ENA, Section 1.4, Exercise 4d

Time bar (total: 9.9s)

analyze23.0ms (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: 11.0ms
ival-<=: 4.0ms (36.2% of total)
ival-sub: 2.0ms (18.1% of total)
ival-mult: 2.0ms (18.1% of total)
ival-sqrt: 2.0ms (18.1% of total)
ival-and: 1.0ms (9% of total)
const: 1.0ms (9% of total)
backward-pass: 0.0ms (0% of total)

sample1.4s (14.1%)

Results
467.0ms4793×0valid
407.0ms2783×1valid
161.0ms680×2valid
13.0ms183×0invalid
Precisions
Click to see histograms. Total time spent on operations: 701.0ms
ival-<=: 168.0ms (24% of total)
ival-sub: 159.0ms (22.7% of total)
ival-mult: 144.0ms (20.5% of total)
ival-sqrt: 124.0ms (17.7% of total)
backward-pass: 60.0ms (8.6% of total)
ival-and: 27.0ms (3.9% of total)
const: 18.0ms (2.6% of total)
Bogosity

preprocess63.0ms (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)))

explain127.0ms (1.3%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1070-1(2.8262746450129985e-94 -1.9432281731791863e-189)(-.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
34.0ms34×2valid
23.0ms174×1valid
22.0ms304×0valid
Compiler

Compiled 64 to 20 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-sub: 10.0ms (36.4% of total)
ival-mult: 7.0ms (25.5% of total)
ival-sqrt: 6.0ms (21.8% of total)
backward-pass: 3.0ms (10.9% 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
62.4%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

simplify31.0ms (0.3%)

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

localize40.0ms (0.4%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy100.0%
(-.f64 (*.f64 x x) eps)
accuracy62.4%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
17.0ms87×1valid
11.0ms152×0valid
3.0ms17×2valid
Compiler

Compiled 27 to 7 computations (74.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-sub: 8.0ms (48.4% of total)
ival-sqrt: 3.0ms (18.1% of total)
ival-mult: 3.0ms (18.1% of total)
backward-pass: 2.0ms (12.1% of total)
const: 0.0ms (0% of total)

series9.0ms (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
2.0ms
x
@inf
(sqrt (- (* x x) eps))
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)))

rewrite317.0ms (3.2%)

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)))

simplify291.0ms (3%)

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)

eval54.0ms (0.5%)

Compiler

Compiled 9912 to 1041 computations (89.5% saved)

prune56.0ms (0.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New27815293
Fresh000
Picked011
Done000
Total27816294
Accuracy
99.6%
Counts
294 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(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))))))))
62.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
35.3%
(/.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)
41.6%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
44.0%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
62.2%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
62.0%
(-.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)))))
62.2%
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
4.1%
(-.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)))))))
7.2%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
6.4%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
62.4%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
57.9%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
4.3%
(-.f64 x x)
3.5%
(*.f64 x #s(literal 2 binary64))
22.8%
(*.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)))))))))
Compiler

Compiled 592 to 310 computations (47.6% saved)

simplify162.0ms (1.6%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))
cost-diff0
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
cost-diff0
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))
cost-diff128
(*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))
cost-diff128
(+.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))))))
cost-diff384
(-.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)))))))
cost-diff0
(/.f64 eps x)
cost-diff0
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
cost-diff0
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
cost-diff256
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
cost-diff0
(*.f64 x #s(literal 2 binary64))
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 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
cost-diff320
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
Rules
1832×sum3-define
1590×fmsub-define
1534×fmm-def
1500×+-lowering-+.f64
1500×+-lowering-+.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
030184
179174
2209171
3473170
42184170
57784170
08142170
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ 1 (/ 1 (- x (pow (- (* x x) eps) 1/2))))
1
(/ 1 (- x (pow (- (* x x) eps) 1/2)))
(- x (pow (- (* x x) eps) 1/2))
x
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(* x x)
eps
1/2
(* x 2)
x
2
(- x (+ x (* -1/2 (/ eps x))))
x
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
-1/2
(/ eps x)
eps
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
x
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
eps
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))
(/ -1/2 x)
-1/2
(/ (* eps -1/8) (* x (* x x)))
(* eps -1/8)
-1/8
(* x (* x x))
(* x x)
(- x (/ 1 (sqrt (/ 1 (- (* x x) eps)))))
x
(/ 1 (sqrt (/ 1 (- (* x x) eps))))
1
(sqrt (/ 1 (- (* x x) eps)))
(/ 1 (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps
Outputs
(/ 1 (/ 1 (- x (pow (- (* x x) eps) 1/2))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1
#s(literal 1 binary64)
(/ 1 (- x (pow (- (* x x) eps) 1/2)))
(/.f64 #s(literal 1 binary64) (-.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)))
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)
eps
1/2
#s(literal 1/2 binary64)
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(- x (+ x (* -1/2 (/ eps x))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(* -1/2 (/ eps x))
(*.f64 eps (/.f64 #s(literal -1/2 binary64) x))
-1/2
#s(literal -1/2 binary64)
(/ eps x)
(/.f64 eps x)
eps
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
(/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x))) x)
x
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))
(-.f64 x (/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x))) x))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
(*.f64 (/.f64 eps x) (-.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x)))
eps
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 eps (/.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x) x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(/ (* eps -1/8) (* x (* x x)))
(*.f64 eps (/.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) 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)
(*.f64 x x)
(- x (/ 1 (sqrt (/ 1 (- (* x x) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
x
(/ 1 (sqrt (/ 1 (- (* x x) eps))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (- (* x x) eps)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))
(/ 1 (- (* x x) eps))
(/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps

localize219.0ms (2.2%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))
accuracy99.8%
(/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))
accuracy62.4%
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
accuracy99.8%
(*.f64 x (*.f64 x x))
accuracy91.5%
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
accuracy89.2%
(*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))
accuracy62.5%
(-.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)))))))
accuracy100.0%
(/.f64 eps x)
accuracy100.0%
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
accuracy62.5%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(-.f64 (*.f64 x x) eps)
accuracy99.6%
(/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
accuracy99.3%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
accuracy62.4%
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
Results
76.0ms87×1valid
70.0ms152×0valid
21.0ms17×2valid
Compiler

Compiled 226 to 31 computations (86.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 93.0ms
ival-div: 31.0ms (33.3% of total)
ival-pow: 18.0ms (19.3% of total)
ival-mult: 17.0ms (18.2% of total)
ival-sub: 10.0ms (10.7% of total)
backward-pass: 8.0ms (8.6% of total)
ival-add: 5.0ms (5.4% of total)
ival-sqrt: 3.0ms (3.2% of total)
const: 1.0ms (1.1% of total)

series45.0ms (0.5%)

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

114 calls:

TimeVariablePointExpression
8.0ms
eps
@0
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
6.0ms
x
@-inf
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
2.0ms
x
@-inf
(* x (* x x))
2.0ms
eps
@inf
(/ 1 (- x (pow (- (* x x) eps) 1/2)))
1.0ms
eps
@inf
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))

rewrite346.0ms (3.5%)

Algorithm
batch-egg-rewrite
Rules
2522×*-lowering-*.f32
2522×*-lowering-*.f64
2416×fma-lowering-fma.f32
2416×fma-lowering-fma.f64
1884×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
030147
1223136
22373136
08214136
Stop Event
iter limit
node limit
Counts
20 → 656
Calls
Call 1
Inputs
(/ 1 (/ 1 (- x (pow (- (* x x) eps) 1/2))))
(/ 1 (- x (pow (- (* x x) eps) 1/2)))
(- x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(* x 2)
(- x (+ x (* -1/2 (/ eps x))))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(/ eps x)
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))
(- x (/ 1 (sqrt (/ 1 (- (* x x) eps)))))
(/ 1 (sqrt (/ 1 (- (* x x) eps))))
(sqrt (/ 1 (- (* x x) eps)))
(/ 1 (- (* x x) eps))
(- (* x x) eps)
(/ (* eps -1/8) (* x (* x x)))
(* x (* 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 x #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(-.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal 1 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)))))
(fma.f64 #s(literal 1 binary64) x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) x)
(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)) x)
(neg.f64 (-.f64 #s(literal 0 binary64) (-.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 (*.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 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 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 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 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 (-.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 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 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (-.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x (-.f64 #s(literal 0 binary64) (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 #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)))))))
(/.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 (-.f64 (*.f64 x x) (-.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 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (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 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (-.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.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 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(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))
(pow.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 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.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))))) #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 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 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 #s(literal -1 binary64) (pow.f64 (-.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 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (/.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)))))))
(*.f64 (-.f64 (*.f64 x x) (-.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 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.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)))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) (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 (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (/.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)))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) #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 #s(literal 1 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)))) #s(literal 1 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 #s(literal -1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(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))
(pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (-.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)))) #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 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 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) (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 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.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 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (/.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)))))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) 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 (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (pow.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))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64)) (pow.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(+.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 x #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(-.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal 1 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)))))
(fma.f64 #s(literal 1 binary64) x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) x)
(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)) x)
(neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
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(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) eps) (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x (*.f64 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 (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x x) eps))
(/.f64 (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 (*.f64 x x) eps)))
(/.f64 (-.f64 (*.f64 x (*.f64 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)))
(/.f64 (*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))
(/.f64 (exp.f64 (log.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (exp.f64 (log.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))))))
(/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (exp.f64 (log.f64 (+.f64 (*.f64 x x) eps))))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 x x) eps) (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)))
(*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps)))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 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 (*.f64 x x) eps)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/4 binary64)) #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal -1/8 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(neg.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x)))
(/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) (*.f64 x x)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal -1/8 binary64)))))
(/.f64 (*.f64 eps #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) (*.f64 x x))
(/.f64 (*.f64 (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (*.f64 x (*.f64 x x)))
(/.f64 (neg.f64 (*.f64 eps #s(literal 1/8 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (neg.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x)) (neg.f64 (*.f64 x x)))
(/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) (*.f64 x x))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) (/.f64 x eps))
(/.f64 (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x)
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) x) x)
(pow.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal -1/8 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 eps (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 eps x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal -1/8 binary64) (*.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x (*.f64 x x))))
(*.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (/.f64 eps x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/8 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal -1/8 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1/8 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))) eps)
(*.f64 (/.f64 eps (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) x))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 eps (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x))
(*.f64 (pow.f64 (/.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(*.f64 x (*.f64 x x))
(*.f64 (*.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

simplify407.0ms (4.1%)

Algorithm
egg-herbie
Rules
5764×*-lowering-*.f32
5764×*-lowering-*.f64
2800×+-lowering-+.f64
2800×+-lowering-+.f32
1460×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06566016
122315790
081585790
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))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* 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)))))
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(* 2 (/ x eps))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -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 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))
(* 2 (/ x eps))
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps)
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps)
(* (sqrt (/ 1 eps)) (sqrt -1))
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(* -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)))))))
(* (sqrt (/ 1 eps)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3)))) (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (* eps (pow (sqrt -1) 2)))) (/ 1 (pow eps 4)))) (sqrt -1)))) (* -1/2 (* (sqrt eps) (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (sqrt -1)))))))))
(/ 1 x)
(/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x)
(/ -1 x)
(* -1 (/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x))
(/ 1 x)
(+ (* 1/2 (/ eps (pow x 3))) (/ 1 x))
(+ (* eps (+ (* 3/8 (/ eps (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* eps (+ (* eps (+ (* 5/16 (/ eps (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(* (sqrt (/ 1 eps)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 1/4 (/ (* eps (pow x 4)) (pow (sqrt -1) 2))) (pow x 6)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt (/ 1 eps)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1/4 (* eps (pow x 4))) (pow x 6)))))) (pow eps 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(/ -1 eps)
(- (* -1 (/ (pow x 2) (pow eps 2))) (/ 1 eps))
(- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(/ 1 (pow x 2))
(/ (+ 1 (/ eps (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (/ eps (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2))
(/ 1 (pow x 2))
(+ (/ 1 (pow x 2)) (/ eps (pow x 4)))
(+ (* eps (+ (/ 1 (pow x 4)) (/ eps (pow x 6)))) (/ 1 (pow x 2)))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 6)) (/ eps (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(/ -1 eps)
(/ (- (* -1 (/ (pow x 2) eps)) 1) eps)
(/ (- (* -1 (/ (pow x 4) (pow eps 2))) (+ 1 (/ (pow x 2) eps))) eps)
(/ (- (* -1 (/ (pow x 6) (pow eps 3))) (+ 1 (+ (/ (pow x 2) eps) (/ (pow x 4) (pow eps 2))))) eps)
(/ -1 eps)
(* -1 (/ (+ 1 (/ (pow x 2) eps)) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) eps)) (pow x 2)) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) eps) (* -1 (pow x 4))) eps)) (pow x 2)) eps))) eps))
(* -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)))))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (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)
(pow x 3)
Outputs
(* -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))))
(- (* 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 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.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 (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 eps (/.f64 #s(literal 1/2 binary64) x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) 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 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 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 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64))))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(*.f64 (+.f64 (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(*.f64 (+.f64 (+.f64 (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (/ eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #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 1/8 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 -1 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 x eps) (-.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64))) (-.f64 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x))) (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 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (-.f64 (/.f64 (+.f64 x (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (-.f64 (/.f64 (-.f64 x (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (*.f64 (sqrt.f64 eps) #s(literal 1/2 binary64)))) eps)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))
(-.f64 (/.f64 x eps) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(-.f64 (*.f64 x (-.f64 (*.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)))) (/.f64 #s(literal -1 binary64) eps))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(-.f64 (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (*.f64 x (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (sqrt.f64 #s(literal -1 binary64)))))))) (/.f64 #s(literal -1 binary64) eps))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))
(* 2 (/ x eps))
(/.f64 (*.f64 x #s(literal 2 binary64)) eps)
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(* x (- (+ (* -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)))))))
(*.f64 x (-.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.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 #s(literal -1/4 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) #s(literal -1/16 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (/.f64 eps (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64)))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) 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 eps (/.f64 #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)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #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)))))))
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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)))
(+.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)))))
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(* (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))))
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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 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))))))
(* -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 (*.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 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 (*.f64 x (*.f64 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)) #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)))))))
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(* (sqrt (/ 1 eps)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3)))) (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))))
(+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (*.f64 (sqrt.f64 eps) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal -1/4 binary64) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (* eps (pow (sqrt -1) 2)))) (/ 1 (pow eps 4)))) (sqrt -1)))) (* -1/2 (* (sqrt eps) (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (sqrt -1)))))))))
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(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x)) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x)) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -3/4 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x)
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -3/4 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -3/4 binary64))) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x))) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x))) x)
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x)) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -3/4 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x))
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -3/4 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -3/4 binary64))) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x))) (-.f64 #s(literal 0 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* 1/2 (/ eps (pow x 3))) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) x))
(+ (* eps (+ (* 3/8 (/ eps (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
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(+ (* eps (+ (* eps (+ (* 5/16 (/ eps (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 5/16 binary64)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* (sqrt (/ 1 eps)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal -1/2 binary64) (+.f64 (/.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 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 1/4 (/ (* eps (pow x 4)) (pow (sqrt -1) 2))) (pow x 6)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 #s(literal -1/2 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 (*.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) (+.f64 (/.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 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))))))
(* (sqrt (/ 1 eps)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+.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 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1/4 (* eps (pow x 4))) (pow x 6)))))) (pow eps 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+.f64 (+.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 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)))) (/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 eps (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal -1/4 binary64))))))) (*.f64 eps (*.f64 eps eps))))
(/ -1 eps)
(/.f64 #s(literal -1 binary64) eps)
(- (* -1 (/ (pow x 2) (pow eps 2))) (/ 1 eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)) (-.f64 #s(literal 0 binary64) eps))
(- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))) (/.f64 #s(literal -1 binary64) eps))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (/.f64 x (pow.f64 eps #s(literal 4 binary64))))) (/.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))) (/.f64 #s(literal -1 binary64) eps))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ eps (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) (*.f64 x x))
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 eps (*.f64 x x))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ eps (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) (*.f64 x x))
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 eps (*.f64 x x))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(+ (/ 1 (pow x 2)) (/ eps (pow x 4)))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 eps (*.f64 x (*.f64 x (*.f64 x x)))))
(+ (* eps (+ (/ 1 (pow x 4)) (/ eps (pow x 6)))) (/ 1 (pow x 2)))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 eps (pow.f64 x #s(literal 6 binary64))))))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 6)) (/ eps (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 eps (pow.f64 x #s(literal 8 binary64))))))))
(/ -1 eps)
(/.f64 #s(literal -1 binary64) eps)
(/ (- (* -1 (/ (pow x 2) eps)) 1) eps)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)) (-.f64 #s(literal 0 binary64) eps))
(/ (- (* -1 (/ (pow x 4) (pow eps 2))) (+ 1 (/ (pow x 2) eps))) eps)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 x x)) eps) #s(literal 1 binary64)) eps)
(/ (- (* -1 (/ (pow x 6) (pow eps 3))) (+ 1 (+ (/ (pow x 2) eps) (/ (pow x 4) (pow eps 2))))) eps)
(/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))) (-.f64 (/.f64 (-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 x x)) eps) #s(literal 1 binary64))) eps)
(/ -1 eps)
(/.f64 #s(literal -1 binary64) eps)
(* -1 (/ (+ 1 (/ (pow x 2) eps)) eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) eps)) (pow x 2)) eps))) eps))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 x x)) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) eps) (* -1 (pow x 4))) eps)) (pow x 2)) eps))) eps))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 6 binary64)) eps)) eps)) (*.f64 x x)) eps)) (-.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)
(-.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 (-.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)))
(* -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)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x 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))
(pow x 3)
(*.f64 x (*.f64 x x))

eval190.0ms (1.9%)

Compiler

Compiled 27954 to 3320 computations (88.1% saved)

prune151.0ms (1.5%)

Pruning

28 alts after pruning (25 fresh and 3 done)

PrunedKeptTotal
New1182171199
Fresh2810
Picked325
Done011
Total1187281215
Accuracy
100.0%
Counts
1215 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(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))))))))
62.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
15.5%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
41.6%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
35.9%
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
43.5%
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
44.0%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
44.4%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
43.1%
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
30.3%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.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)))) eps))
43.6%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
62.2%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
43.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
43.9%
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
62.0%
(-.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)))))
7.2%
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
5.3%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
57.6%
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
7.2%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
6.4%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
6.4%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
62.4%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
57.9%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
4.3%
(-.f64 x x)
35.9%
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
43.4%
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
3.5%
(*.f64 x #s(literal 2 binary64))
43.8%
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 1070 to 535 computations (50% saved)

simplify226.0ms (2.3%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 0 binary64) eps)
cost-diff0
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
cost-diff0
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
cost-diff0
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))
cost-diff128
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
cost-diff128
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)))
cost-diff768
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
cost-diff0
(*.f64 x x)
cost-diff0
(+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))
cost-diff0
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)
cost-diff0
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
cost-diff128
(-.f64 x x)
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff0
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
Rules
4012×*-lowering-*.f32
4012×*-lowering-*.f64
2374×fma-lowering-fma.f32
2374×fma-lowering-fma.f64
2074×/-lowering-/.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
028149
170147
2187145
3650142
43162139
57215139
08143139
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))
1
(/ 1 (- x (sqrt (- (* x x) eps))))
(- x (sqrt (- (* x x) eps)))
x
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps
(- x x)
x
(- x (/ (+ (* x x) (* eps -1/2)) x))
x
(/ (+ (* x x) (* eps -1/2)) x)
(+ (* x x) (* eps -1/2))
(* x x)
(* eps -1/2)
eps
-1/2
(/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps))))
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
0
(* (/ 1/4 (* x x)) (* eps eps))
(/ 1/4 (* x x))
1/4
(* x x)
x
(* eps eps)
eps
(+ 0 (/ -1/2 (/ x eps)))
(/ -1/2 (/ x eps))
-1/2
(/ x eps)
(- x (sqrt (- 0 eps)))
x
(sqrt (- 0 eps))
(- 0 eps)
0
eps
Outputs
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1
#s(literal 1 binary64)
(/ 1 (- x (sqrt (- (* x x) eps))))
(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(- 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
(- x x)
#s(literal 0 binary64)
x
(- x (/ (+ (* x x) (* eps -1/2)) x))
(+.f64 x (/.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)) x))
x
(/ (+ (* x x) (* eps -1/2)) x)
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)
(+ (* x x) (* eps -1/2))
(+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))
(* x x)
(*.f64 x x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)
(/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps))))
(*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps #s(literal 1/2 binary64)) x))
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x)
0
#s(literal 0 binary64)
(* (/ 1/4 (* x x)) (* eps eps))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x))
(/ 1/4 (* x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
x
(* eps eps)
(*.f64 eps eps)
eps
(+ 0 (/ -1/2 (/ x eps)))
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
(/ -1/2 (/ x eps))
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
-1/2
#s(literal -1/2 binary64)
(/ x eps)
(/.f64 x eps)
(- x (sqrt (- 0 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
x
(sqrt (- 0 eps))
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
(- 0 eps)
(-.f64 #s(literal 0 binary64) eps)
0
#s(literal 0 binary64)
eps

localize150.0ms (1.5%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(-.f64 #s(literal 0 binary64) eps)
accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
accuracy100.0%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
accuracy99.8%
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
accuracy99.3%
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
accuracy82.6%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
accuracy62.1%
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))
accuracy100.0%
(*.f64 eps #s(literal -1/2 binary64))
accuracy100.0%
(+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))
accuracy99.9%
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)
accuracy80.6%
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
accuracy100.0%
(-.f64 x x)
accuracy100.0%
(-.f64 (*.f64 x x) eps)
accuracy99.7%
(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy99.4%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
accuracy80.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
60.0ms150×0valid
24.0ms44×1valid
13.0ms52×0invalid
8.0ms10×2valid
Compiler

Compiled 176 to 29 computations (83.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-sub: 29.0ms (44.3% of total)
ival-div: 14.0ms (21.4% of total)
ival-mult: 10.0ms (15.3% of total)
ival-sqrt: 5.0ms (7.6% of total)
backward-pass: 4.0ms (6.1% of total)
ival-add: 3.0ms (4.6% of total)
const: 1.0ms (1.5% of total)

series17.0ms (0.2%)

Counts
20 → 408
Calls
Call 1
Inputs
#<alt (/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))>
#<alt (/ 1 (- x (sqrt (- (* x x) eps))))>
#<alt (- x (sqrt (- (* x x) eps)))>
#<alt (sqrt (- (* x x) eps))>
#<alt (- x x)>
#<alt (- x (/ (+ (* x x) (* eps -1/2)) x))>
#<alt (/ (+ (* x x) (* eps -1/2)) x)>
#<alt (+ (* x x) (* eps -1/2))>
#<alt (* x x)>
#<alt (/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps))))>
#<alt (- 0 (* (/ 1/4 (* x x)) (* eps eps)))>
#<alt (+ 0 (/ -1/2 (/ x eps)))>
#<alt (* (/ 1/4 (* x x)) (* eps eps))>
#<alt (- x (sqrt (- 0 eps)))>
#<alt (sqrt (- 0 eps))>
#<alt (- 0 eps)>
#<alt (- (* x x) eps)>
#<alt (* eps -1/2)>
#<alt (/ -1/2 (/ x eps))>
#<alt (/ 1/4 (* 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))) (* 1/2 (/ eps (pow x 2)))) 2)))>
#<alt (* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))>
#<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 (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))>
#<alt (* 2 (/ x eps))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ (* -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 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))>
#<alt (* 2 (/ x eps))>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)>
#<alt (/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps)>
#<alt (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))>
#<alt (/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)>
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps)>
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps)>
#<alt (* (sqrt (/ 1 eps)) (sqrt -1))>
#<alt (* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps))>
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (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 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps))>
#<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 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 (* 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 (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (pow x 2))>
#<alt (+ (* -1/2 eps) (pow x 2))>
#<alt (+ (* -1/2 eps) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (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)>
#<alt (* eps (- (/ (pow x 2) eps) 1/2))>
#<alt (* eps (- (/ (pow x 2) eps) 1/2))>
#<alt (* eps (- (/ (pow x 2) eps) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* -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)>
#<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) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (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 (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt x>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt x>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (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 eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -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 (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<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 x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
Calls

102 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(- x (/ (+ (* x x) (* eps -1/2)) x))
1.0ms
eps
@0
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
1.0ms
x
@0
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
1.0ms
eps
@inf
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
0.0ms
eps
@0
(- x (sqrt (- 0 eps)))

rewrite384.0ms (3.9%)

Algorithm
batch-egg-rewrite
Rules
3046×/-lowering-/.f32
3046×/-lowering-/.f64
2802×*-lowering-*.f32
2802×*-lowering-*.f64
1600×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
028123
1218120
22097109
09748109
Stop Event
iter limit
node limit
Counts
20 → 816
Calls
Call 1
Inputs
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))
(/ 1 (- x (sqrt (- (* x x) eps))))
(- x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- x x)
(- x (/ (+ (* x x) (* eps -1/2)) x))
(/ (+ (* x x) (* eps -1/2)) x)
(+ (* x x) (* eps -1/2))
(* x x)
(/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps))))
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
(+ 0 (/ -1/2 (/ x eps)))
(* (/ 1/4 (* x x)) (* eps eps))
(- x (sqrt (- 0 eps)))
(sqrt (- 0 eps))
(- 0 eps)
(- (* x x) eps)
(* eps -1/2)
(/ -1/2 (/ x eps))
(/ 1/4 (* x x))
Outputs
(+.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) x)
(+.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps)))))
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))
(exp.f64 (*.f64 (log.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)))
(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))) #s(literal -1 binary64)))
(-.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) (/.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 (sqrt.f64 (+.f64 (*.f64 x x) eps)))))))
(-.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)))))
(-.f64 (/.f64 (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) #s(literal 1 binary64)) (/.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 (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) #s(literal 1 binary64)))
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(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))))
(*.f64 (+.f64 x (sqrt.f64 eps)) (-.f64 x (sqrt.f64 eps)))
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(*.f64 eps #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) eps)
(+.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(+.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(fma.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) #s(literal 0 binary64))
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(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps #s(literal 0 binary64))
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(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
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(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))))
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(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
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(/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (neg.f64 (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
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(/.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 (/.f64 #s(literal 1 binary64) eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(pow.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(*.f64 eps (/.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
(*.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 eps x)))
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(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
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(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
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(*.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) eps)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
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(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/.f64 #s(literal 1/4 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
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(/.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
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(/.f64 (/.f64 #s(literal 1/4 binary64) x) x)
(/.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(pow.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/4 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1 binary64) x))

simplify392.0ms (4%)

Algorithm
egg-herbie
Rules
4134×*-lowering-*.f32
4134×*-lowering-*.f64
2200×+-lowering-+.f64
2200×+-lowering-+.f32
1694×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04453907
115153762
256233712
080283712
Stop Event
iter limit
node limit
Counts
408 → 408
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))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* 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)))))
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(* 2 (/ x eps))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -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 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))
(* 2 (/ x eps))
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps)
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps)
(* (sqrt (/ 1 eps)) (sqrt -1))
(* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (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 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps))
(* -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)))))))
0
0
0
0
0
0
0
0
0
0
0
0
(* 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)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -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)))))
(* -1/2 eps)
(+ (* -1/2 eps) (pow x 2))
(+ (* -1/2 eps) (pow x 2))
(+ (* -1/2 eps) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1/2 eps) (pow x 2))
(+ (* -1/2 eps) (pow x 2))
(+ (* -1/2 eps) (pow x 2))
(* -1/2 eps)
(* eps (- (/ (pow x 2) eps) 1/2))
(* eps (- (/ (pow x 2) eps) 1/2))
(* eps (- (/ (pow x 2) eps) 1/2))
(* -1/2 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) 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)
(* 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))
(* -1/4 (/ (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)))
(* -1/2 (/ 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))
(* 1/4 (/ (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 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -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)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 (/ eps 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))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
Outputs
(* -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))))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (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 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.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 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.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)
(-.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 #s(literal 0 binary64) (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))

eval186.0ms (1.9%)

Compiler

Compiled 27639 to 3043 computations (89% saved)

prune210.0ms (2.1%)

Pruning

33 alts after pruning (29 fresh and 4 done)

PrunedKeptTotal
New1254101264
Fresh11920
Picked325
Done123
Total1259331292
Accuracy
100.0%
Counts
1292 → 33
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(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))))))))
62.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
16.5%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
15.5%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
41.6%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
35.9%
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
43.5%
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
26.2%
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
44.0%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
44.4%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
43.1%
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
30.3%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.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)))) eps))
43.6%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps))
62.2%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
43.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
43.9%
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
62.0%
(-.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)))))
4.1%
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x))
3.5%
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))))
7.2%
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
5.3%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
57.6%
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
7.2%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
6.4%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
6.4%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
62.4%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
57.9%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
35.9%
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
43.4%
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
43.8%
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
42.9%
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
3.5%
x
4.3%
#s(literal 0 binary64)
Compiler

Compiled 1334 to 674 computations (49.5% saved)

simplify236.0ms (2.4%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
cost-diff128
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
cost-diff128
(*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
cost-diff2944
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
cost-diff0
(/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)
cost-diff128
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
cost-diff128
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x))
cost-diff512
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
cost-diff0
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
cost-diff128
(/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x))
cost-diff128
(*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)
cost-diff192
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
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))))
Rules
5144×*-lowering-*.f32
5144×*-lowering-*.f64
3700×+-lowering-+.f64
3700×+-lowering-+.f32
1782×times-frac
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033373
198329
2335233
31636229
08436229
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ (- (* 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
0
(neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps))
(* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)
(/ (/ 1/4 (* x x)) (/ -1/2 x))
(/ 1/4 (* x x))
1/4
(* x x)
x
(/ -1/2 x)
-1/2
eps
(/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps))))
(- 0 (/ (* (/ 1/4 x) (* eps eps)) x))
0
(/ (* (/ 1/4 x) (* eps eps)) x)
(* (/ 1/4 x) (* eps eps))
(/ 1/4 x)
1/4
x
(* eps eps)
eps
(+ 0 (/ -1/2 (/ x eps)))
(/ -1/2 (/ x eps))
-1/2
(/ x eps)
(/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))))
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps))))
(+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))
(* x x)
x
(* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))
(+ x (/ -1/2 (/ x eps)))
(/ -1/2 (/ x eps))
-1/2
(/ x eps)
eps
(+ x (+ x (/ -1/2 (/ x eps))))
(- 0 (/ -1/2 (/ x eps)))
0
Outputs
(/ (- (* 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)
0
#s(literal 0 binary64)
(neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps))
(*.f64 x (*.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) x)))
(/ (/ 1/4 (* x x)) (/ -1/2 x))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x x))
(/ 1/4 (* x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
x
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
eps
(/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps))))
(*.f64 (*.f64 x (*.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) #s(literal 1 binary64))
(- 0 (/ (* (/ 1/4 x) (* eps eps)) x))
(*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps (/.f64 eps x)) x))
0
#s(literal 0 binary64)
(/ (* (/ 1/4 x) (* eps eps)) x)
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps (/.f64 eps x))) x)
(* (/ 1/4 x) (* eps eps))
(*.f64 #s(literal 1/4 binary64) (*.f64 eps (/.f64 eps x)))
(/ 1/4 x)
(/.f64 #s(literal 1/4 binary64) x)
1/4
#s(literal 1/4 binary64)
x
(* eps eps)
(*.f64 eps eps)
eps
(+ 0 (/ -1/2 (/ x eps)))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ -1/2 (/ x eps))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
-1/2
#s(literal -1/2 binary64)
(/ x eps)
(/.f64 x eps)
(/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))
(+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64)))))
(* x x)
(*.f64 x x)
x
(* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))
(*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64))))
(+ x (/ -1/2 (/ x eps)))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/ -1/2 (/ x eps))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
-1/2
#s(literal -1/2 binary64)
(/ x eps)
(/.f64 x eps)
eps
(+ x (+ x (/ -1/2 (/ x eps))))
(+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64)))
(- 0 (/ -1/2 (/ x eps)))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
0
#s(literal 0 binary64)

localize230.0ms (2.3%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy99.6%
(*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
accuracy99.6%
(*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
accuracy99.3%
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
accuracy74.0%
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
accuracy99.3%
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
accuracy87.2%
(/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)
accuracy83.8%
(*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps))
accuracy74.7%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
accuracy100.0%
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
accuracy99.7%
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
accuracy99.6%
(*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)
accuracy63.4%
(/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x))
accuracy100.0%
(-.f64 (*.f64 x x) eps)
accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
accuracy99.5%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
accuracy62.9%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
Results
77.0ms86×1valid
61.0ms153×0valid
26.0ms17×2valid
Compiler

Compiled 334 to 34 computations (89.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 105.0ms
ival-div: 26.0ms (24.8% of total)
ival-pow: 25.0ms (23.8% of total)
ival-mult: 16.0ms (15.3% of total)
ival-add: 14.0ms (13.3% of total)
ival-sub: 13.0ms (12.4% of total)
backward-pass: 8.0ms (7.6% of total)
ival-neg: 2.0ms (1.9% of total)
const: 1.0ms (1% of total)

series39.0ms (0.4%)

Counts
20 → 444
Calls
Call 1
Inputs
#<alt (/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (- (* x x) (- (* x x) eps))>
#<alt (* x x)>
#<alt (- (* x x) eps)>
#<alt (neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps))>
#<alt (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)>
#<alt (/ (/ 1/4 (* x x)) (/ -1/2 x))>
#<alt (/ 1/4 (* x x))>
#<alt (/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps))))>
#<alt (- 0 (/ (* (/ 1/4 x) (* eps eps)) x))>
#<alt (+ 0 (/ -1/2 (/ x eps)))>
#<alt (/ (* (/ 1/4 x) (* eps eps)) x)>
#<alt (/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))))>
#<alt (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps))))>
#<alt (- 0 (/ -1/2 (/ x eps)))>
#<alt (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (* (/ 1/4 x) (* eps eps))>
#<alt (/ -1/2 (/ x eps))>
#<alt (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))>
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 (* -1 (* (sqrt eps) (sqrt -1))))>
#<alt (+ (* -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)))>
#<alt (+ (* -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)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt 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 (* -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 (* 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 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 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (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 (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/4 (/ (pow eps 2) (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 (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (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 (/ (pow eps 3) (pow x 3)))>
#<alt (/ (+ (* 1/8 (pow eps 3)) (* 1/2 (* eps (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3))>
#<alt (* 3/2 (* eps x))>
#<alt (* x (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps)))>
#<alt (* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps))))>
#<alt (* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps))))>
#<alt (* 3/2 (* eps x))>
#<alt (* -1 (* x (+ (* -3/2 eps) (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))))))>
#<alt (* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4)))))))>
#<alt (* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4)))))))>
#<alt (* 1/2 (/ (* eps (+ (* 2 (pow x 2)) (pow x 2))) x))>
#<alt (* eps (+ (* -3/4 (/ eps x)) (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x))))>
#<alt (* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x))))))>
#<alt (* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x))))))>
#<alt (* 1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* (pow eps 3) (- (* 1/8 (/ 1 (pow x 3))) (* 3/4 (/ 1 (* eps x)))))>
#<alt (* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x))))>
#<alt (* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x))))>
#<alt (* 1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1 (* (pow eps 3) (- (* 3/4 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))>
#<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)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2))>
#<alt (* 3 (pow x 2))>
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))>
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* 3 (pow x 2))>
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))>
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (+ (* 2 (pow x 2)) (pow x 2))>
#<alt (+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2)))>
#<alt (+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2)))>
#<alt (+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps))))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<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 (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 2) x))>
#<alt (* 1/4 (/ (pow eps 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 (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))>
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))>
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* 2 (pow x 2))>
#<alt (+ (* -3/2 eps) (* 2 (pow x 2)))>
#<alt (+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))>
#<alt (+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))>
Calls

111 calls:

TimeVariablePointExpression
15.0ms
x
@inf
(+ x (pow (- (* x x) eps) 1/2))
6.0ms
eps
@inf
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
1.0ms
x
@0
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
1.0ms
eps
@0
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps))))
1.0ms
x
@0
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps))))

rewrite442.0ms (4.5%)

Algorithm
batch-egg-rewrite
Rules
4286×*-lowering-*.f32
4286×*-lowering-*.f64
3058×/-lowering-/.f32
3058×/-lowering-/.f64
1938×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033261
1259230
22840198
09781198
Stop Event
iter limit
node limit
Counts
20 → 878
Calls
Call 1
Inputs
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
(- (* x x) (- (* x x) eps))
(* x x)
(- (* x x) eps)
(neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps))
(* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)
(/ (/ 1/4 (* x x)) (/ -1/2 x))
(/ 1/4 (* x x))
(/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps))))
(- 0 (/ (* (/ 1/4 x) (* eps eps)) x))
(+ 0 (/ -1/2 (/ x eps)))
(/ (* (/ 1/4 x) (* eps eps)) x)
(/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))))
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps))))
(- 0 (/ -1/2 (/ x eps)))
(+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))
(+ x (pow (- (* x x) eps) 1/2))
(* (/ 1/4 x) (* eps eps))
(/ -1/2 (/ x eps))
(* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))
Outputs
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.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 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
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(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))
(*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))

simplify305.0ms (3.1%)

Algorithm
egg-herbie
Rules
5924×*-lowering-*.f32
5924×*-lowering-*.f64
2130×+-lowering-+.f64
2130×+-lowering-+.f32
1744×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04613973
115773840
258443798
087713798
Stop Event
iter limit
node limit
Counts
444 → 444
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 (* -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)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
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)
(* -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))
(* 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 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 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (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))
(* -1/4 (/ (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)))
(* -1/2 (/ 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))
(* 1/4 (/ (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)))
(* 1/2 (/ 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 (/ (pow eps 3) (pow x 3)))
(/ (+ (* 1/8 (pow eps 3)) (* 1/2 (* eps (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))))) (pow x 3))
(/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3))
(/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3))
(* 3/2 (* eps x))
(* x (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps)))
(* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps))))
(* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps))))
(* 3/2 (* eps x))
(* -1 (* x (+ (* -3/2 eps) (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))))))
(* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4)))))))
(* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4)))))))
(* 1/2 (/ (* eps (+ (* 2 (pow x 2)) (pow x 2))) x))
(* eps (+ (* -3/4 (/ eps x)) (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x))))
(* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x))))))
(* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x))))))
(* 1/8 (/ (pow eps 3) (pow x 3)))
(* (pow eps 3) (- (* 1/8 (/ 1 (pow x 3))) (* 3/4 (/ 1 (* eps x)))))
(* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x))))
(* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x))))
(* 1/8 (/ (pow eps 3) (pow x 3)))
(* -1 (* (pow eps 3) (- (* 3/4 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))
(* 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))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* 3 (pow x 2))
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(+ (* 2 (pow x 2)) (pow x 2))
(+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2)))
(+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (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)))))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 2) x))
(* 1/4 (/ (pow eps 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))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* 2 (pow x 2))
(+ (* -3/2 eps) (* 2 (pow x 2)))
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))
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 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #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 #s(literal 1 binary64) (*.f64 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 (/.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 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (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 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 (*.f64 (*.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 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 (*.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))))) 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)) (neg.f64 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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(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(* 2 (pow x 2))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(+ (* -3/2 eps) (* 2 (pow x 2)))
(+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -3/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal 1/4 binary64)) x))))
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -3/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal 1/4 binary64)) x))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -3/2 binary64) eps)))
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 x x) eps) eps)) (/.f64 #s(literal -3/2 binary64) eps))))
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 x x) eps) eps)) (/.f64 #s(literal -3/2 binary64) eps))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -3/2 binary64) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 x x) eps))) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 x x) eps))) eps)))

eval569.0ms (5.8%)

Compiler

Compiled 96830 to 4642 computations (95.2% saved)

prune290.0ms (2.9%)

Pruning

49 alts after pruning (44 fresh and 5 done)

PrunedKeptTotal
New2106332139
Fresh131124
Picked325
Done134
Total2123492172
Accuracy
100.0%
Counts
2172 → 49
Alt Table
Click to see full alt table
StatusAccuracyProgram
18.9%
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) eps)
3.5%
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
7.5%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
7.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
18.8%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
16.5%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
16.5%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
27.1%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
41.6%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
28.7%
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))))
35.9%
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
36.1%
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
36.1%
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
26.2%
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
34.5%
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
35.1%
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
42.7%
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
36.5%
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
44.0%
(/.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))))
25.8%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))
44.4%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
43.1%
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
43.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
43.9%
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
43.6%
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
3.5%
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))))
7.2%
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
5.3%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
57.6%
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
7.2%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
62.4%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
57.9%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
6.3%
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
6.7%
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
33.4%
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))
43.8%
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
25.8%
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))
43.8%
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)))
25.8%
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))
43.0%
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps))
42.9%
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps))
42.9%
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps))
42.9%
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
42.7%
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x))
35.0%
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps)))
25.7%
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
3.5%
x
4.3%
#s(literal 0 binary64)
Compiler

Compiled 2790 to 940 computations (66.3% saved)

regimes86.0ms (0.9%)

Counts
76 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.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))
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps)))
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) 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 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.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)
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))))
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))))
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.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 (-.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 (*.f64 x #s(literal 2 binary64)) (*.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)))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.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)))) eps))
(-.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 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)))))))))
(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))))))))
Outputs
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
Calls

3 calls:

26.0ms
x
26.0ms
eps
24.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 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)

regimes92.0ms (0.9%)

Counts
66 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.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))
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps)))
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) 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 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.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)
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))))
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))))
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
Calls

3 calls:

21.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
21.0ms
eps
21.0ms
x
Results
AccuracySegmentsBranch
89.0%2x
81.5%2eps
98.8%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes31.0ms (0.3%)

Counts
64 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.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))
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps)))
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) 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 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.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)
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))))
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))))
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
Outputs
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
Calls

1 calls:

21.0ms
x
Results
AccuracySegmentsBranch
87.4%2x
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes38.0ms (0.4%)

Counts
62 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.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))
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps)))
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps))
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x)
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) 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 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.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)
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))))
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))))
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
Calls

2 calls:

18.0ms
eps
17.0ms
x
Results
AccuracySegmentsBranch
44.4%1eps
44.4%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes16.0ms (0.2%)

Counts
23 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.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))
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x))
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps)))
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps))
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
Outputs
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
Calls

2 calls:

8.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
44.0%1eps
44.0%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0.1%)

Counts
7 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
Outputs
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
Calls

2 calls:

3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
43.8%1x
43.8%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0.1%)

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

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

2 calls:

4.0ms
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
-4.036970285649756e-148
0.0
Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch17.0ms (0.2%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
15.0ms
5.4015481891800596e-92
3.959523178213477e-89
Results
6.0ms55×1valid
4.0ms73×0valid
0.0ms0invalid
Compiler

Compiled 207 to 154 computations (25.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-mult: 2.0ms (34.2% of total)
ival-sub: 2.0ms (34.2% of total)
ival-sqrt: 2.0ms (34.2% of total)
backward-pass: 1.0ms (17.1% of total)
const: 0.0ms (0% of total)

simplify12.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
04297
16297
27197
37697
47897
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -5758609657015291/14396524142538228424993723224595141948383030778566133225922417832357880258148761185020930195532450742879746914027266864394266451377581759004827248578768524336431104 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps)))
(if (<=.f64 x #s(literal 3554922854784611/1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(/.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 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -5758609657015291/14396524142538228424993723224595141948383030778566133225922417832357880258148761185020930195532450742879746914027266864394266451377581759004827248578768524336431104 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.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))) eps)))
(if (<=.f64 x #s(literal 3554922854784611/1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)))
(if (<=.f64 x #s(literal 3554922854784611/1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
#s(literal 0 binary64)

soundness1.9s (19.3%)

Rules
5924×*-lowering-*.f32
5924×*-lowering-*.f64
5764×*-lowering-*.f32
5764×*-lowering-*.f64
4906×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04613973
115773840
258443798
087713798
0619
14019
232419
3405519
0821819
028123
1218120
22097109
09748109
02571162
18561135
230301098
080341098
06566016
122315790
081585790
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 211 to 118 computations (44.1% saved)

preprocess49.0ms (0.5%)

Compiler

Compiled 244 to 110 computations (54.9% saved)

end0.0ms (0%)

Profiling

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