.f64 x x))))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 eps (*.f64 x x))) (/.f64 (*.f64 eps eps) (+.f64 eps (*.f64 x x))))
(sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(fma.f64 x x (-.f64 #s(literal 0 binary64) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 eps (*.f64 x x)))) (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (*.f64 x x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 eps (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (+.f64 eps (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 eps (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (neg.f64 (+.f64 eps (*.f64 x x))))
(/.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (pow.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps))) (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps)))
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(/.f64 (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) x) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x))
(/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (*.f64 #s(literal 0 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 0 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (+.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64)))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 x (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))))) (*.f64 x (+.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 x x) #s(literal 0 binary64))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64)))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) (neg.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (-.f64 (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (neg.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) #s(literal 3 binary64))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(*.f64 (/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 1 binary64))
(*.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (-.f64 (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))
(*.f64 (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))

simplify339.0ms (3.4%)

Algorithm
egg-herbie
Rules
5176×*-lowering-*.f32
5176×*-lowering-*.f64
2642×+-lowering-+.f64
2642×+-lowering-+.f32
1400×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
06244793
120984645
274234644
083334644
Stop Event
iter limit
node limit
Counts
444 → 444
Calls
Call 1
Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (- (* -1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (* eps (- (* -1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (* eps (- (* eps (- (* -1/512 (/ eps (pow x 9))) (* 1/128 (/ 1 (pow x 7))))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/2 (/ eps x))
(* eps (+ (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (+ (* 8 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x))) (* -2 (/ x eps))))
(* eps (- (+ (* 32 (/ (pow x 5) (pow eps 3))) (* 1/2 (/ 1 x))) (+ (* -8 (/ (pow x 3) (pow eps 2))) (* -2 (/ x eps)))))
(* 1/2 (/ eps x))
(* -1 (* eps (- (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -2 x)) eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps)) (* -2 x)) eps)) (* 1/2 (/ 1 x)))))
(* 1/2 (/ eps x))
(/ (+ (* 1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* 1/2 eps) (* (pow x 2) (+ 2 (* 8 (/ (pow x 2) eps))))) x)
(/ (+ (* 1/2 eps) (* (pow x 2) (+ 2 (* (pow x 2) (+ (* 32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps))))))) x)
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/8 (pow eps 2)) (* -1/32 (/ (pow eps 3) (pow x 2)))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (+ (* -1/32 (/ (pow eps 3) (pow x 2))) (* -1/128 (/ (pow eps 4) (pow x 4))))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (+ (* -1/32 (/ (pow eps 3) (pow x 2))) (+ (* -1/128 (/ (pow eps 4) (pow x 4))) (* -1/512 (/ (pow eps 5) (pow x 6)))))) (pow x 3))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (/ (+ (* 1/32 (/ (pow eps 3) (pow x 2))) (* 1/8 (pow eps 2))) (pow x 3)))
(* -1 (/ (+ (* 1/128 (/ (pow eps 4) (pow x 4))) (+ (* 1/32 (/ (pow eps 3) (pow x 2))) (* 1/8 (pow eps 2)))) (pow x 3)))
(* -1 (/ (+ (* 1/512 (/ (pow eps 5) (pow x 6))) (+ (* 1/128 (/ (pow eps 4) (pow x 4))) (+ (* 1/32 (/ (pow eps 3) (pow x 2))) (* 1/8 (pow eps 2))))) (pow x 3)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(* -1/4 (/ eps (pow x 2)))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(* 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))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
eps
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
eps
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
eps
(* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))
(* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))
(* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* 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))
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* 1/8 eps)
(* -2 (/ x eps))
(* x (- (* -8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps))))
(* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 3))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 4))) (* 32 (/ 1 (pow eps 3))))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/32 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/128 (/ (pow eps 3) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4))))) x)
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/32 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(* -1 (/ (- (* -1/128 (/ (pow eps 3) (pow x 6))) (+ 1/2 (+ (* 1/32 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(* -2 (/ x eps))
(/ (+ (* -8 (/ (pow x 3) eps)) (* -2 x)) eps)
(/ (- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps))) eps)
(/ (- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2))))) eps)
(* -2 (/ x eps))
(* -1 (/ (+ (* 2 x) (* 8 (/ (pow x 3) eps))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 128 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(* -1/2 (/ eps x))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
Outputs
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 x (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps (*.f64 x (*.f64 x x))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (neg.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1 binary64)) #s(literal -1/2 binary64))) x))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps))) (*.f64 eps x)) eps))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(-.f64 (/.f64 (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 eps (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)))))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 eps x)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) x)))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))))))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 4 binary64)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(*.f64 (neg.f64 (+.f64 (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) eps) (+.f64 (*.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64))) #s(literal -1/8 binary64)) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))))) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x)) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal -1/2 binary64) (+.f64 eps (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (/.f64 x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(*.f64 eps (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps))) (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (*.f64 x (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(*.f64 x (+.f64 (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(*.f64 (+.f64 (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (+.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (+.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
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(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* 1/8 eps)
(*.f64 eps #s(literal 1/8 binary64))
(* -2 (/ x eps))
(/.f64 (*.f64 x #s(literal -2 binary64)) eps)
(* x (- (* -8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps))))
(*.f64 x (+.f64 (*.f64 #s(literal -8 binary64) (/.f64 (/.f64 (*.f64 x x) eps) eps)) (/.f64 #s(literal -2 binary64) eps)))
(* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 3))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -32 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal -8 binary64) (*.f64 eps eps)))) (/.f64 #s(literal -2 binary64) eps)))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 4))) (* 32 (/ 1 (pow eps 3))))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps))))
(*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -128 binary64)) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -32 binary64) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal -8 binary64) (*.f64 eps eps))))) (/.f64 #s(literal -2 binary64) eps)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)))) x)
(/ (- (+ 1/2 (* 1/32 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/32 binary64)) (pow.f64 x #s(literal 4 binary64))))) x)
(/ (- (+ 1/2 (* 1/128 (/ (pow eps 3) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/128 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)))) x)
(* -1 (/ (- (* -1/32 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/32 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (* -1/128 (/ (pow eps 3) (pow x 6))) (+ 1/2 (+ (* 1/32 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/128 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/32 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) x))
(+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/32 binary64)) (pow.f64 x #s(literal 5 binary64))))))
(+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 x #s(literal 5 binary64))) (*.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 1/128 binary64)))))))
(* -2 (/ x eps))
(/.f64 (*.f64 x #s(literal -2 binary64)) eps)
(/ (+ (* -8 (/ (pow x 3) eps)) (* -2 x)) eps)
(/.f64 (+.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64)) eps)) eps)
(/ (- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps))) eps)
(/.f64 (+.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) (/.f64 #s(literal -32 binary64) eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) eps)) eps)
(/ (- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2))))) eps)
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -128 binary64)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) eps) (*.f64 (/.f64 #s(literal 32 binary64) eps) (/.f64 (pow.f64 x #s(literal 5 binary64)) eps))))) eps)
(* -2 (/ x eps))
(/.f64 (*.f64 x #s(literal -2 binary64)) eps)
(* -1 (/ (+ (* 2 x) (* 8 (/ (pow x 3) eps))) eps))
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (/ (+ (* -1 (/ (- (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) (/.f64 #s(literal -32 binary64) eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 128 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps)) (* 2 x)) eps))
(/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 128 binary64)) eps) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 32 binary64))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -8 binary64))) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps)))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps)))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps)))

eval145.0ms (1.4%)

Compiler

Compiled 24372 to 2243 computations (90.8% saved)

prune170.0ms (1.7%)

Pruning

43 alts after pruning (39 fresh and 4 done)

PrunedKeptTotal
New94524969
Fresh171532
Picked415
Done033
Total966431009
Accuracy
100.0%
Counts
1009 → 43
Alt Table
Click to see full alt table
StatusAccuracyProgram
26.8%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
11.1%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
45.6%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
46.3%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
45.0%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))
99.5%
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
99.6%
(/.f64 eps (+.f64 x (pow.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) eps)) #s(literal 1/2 binary64))))
46.3%
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
45.9%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
26.8%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
5.1%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x)))
40.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
11.1%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
46.2%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
46.2%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
44.8%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
45.1%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
45.4%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
45.4%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
45.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
25.6%
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
5.5%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
7.0%
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
4.7%
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
3.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
3.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
6.8%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
60.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
56.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
5.2%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
46.1%
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.7%
(*.f64 (*.f64 eps (/.f64 (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
26.0%
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
4.7%
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))))
3.6%
(*.f64 x #s(literal 2 binary64))
46.1%
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
45.4%
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
40.0%
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
5.5%
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)))
4.3%
#s(literal 0 binary64)
Compiler

Compiled 2820 to 831 computations (70.5% saved)

regimes99.0ms (1%)

Counts
92 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (*.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps x) (/.f64 x eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (/.f64 (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))))
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 eps (*.f64 x x))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 x x) eps)))) x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (-.f64 x (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
(-.f64 x (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) x))
(-.f64 x (sqrt.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) (+.f64 x (*.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))))
(/.f64 eps (+.f64 x (pow.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) eps)) #s(literal 1/2 binary64))))
(fma.f64 x (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) x)
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) x)
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x)) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
(fma.f64 (*.f64 x x) (/.f64 x (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
Outputs
(/.f64 eps (+.f64 x (pow.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) eps)) #s(literal 1/2 binary64))))
Calls

3 calls:

29.0ms
eps
28.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
25.0ms
x
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
99.6%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes95.0ms (0.9%)

Counts
82 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (*.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps x) (/.f64 x eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (/.f64 (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))))
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 eps (*.f64 x x))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 x x) eps)))) x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (-.f64 x (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
(-.f64 x (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) x))
(-.f64 x (sqrt.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) (+.f64 x (*.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))))
Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Calls

3 calls:

32.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
28.0ms
x
25.0ms
eps
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes87.0ms (0.9%)

Counts
73 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (*.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps x) (/.f64 x eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (/.f64 (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))))
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 eps (*.f64 x x))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 x x) eps)))) x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (-.f64 x (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))
Calls

3 calls:

33.0ms
eps
24.0ms
x
20.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
89.6%2x
81.4%2eps
99.6%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes33.0ms (0.3%)

Counts
72 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (*.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps x) (/.f64 x eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (/.f64 (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))))
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 eps (*.f64 x x))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 x x) eps)))) x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (-.f64 x (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
Outputs
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

1 calls:

22.0ms
x
Results
AccuracySegmentsBranch
88.5%2x
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes48.0ms (0.5%)

Counts
71 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (*.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 (/.f64 x eps) eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps x) (/.f64 x eps))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 eps (*.f64 x x)) eps)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 eps (/.f64 (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 (*.f64 eps (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64))))))
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 eps (*.f64 x x))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 x x) eps)))) x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) #s(literal -2 binary64)))) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (-.f64 x (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 (-.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
Outputs
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

2 calls:

23.0ms
eps
22.0ms
x
Results
AccuracySegmentsBranch
46.3%1eps
46.3%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes52.0ms (0.5%)

Counts
15 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
Outputs
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
Calls

2 calls:

46.0ms
x
5.0ms
eps
Results
AccuracySegmentsBranch
45.6%1eps
45.6%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
Outputs
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
Calls

2 calls:

2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
45.4%1x
45.4%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes37.0ms (0.4%)

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
Outputs
#s(literal 0 binary64)
Calls

2 calls:

2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
4.3%1x
4.3%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch1.0ms (0%)

Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-1.5409768028887703e-154
0.0
Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch9.0ms (0.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
7.0ms
1.0566475213109775e-111
1.5420353168753938e-111
Results
2.0ms46×0valid
2.0ms18×1valid
1.0ms12×0invalid
Compiler

Compiled 107 to 74 computations (30.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 1.0ms (37% of total)
ival-sub: 1.0ms (37% of total)
ival-sqrt: 1.0ms (37% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
24×+-commutative_binary64
18×*-commutative_binary64
12×sub-neg_binary64
neg-mul-1_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043101
164101
274101
379101
481101
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 eps (+.f64 x (pow.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) eps)) #s(literal 1/2 binary64))))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))))
(if (<=.f64 x #s(literal 8231363154421169/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
#s(literal 0 binary64)
Outputs
(/.f64 eps (+.f64 x (pow.f64 (fma.f64 x x (-.f64 #s(literal 0 binary64) eps)) #s(literal 1/2 binary64))))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))))
(if (<=.f64 x #s(literal 8231363154421169/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
#s(literal 0 binary64)

soundness2.4s (23.6%)

Rules
6530×*-lowering-*.f32
6530×*-lowering-*.f64
5572×*-lowering-*.f32
5572×*-lowering-*.f64
5176×*-lowering-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06244793
120984645
274234644
083334644
031174
1263139
03218139
032184
1235174
22312146
08889146
07105438
124525105
081935105
09596793
134406497
082856497
02571162
18561135
230301098
080341098
031217
1212151
02005151
Stop Event
fuel
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 355 to 204 computations (42.5% saved)

preprocess54.0ms (0.5%)

Compiler

Compiled 254 to 112 computations (55.9% saved)

end0.0ms (0%)

Profiling

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