ENA, Section 1.4, Exercise 4d

Time bar (total: 10.4s)

analyze28.0ms (0.3%)

Algorithm
1×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: 13.0ms
ival-<=: 7.0ms (51.9% of total)
ival-sub: 2.0ms (14.8% of total)
ival-mult: 2.0ms (14.8% of total)
ival-sqrt: 2.0ms (14.8% of total)
ival-and: 1.0ms (7.4% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.6s (15.2%)

Results
598.0ms4859×0valid
458.0ms2744×1valid
153.0ms653×2valid
16.0ms198×0invalid
Precisions
Click to see histograms. Total time spent on operations: 909.0ms
ival-<=: 311.0ms (34.2% of total)
ival-sub: 194.0ms (21.3% of total)
ival-mult: 160.0ms (17.6% of total)
ival-sqrt: 125.0ms (13.7% of total)
backward-pass: 72.0ms (7.9% of total)
ival-and: 27.0ms (3% of total)
const: 20.0ms (2.2% of total)
Bogosity

preprocess62.0ms (0.6%)

Algorithm
2×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
1×iter limit
1×saturated
1×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)))

explain337.0ms (3.3%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
980-0-(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
00-0-x
00-0-(*.f64 x x)
00-0-(-.f64 (*.f64 x x) eps)
00-0-(sqrt.f64 (-.f64 (*.f64 x x) eps))
00-0-eps
Results
270.0ms318×0valid
28.0ms160×1valid
7.0ms34×2valid
Compiler

Compiled 64 to 20 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 31.0ms
ival-sub: 12.0ms (38.7% of total)
ival-mult: 9.0ms (29% of total)
ival-sqrt: 6.0ms (19.3% of total)
backward-pass: 3.0ms (9.7% of total)
const: 1.0ms (3.2% 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
▶65.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

simplify25.0ms (0.2%)

Algorithm
1×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
1×iter limit
1×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

localize54.0ms (0.5%)

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)
✓accuracy65.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
30.0ms159×0valid
12.0ms80×1valid
3.0ms17×2valid
Compiler

Compiled 27 to 7 computations (74.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-sub: 4.0ms (32.7% of total)
ival-sqrt: 3.0ms (24.5% of total)
ival-mult: 3.0ms (24.5% of total)
backward-pass: 2.0ms (16.3% of total)
const: 0.0ms (0% of total)

series8.0ms (0.1%)

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

21 calls:

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

rewrite331.0ms (3.2%)

Algorithm
1×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
1×iter limit
1×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)))

simplify377.0ms (3.6%)

Algorithm
1×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
1×iter limit
1×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)

eval39.0ms (0.4%)

Compiler

Compiled 9912 to 1041 computations (89.5% saved)

prune45.0ms (0.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New27914293
Fresh000
Picked011
Done000
Total27915294
Accuracy
99.6%
Counts
294 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
48.1%
(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))))))))
48.2%
(/.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))))))
▶64.8%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
32.7%
(/.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)
38.7%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
41.1%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
64.4%
(-.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
▶3.4%
(-.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))))
6.3%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓65.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
61.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
4.1%
(-.f64 x x)
▶3.4%
(*.f64 x #s(literal 2 binary64))
▶29.5%
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
Compiler

Compiled 556 to 290 computations (47.8% saved)

simplify218.0ms (2.1%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.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)))))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(+.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))))))
✓cost-diff0
(*.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)))))))
✓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-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
2384×*-lowering-*.f32
2384×*-lowering-*.f64
1936×fmsub-define
1852×fmm-def
1788×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037280
1104240
2311225
3715224
44049224
08411224
Stop Event
1×iter limit
1×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
(* 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)
(* eps (+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))))
eps
(+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))))
(/ 1/2 x)
1/2
x
(* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))
(+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))
(/ 1/8 (* x (* x x)))
1/8
(* x (* x x))
(* x x)
(/ (* eps 1/16) (pow x 5))
(* eps 1/16)
1/16
(pow x 5)
5
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)
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(- x (+ x (* -1/2 (/ eps x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps 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 x) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) 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 (/.f64 eps x) #s(literal -1/8 binary64)) x))) x))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
(/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #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 (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) 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 (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) 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)
(* eps (+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))))
(*.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 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))))))
eps
(+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x
(* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))))
(+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))
(+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))))
(/ 1/8 (* x (* x x)))
(/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))
1/8
#s(literal 1/8 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
(* x x)
(*.f64 x x)
(/ (* eps 1/16) (pow x 5))
(*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))
(* eps 1/16)
(*.f64 eps #s(literal 1/16 binary64))
1/16
#s(literal 1/16 binary64)
(pow x 5)
(pow.f64 x #s(literal 5 binary64))
5
#s(literal 5 binary64)

localize225.0ms (2.2%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy95.1%
(*.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)))))))
✓accuracy91.7%
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
✓accuracy88.1%
(*.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)))))
✓accuracy48.8%
(+.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))))
✓accuracy99.8%
(*.f64 x (*.f64 x x))
✓accuracy89.7%
(*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))
✓accuracy85.1%
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
✓accuracy65.2%
(-.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 #s(literal -1/2 binary64) (/.f64 eps x))
✓accuracy100.0%
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
✓accuracy65.2%
(-.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)
✓accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓accuracy99.6%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
✓accuracy65.7%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
Results
77.0ms81×1valid
69.0ms159×0valid
23.0ms16×2valid
Compiler

Compiled 294 to 38 computations (87.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 106.0ms
ival-pow: 26.0ms (24.4% of total)
ival-div: 25.0ms (23.5% of total)
ival-mult: 25.0ms (23.5% of total)
ival-add: 12.0ms (11.3% of total)
backward-pass: 9.0ms (8.5% of total)
ival-sub: 8.0ms (7.5% of total)
const: 2.0ms (1.9% of total)

series61.0ms (0.6%)

Counts
22 → 480
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 (* 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 (* eps (+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))))>
#<alt (+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))))>
#<alt (/ 1/2 x)>
#<alt (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (/ (* eps -1/8) (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))>
#<alt (/ (* eps 1/16) (pow x 5))>
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 (* 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 (* 1/2 (/ 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 (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 5)))>
#<alt (* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))>
#<alt (* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 5)))>
#<alt (* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 5)))>
#<alt (/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))>
#<alt (/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))>
#<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))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)>
#<alt (/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))>
#<alt (* 1/16 (/ (pow eps 2) (pow x 5)))>
#<alt (/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))>
#<alt (/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)>
#<alt (/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x))>
#<alt (* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))>
#<alt (* 1/16 (/ (pow eps 2) (pow x 5)))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))>
#<alt (* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))>
#<alt (* 1/16 (/ (pow eps 2) (pow x 5)))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))>
#<alt (* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))>
#<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 (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/16 (/ (pow eps 2) (pow x 5)))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* 1/16 (/ (pow eps 2) (pow x 5)))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* 1/16 (/ (pow eps 2) (pow x 5)))>
#<alt (/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))>
#<alt (/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* 1/16 (/ (pow eps 2) (pow x 2))) (* 1/8 eps)) (pow x 3))>
#<alt (/ (+ (* 1/16 (/ (pow eps 2) (pow x 2))) (* 1/8 eps)) (pow x 3))>
#<alt (/ (+ (* 1/16 (/ (pow eps 2) (pow x 2))) (* 1/8 eps)) (pow x 3))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* -1 (/ (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2)))) (pow x 3)))>
#<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 (* -1/8 (/ 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)>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))>
#<alt (/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))>
#<alt (/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))>
#<alt (/ 1/8 (pow x 3))>
#<alt (/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))>
#<alt (/ 1/8 (pow x 3))>
#<alt (* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))>
#<alt (* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))>
#<alt (* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))>
#<alt (/ 1/8 (pow x 3))>
#<alt (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))>
#<alt (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))>
#<alt (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))>
#<alt (* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))>
#<alt (* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
#<alt (* 1/16 (/ eps (pow x 5)))>
Calls

120 calls:

TimeVariablePointExpression
12.0ms
eps
@inf
(/ (* eps 1/16) (pow x 5))
9.0ms
eps
@-inf
(/ (* eps 1/16) (pow x 5))
4.0ms
x
@inf
(* -1/2 (/ eps x))
3.0ms
eps
@0
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
2.0ms
eps
@-inf
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))

rewrite365.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
3350×*-lowering-*.f32
3350×*-lowering-*.f64
2448×fma-lowering-fma.f32
2448×fma-lowering-fma.f64
1688×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
037207
1280179
23364179
08328179
Stop Event
1×iter limit
1×node limit
Counts
22 → 611
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)
(* 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))))
(* eps (+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))))
(+ (/ 1/2 x) (* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))))
(/ 1/2 x)
(* eps (+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5))))
(+ x (pow (- (* x x) eps) 1/2))
(/ (* eps -1/8) (* x (* x x)))
(* x (* x x))
(+ (/ 1/8 (* x (* x x))) (/ (* eps 1/16) (pow x 5)))
(/ (* eps 1/16) (pow x 5))
Outputs
(+.f64 x (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 x (*.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(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)))
(-.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 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (/.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 (*.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))))))
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(/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 eps #s(literal 1/16 binary64)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (*.f64 eps #s(literal -1/16 binary64)))) (*.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))
(/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64)))) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 (*.f64 x x) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64)))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal 1/16 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) #s(literal -1/8 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal 1/16 binary64)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/16 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) #s(literal -1/8 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/16 binary64)) (*.f64 x (*.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/16 binary64)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))
(/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/16 binary64)) (*.f64 x x)) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 x x)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) #s(literal -1/8 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) #s(literal 1/8 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) (*.f64 x (*.f64 x x))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) #s(literal 1 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) (/.f64 #s(literal 1/8 binary64) x))) (*.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) (*.f64 x x)))
(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal 1/16 binary64))))) (neg.f64 (*.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/4096 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))) (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))))))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64)))))) (neg.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))))
(/.f64 (-.f64 (/.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64)))) (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (+.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))
(/.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal 1/16 binary64)))) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))
(pow.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal 1/16 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))) (+.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/4096 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))) (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64)))))) #s(literal -1 binary64))
(*.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal 1/16 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/4096 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))))))
(*.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))
(neg.f64 (/.f64 (*.f64 eps #s(literal -1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))
(/.f64 (*.f64 eps #s(literal -1/16 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64)))))
(/.f64 (*.f64 (*.f64 eps #s(literal 1/16 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))
(/.f64 (neg.f64 (*.f64 eps #s(literal -1/16 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))
(/.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5/2 binary64))) (pow.f64 x #s(literal 5/2 binary64)))
(pow.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal 1/16 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(*.f64 #s(literal 1/16 binary64) (*.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))
(*.f64 #s(literal 1/16 binary64) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(*.f64 (*.f64 eps #s(literal 1/16 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(*.f64 (*.f64 eps #s(literal -1/16 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))))))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (*.f64 eps #s(literal 1/16 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/16 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))) eps)
(*.f64 (/.f64 eps (pow.f64 x #s(literal 5/2 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5/2 binary64))) (/.f64 eps (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 5/2 binary64)) (*.f64 eps #s(literal 1/16 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 5/2 binary64)) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 1/16 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 1/16 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 5/2 binary64)) eps) #s(literal -1 binary64)))

simplify361.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
3940×*-lowering-*.f32
3940×*-lowering-*.f64
2070×+-lowering-+.f64
2070×+-lowering-+.f32
1624×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04634784
115364617
254714582
080814582
Stop Event
1×iter limit
1×node limit
Counts
480 → 480
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))))
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(* -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)
(* 1/16 (/ eps (pow x 5)))
(/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))
(/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))
(/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))
(/ 1/8 (pow x 3))
(/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))
(/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))
(/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))
(/ 1/8 (pow x 3))
(* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))
(* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))
(* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))
(/ 1/8 (pow x 3))
(+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))
(+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))
(+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))
(* 1/16 (/ eps (pow x 5)))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* 1/16 (/ eps (pow x 5)))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
(* 1/16 (/ eps (pow x 5)))
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 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) x)))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 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 (*.f64 #s(literal 1/8 binary64) (*.f64 eps 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 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x (*.f64 x x))))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (-.f64 (*.f64 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 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (*.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 (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.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)))))))
(*.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))) (neg.f64 x))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 5/64 binary64)) eps) (+.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) eps) (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)))) (neg.f64 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 (*.f64 #s(literal 1/8 binary64) (*.f64 eps 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)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 (/.f64 x #s(literal 1 binary64)) (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (*.f64 eps eps))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps (*.f64 x (*.f64 x x))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (/.f64 x #s(literal -1 binary64)) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (*.f64 (sqrt.f64 eps) (*.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64))) (*.f64 eps x)) eps))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (-.f64 (*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) (*.f64 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)
(*.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)
(* -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)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 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)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))) (neg.f64 x))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))) (neg.f64 x))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))) (neg.f64 x))
x
(+ x (* -1/2 (/ eps x)))
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(*.f64 eps (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 x (*.f64 x x))))))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 x (*.f64 x x))))))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 x (*.f64 x x))))))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 x (*.f64 x x))))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 x (*.f64 x x))))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 x (*.f64 x x))))))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))

eval192.0ms (1.9%)

Compiler

Compiled 34054 to 3207 computations (90.6% saved)

prune141.0ms (1.4%)

Pruning

30 alts after pruning (27 fresh and 3 done)

PrunedKeptTotal
New1214221236
Fresh459
Picked325
Done011
Total1221301251
Accuracy
100.0%
Counts
1251 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.3%
(/.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)))
▶5.7%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
7.2%
(/.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))))
8.1%
(/.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 0 binary64) (+.f64 (*.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))))))
▶18.0%
(/.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))))
27.3%
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x (*.f64 x x)))
41.1%
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
41.1%
(/.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))))
32.9%
(/.f64 #s(literal 1 binary64) (/.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 (+.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 eps (/.f64 x #s(literal 1/2 binary64)))))))
64.4%
(-.f64 x (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
5.4%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
5.4%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
4.3%
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
✓7.2%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
3.7%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
6.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
▶6.3%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓65.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
61.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
▶4.1%
(-.f64 x x)
41.0%
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
32.9%
(*.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 eps (/.f64 x #s(literal 1/2 binary64))))) (/.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))))))))
40.9%
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
✓3.4%
(*.f64 x #s(literal 2 binary64))
38.8%
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
41.0%
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
38.8%
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
35.8%
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))) (*.f64 x (*.f64 x x))))))
29.4%
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))))
Compiler

Compiled 1202 to 661 computations (45% saved)

simplify210.0ms (2%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f64 (*.f64 x x) eps)
✓cost-diff0
(*.f64 x x)
✓cost-diff512
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
✓cost-diff512
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
✓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-diff896
(/.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 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))
✓cost-diff256
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓cost-diff512
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓cost-diff128
(-.f64 x x)
✓cost-diff0
(-.f64 (*.f64 x x) eps)
✓cost-diff0
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
✓cost-diff0
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
Rules
3378×*-lowering-*.f32
3378×*-lowering-*.f64
1828×fma-lowering-fma.f32
1828×fma-lowering-fma.f64
1678×fmsub-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037245
1106229
2303225
31160211
46100211
08358211
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
eps
(+ x (pow (- (* x x) eps) 1/2))
x
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(* x x)
1/2
(- x x)
x
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
x
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+ 1 (/ (* eps -1/2) (* x x)))
1
(/ (* eps -1/2) (* x x))
(* eps -1/2)
eps
-1/2
(* x x)
(/ (- 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 x) (- (* x x) eps)) (+ (* x 2) (* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))))
(- (* x x) (- (* x x) eps))
(* x x)
x
(- (* x x) eps)
eps
(+ (* x 2) (* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x)))
(* x 2)
2
(* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))
(/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x)
(+ -1/2 (* eps (/ -1/8 (* x x))))
-1/2
(* eps (/ -1/8 (* x x)))
(/ -1/8 (* x x))
-1/8
Outputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
eps
(+ x (pow (- (* x x) eps) 1/2))
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
x
(pow (- (* x x) eps) 1/2)
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
1/2
#s(literal 1/2 binary64)
(- x x)
#s(literal 0 binary64)
x
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
x
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+ 1 (/ (* eps -1/2) (* x x)))
(+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))
1
#s(literal 1 binary64)
(/ (* eps -1/2) (* x x))
(/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
(/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps))))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 x x))
0
#s(literal 0 binary64)
(* (/ 1/4 (* x x)) (* eps eps))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/4 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
(* 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 x) (- (* x x) eps)) (+ (* x 2) (* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))) x)))
(- (* x x) (- (* x x) eps))
eps
(* x x)
(*.f64 x x)
x
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
(+ (* x 2) (* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x)))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))) x))
(* x 2)
(*.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))
(/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))) x)
(/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x)
(+ -1/2 (* eps (/ -1/8 (* x x))))
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))
-1/2
#s(literal -1/2 binary64)
(* eps (/ -1/8 (* x x)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(/ -1/8 (* x x))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
-1/8
#s(literal -1/8 binary64)

localize270.0ms (2.6%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy99.8%
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
✓accuracy89.7%
(*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))
✓accuracy83.4%
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
✓accuracy65.7%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
✓accuracy99.8%
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓accuracy99.5%
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
✓accuracy75.9%
(/.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))))
✓accuracy59.6%
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))
✓accuracy100.0%
(*.f64 eps #s(literal -1/2 binary64))
✓accuracy83.9%
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
✓accuracy80.5%
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓accuracy65.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓accuracy100.0%
(-.f64 x x)
✓accuracy100.0%
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓accuracy99.6%
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
Results
107.0ms81×1valid
67.0ms159×0valid
22.0ms16×2valid
Compiler

Compiled 279 to 38 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 117.0ms
ival-div: 49.0ms (41.8% of total)
ival-mult: 21.0ms (17.9% of total)
ival-pow: 19.0ms (16.2% of total)
ival-add: 10.0ms (8.5% of total)
ival-sub: 9.0ms (7.7% of total)
backward-pass: 8.0ms (6.8% of total)
const: 1.0ms (0.9% of total)

series31.0ms (0.3%)

Counts
22 → 468
Calls
Call 1
Inputs
#<alt (/ eps (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (pow (- (* x x) eps) 1/2)>
#<alt (- (* x x) eps)>
#<alt (- x x)>
#<alt (- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))>
#<alt (* x (+ 1 (/ (* eps -1/2) (* x x))))>
#<alt (+ 1 (/ (* eps -1/2) (* x x)))>
#<alt (/ (* eps -1/2) (* x x))>
#<alt (/ (- 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 x) (- (* x x) eps)) (+ (* x 2) (* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))))>
#<alt (- (* x x) (- (* x x) eps))>
#<alt (* x x)>
#<alt (* eps -1/2)>
#<alt (/ -1/2 (/ x eps))>
#<alt (/ 1/4 (* x x))>
#<alt (* eps (/ -1/8 (* x x)))>
#<alt (* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))>
#<alt (/ -1/8 (* x x))>
Outputs
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<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 (* (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 (* (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 (* (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 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>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ eps (pow x 2))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ 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 (* -8 (/ (pow x 3) eps))>
#<alt (* (pow x 3) (- (* 32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps))))>
#<alt (* (pow x 3) (- (* (pow x 2) (+ (* -256 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))>
#<alt (* (pow x 3) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1536 (/ (pow x 2) (pow eps 4))) (* 256 (/ 1 (pow eps 3))))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))>
#<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 (/ (+ (* -1/64 (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 (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (pow eps 4)) (* 1/64 (pow eps 4))) (pow x 6))) (* -1/2 eps)) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))>
#<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 (+ (* 3/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (/ (+ (* -8 (pow x 3)) (* 32 (/ (pow x 5) eps))) eps)>
#<alt (/ (- (+ (* -256 (/ (pow x 7) (pow eps 2))) (* -8 (pow x 3))) (* -32 (/ (pow x 5) eps))) eps)>
#<alt (/ (- (+ (* -8 (pow x 3)) (* -1 (/ (+ (* -1024 (pow x 9)) (* -512 (pow x 9))) (pow eps 3)))) (+ (* -32 (/ (pow x 5) eps)) (* 256 (/ (pow x 7) (pow eps 2))))) eps)>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -256 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1024 (/ (pow x 9) eps)) (* -512 (/ (pow x 9) eps))) (* -256 (pow x 7))) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) 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 (* -1/2 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))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<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 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
Calls

117 calls:

TimeVariablePointExpression
6.0ms
x
@0
(- 0 (* (/ 1/4 (* x x)) (* eps eps)))
3.0ms
eps
@inf
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
1.0ms
eps
@0
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
1.0ms
x
@-inf
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
1.0ms
x
@0
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))

rewrite369.0ms (3.6%)

Algorithm
1×batch-egg-rewrite
Rules
2906×*-lowering-*.f32
2906×*-lowering-*.f64
2470×fma-lowering-fma.f32
2470×fma-lowering-fma.f64
2086×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037178
1281162
22819153
08632153
Stop Event
1×iter limit
1×node limit
Counts
22 → 652
Calls
Call 1
Inputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(- x x)
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+ 1 (/ (* eps -1/2) (* x x)))
(/ (* eps -1/2) (* x x))
(/ (- 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 x) (- (* x x) eps)) (+ (* x 2) (* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))))
(- (* x x) (- (* x x) eps))
(* x x)
(* eps -1/2)
(/ -1/2 (/ x eps))
(/ 1/4 (* x x))
(* eps (/ -1/8 (* x x)))
(* eps (/ (+ -1/2 (* eps (/ -1/8 (* x x)))) x))
(/ -1/8 (* x x))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) eps)
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(*.f64 (/.f64 eps (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 eps (+.f64 eps #s(literal 0 binary64))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(fma.f64 x #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 (*.f64 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 eps #s(literal 0 binary64))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.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 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (*.f64 x (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 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x))
(pow.f64 (/.f64 (-.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 (*.f64 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 eps #s(literal 0 binary64))) #s(literal -1 binary64))
(*.f64 (+.f64 eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))))
(exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))) (pow.f64 (+.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)))
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(pow.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal -3 binary64))
(pow.f64 (/.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 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 1/2 binary64) (pow.f64 (*.f64 x (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #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) x) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal -1 binary64)))
(*.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))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/64 binary64))
(*.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))
(*.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(*.f64 #s(literal -1/64 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/8 binary64))))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x x))
(/.f64 (neg.f64 (*.f64 eps #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (*.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 (*.f64 eps #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (*.f64 eps (/.f64 #s(literal -1/8 binary64) x)) x)
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) x) eps) x)
(/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) x)
(pow.f64 (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/8 binary64))) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) eps))
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) eps)
(*.f64 (/.f64 eps x) (/.f64 #s(literal -1/8 binary64) x))
(*.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 eps (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))))))
(/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))) x)
(/.f64 (neg.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) eps) (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))))
(/.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))) eps) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))))) #s(literal -1 binary64))
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(*.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))) x) eps)
(*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) #s(literal -1/8 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -1/8 binary64) x)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal -1/8 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal -1/8 binary64) x) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/8 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal 1 binary64) x))

simplify309.0ms (3%)

Algorithm
1×egg-herbie
Rules
4670×*-lowering-*.f32
4670×*-lowering-*.f64
2240×+-lowering-+.f64
2240×+-lowering-+.f32
1726×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05264310
117584177
264454173
080494173
Stop Event
1×iter limit
1×node limit
Counts
468 → 468
Calls
Call 1
Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
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(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
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(+ (* 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)
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(* 2 x)
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(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
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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)) (/ x eps)))))
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(* (sqrt eps) (sqrt -1))
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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)
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(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
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x
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(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 eps)
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(pow x 2)
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(* -1 eps)
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(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
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(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
0
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(* 1/2 (/ eps x))
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(/ (+ (* -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)))))
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x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
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x
(+ x (* -1/2 (/ eps x)))
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(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
1
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(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ eps (pow x 2)))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
(* -1/2 (/ eps (pow x 2)))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
1
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
1
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -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)))
(* -8 (/ (pow x 3) eps))
(* (pow x 3) (- (* 32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps))))
(* (pow x 3) (- (* (pow x 2) (+ (* -256 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))
(* (pow x 3) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1536 (/ (pow x 2) (pow eps 4))) (* 256 (/ 1 (pow eps 3))))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))
(* 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 (/ (+ (* -1/64 (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)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (pow eps 4)) (* 1/64 (pow eps 4))) (pow x 6))) (* -1/2 eps)) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))
(* 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 (+ (* 3/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -8 (/ (pow x 3) eps))
(/ (+ (* -8 (pow x 3)) (* 32 (/ (pow x 5) eps))) eps)
(/ (- (+ (* -256 (/ (pow x 7) (pow eps 2))) (* -8 (pow x 3))) (* -32 (/ (pow x 5) eps))) eps)
(/ (- (+ (* -8 (pow x 3)) (* -1 (/ (+ (* -1024 (pow x 9)) (* -512 (pow x 9))) (pow eps 3)))) (+ (* -32 (/ (pow x 5) eps)) (* 256 (/ (pow x 7) (pow eps 2))))) eps)
(* -8 (/ (pow x 3) eps))
(* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -256 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1024 (/ (pow x 9) eps)) (* -512 (/ (pow x 9) eps))) (* -256 (pow x 7))) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) 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)
(* -1/2 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))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/2 (/ eps x))
(* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(* -1/2 (/ eps x))
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
Outputs
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 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 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 x (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (neg.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps))) (*.f64 eps x)) eps))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) #s(literal -1/2 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) #s(literal -1 binary64))) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 eps x)) eps))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) x)))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) eps) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))))))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps)) 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 eps #s(literal 1/8 binary64))) (*.f64 x x)) (+.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 x x)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(*.f64 (+.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) eps) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/4 binary64)))) #s(literal -1/8 binary64)))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(*.f64 x (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x)) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x)) (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal -1/2 binary64) (+.f64 eps (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (/.f64 x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(*.f64 eps (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (/.f64 x eps))) (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x 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 (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 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))) eps)) eps))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 x 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 -1/8 binary64))) (*.f64 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #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 (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.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))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(*.f64 x (+.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.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 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(*.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(*.f64 (+.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.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)))) (-.f64 #s(literal 0 binary64) x))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (*.f64 eps (+.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)))) (/.f64 (*.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)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.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 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (+.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 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 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
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(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps)))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps)))
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps)))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/.f64 (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/.f64 (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/.f64 (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x)) (*.f64 eps #s(literal -1/2 binary64))) x)
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x)) (*.f64 eps #s(literal -1/2 binary64))) x)
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x)) (*.f64 eps #s(literal -1/2 binary64))) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))
(/.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))

eval237.0ms (2.3%)

Compiler

Compiled 32483 to 2896 computations (91.1% saved)

prune202.0ms (2%)

Pruning

38 alts after pruning (35 fresh and 3 done)

PrunedKeptTotal
New1257251282
Fresh121022
Picked505
Done033
Total1274381312
Accuracy
100.0%
Counts
1312 → 38
Alt Table
Click to see full alt table
StatusAccuracyProgram
17.9%
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) (/.f64 eps x))
▶7.2%
(/.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))))
5.7%
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
19.0%
(/.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))))
18.0%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
25.0%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
18.0%
(/.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))))
19.0%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (*.f64 eps eps) x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
17.9%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) 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))))
▶19.0%
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
41.1%
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
8.3%
(/.f64 (neg.f64 (/.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))))
42.0%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
40.5%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
42.0%
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
▶99.5%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
41.1%
(/.f64 eps (+.f64 x x))
41.7%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
99.3%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps))
41.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
5.4%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
5.4%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
4.3%
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
✓7.2%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
4.5%
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
6.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
6.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
6.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
6.3%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
✓65.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
61.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
7.9%
(*.f64 (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.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))))
32.9%
(*.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 eps (/.f64 x #s(literal 1/2 binary64))))) (/.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))))))))
40.9%
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
✓3.4%
(*.f64 x #s(literal 2 binary64))
▶38.8%
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
41.0%
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
▶4.1%
#s(literal 0 binary64)
Compiler

Compiled 1358 to 819 computations (39.7% saved)

simplify185.0ms (1.8%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x x)
✓cost-diff128
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))
✓cost-diff512
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
✓cost-diff640
(/.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))))
✓cost-diff0
(/.f64 (/.f64 (*.f64 eps eps) x) x)
✓cost-diff0
(*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64))
✓cost-diff128
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
✓cost-diff768
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
✓cost-diff0
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
✓cost-diff0
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)
✓cost-diff0
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x 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)))
✓cost-diff0
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Rules
3724×*-lowering-*.f32
3724×*-lowering-*.f64
1738×fma-define
1554×sum3-define
1492×/-lowering-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033206
181197
2212192
3595180
43442180
09127180
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ eps (+ x (sqrt (- (* x x) eps))))
eps
(+ x (sqrt (- (* x x) eps)))
x
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
0
(* eps (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x))
eps
(/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x)
(+ 1/2 (* eps (/ 1/8 (* x x))))
1/2
(* eps (/ 1/8 (* x x)))
(/ 1/8 (* x x))
1/8
(* x x)
x
(/ (* (/ (/ (* eps eps) x) x) -1/4) (+ 0 (/ -1/2 (/ x eps))))
(* (/ (/ (* eps eps) x) x) -1/4)
(/ (/ (* eps eps) x) x)
(/ (* eps eps) x)
(* eps eps)
eps
x
-1/4
(+ 0 (/ -1/2 (/ x eps)))
0
(/ -1/2 (/ x eps))
-1/2
(/ x eps)
(/ (- (* x x) (- (* x x) eps)) (* x (+ 2 (/ (/ (* eps -1/2) x) x))))
(- (* x x) (- (* x x) eps))
(* x x)
x
(- (* x x) eps)
eps
(* x (+ 2 (/ (/ (* eps -1/2) x) x)))
(+ 2 (/ (/ (* eps -1/2) x) x))
2
(/ (/ (* eps -1/2) x) x)
(/ (* eps -1/2) x)
(* eps -1/2)
-1/2
Outputs
(/ eps (+ x (sqrt (- (* x x) eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
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)
0
#s(literal 0 binary64)
(* eps (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x)) (/.f64 eps x))
eps
(/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x)) x)
(+ 1/2 (* eps (/ 1/8 (* x x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x))
1/2
#s(literal 1/2 binary64)
(* eps (/ 1/8 (* x x)))
(/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x)
(/ 1/8 (* x x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
x
(/ (* (/ (/ (* eps eps) x) x) -1/4) (+ 0 (/ -1/2 (/ x eps))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* (/ (/ (* eps eps) x) x) -1/4)
(*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64))
(/ (/ (* eps eps) x) x)
(/.f64 (/.f64 (*.f64 eps eps) x) x)
(/ (* eps eps) x)
(/.f64 (*.f64 eps eps) x)
(* eps eps)
(*.f64 eps eps)
eps
x
-1/4
#s(literal -1/4 binary64)
(+ 0 (/ -1/2 (/ x eps)))
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
0
#s(literal 0 binary64)
(/ -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 x) (- (* x x) eps)) (* x (+ 2 (/ (/ (* eps -1/2) x) x))))
(/.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (*.f64 x #s(literal 2 binary64))))
(- (* x x) (- (* x x) eps))
eps
(* x x)
(*.f64 x x)
x
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
(* x (+ 2 (/ (/ (* eps -1/2) x) x)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (*.f64 x #s(literal 2 binary64)))
(+ 2 (/ (/ (* eps -1/2) x) x))
(+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))
2
#s(literal 2 binary64)
(/ (/ (* eps -1/2) x) x)
(/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)
(/ (* eps -1/2) x)
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)

localize236.0ms (2.3%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy99.9%
(/.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))))
✓accuracy99.7%
(/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
✓accuracy80.5%
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))
✓accuracy65.7%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
✓accuracy99.5%
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
✓accuracy89.1%
(/.f64 (/.f64 (*.f64 eps eps) x) x)
✓accuracy78.9%
(/.f64 (*.f64 eps eps) x)
✓accuracy75.9%
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
✓accuracy99.9%
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)
✓accuracy99.8%
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓accuracy89.7%
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
✓accuracy83.4%
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
✓accuracy100.0%
(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓accuracy99.6%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Results
86.0ms77×1valid
71.0ms163×0valid
15.0ms16×2valid
Compiler

Compiled 228 to 34 computations (85.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 110.0ms
ival-mult: 54.0ms (49.2% of total)
ival-div: 25.0ms (22.8% of total)
ival-sub: 13.0ms (11.9% of total)
ival-add: 7.0ms (6.4% of total)
backward-pass: 6.0ms (5.5% of total)
ival-sqrt: 3.0ms (2.7% of total)
const: 1.0ms (0.9% of total)

series19.0ms (0.2%)

Counts
20 → 456
Calls
Call 1
Inputs
#<alt (/ eps (+ x (sqrt (- (* x x) eps))))>
#<alt (+ x (sqrt (- (* x x) eps)))>
#<alt (sqrt (- (* x x) eps))>
#<alt (- (* x x) eps)>
#<alt (* eps (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x))>
#<alt (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x)>
#<alt (+ 1/2 (* eps (/ 1/8 (* x x))))>
#<alt (* eps (/ 1/8 (* x x)))>
#<alt (/ (* (/ (/ (* eps eps) x) x) -1/4) (+ 0 (/ -1/2 (/ x eps))))>
#<alt (+ 0 (/ -1/2 (/ x eps)))>
#<alt (* (/ (/ (* eps eps) x) x) -1/4)>
#<alt (/ (/ (* eps eps) x) x)>
#<alt (/ (- (* x x) (- (* x x) eps)) (* x (+ 2 (/ (/ (* eps -1/2) x) x))))>
#<alt (- (* x x) (- (* x x) eps))>
#<alt (* x (+ 2 (/ (/ (* eps -1/2) x) x)))>
#<alt (* x x)>
#<alt (/ 1/8 (* x x))>
#<alt (/ (* eps eps) x)>
#<alt (/ -1/2 (/ x eps))>
#<alt (/ (/ (* eps -1/2) x) x)>
Outputs
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<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 (* (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 (* (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 (* (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 (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/8 (/ eps (pow x 2)))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
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#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
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#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ 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 (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (/ (pow eps 2) (pow x 2))>
#<alt (* -2 x)>
#<alt (* x (- (* -8 (/ (pow x 2) eps)) 2))>
#<alt (* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps)))) 2))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps)))) 2))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* 1/128 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/32 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/32 (/ (pow eps 3) (pow x 4))))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 4) (pow x 6)))))) x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -2 x)>
#<alt (+ (* -8 (/ (pow x 3) eps)) (* -2 x))>
#<alt (- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps)))>
#<alt (- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2)))))>
#<alt (* -2 x)>
#<alt (+ (* -8 (/ (pow x 3) eps)) (* -2 x))>
#<alt (+ (* -2 x) (* -1 (/ (- (* 32 (/ (pow x 5) eps)) (* -8 (pow x 3))) eps)))>
#<alt (+ (* -2 x) (* -1 (/ (- (* -1 (/ (- (* -128 (/ (pow x 7) eps)) (* 32 (pow x 5))) eps)) (* -8 (pow x 3))) 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 (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<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 (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (pow eps 2) x)>
#<alt (/ (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 (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
Calls

114 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(/ (* eps eps) x)
0.0ms
x
@0
(* eps (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x))
0.0ms
eps
@0
(* eps (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x))
0.0ms
x
@0
(/ (- (* x x) (- (* x x) eps)) (* x (+ 2 (/ (/ (* eps -1/2) x) x))))
0.0ms
eps
@-inf
(* eps (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x))

rewrite339.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
4244×/-lowering-/.f32
4244×/-lowering-/.f64
3020×*-lowering-*.f32
3020×*-lowering-*.f64
1460×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033163
1226142
22200136
08339136
Stop Event
1×iter limit
1×node limit
Counts
20 → 903
Calls
Call 1
Inputs
(/ eps (+ x (sqrt (- (* x x) eps))))
(+ x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* eps (/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x))
(/ (+ 1/2 (* eps (/ 1/8 (* x x)))) x)
(+ 1/2 (* eps (/ 1/8 (* x x))))
(* eps (/ 1/8 (* x x)))
(/ (* (/ (/ (* eps eps) x) x) -1/4) (+ 0 (/ -1/2 (/ x eps))))
(+ 0 (/ -1/2 (/ x eps)))
(* (/ (/ (* eps eps) x) x) -1/4)
(/ (/ (* eps eps) x) x)
(/ (- (* x x) (- (* x x) eps)) (* x (+ 2 (/ (/ (* eps -1/2) x) x))))
(- (* x x) (- (* x x) eps))
(* x (+ 2 (/ (/ (* eps -1/2) x) x)))
(* x x)
(/ 1/8 (* x x))
(/ (* eps eps) x)
(/ -1/2 (/ x eps))
(/ (/ (* eps -1/2) x) x)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (*.f64 eps #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 #s(literal 1 binary64) (/.f64 eps (+.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)))) eps)
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(*.f64 (/.f64 eps (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 eps (+.f64 eps #s(literal 0 binary64))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x (*.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)))) (/.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)) (/.f64 (*.f64 x x) (-.f64 (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)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
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(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (/.f64 x (/.f64 (*.f64 eps eps) x))))
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(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) eps) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (/.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 #s(literal -1/2 binary64) x)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x)))))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
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(pow.f64 (/.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
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(*.f64 eps (/.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (/.f64 x eps)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x)))))
(*.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x)))) (/.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) eps))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) x))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) x) (/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) x))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) (neg.f64 (-.f64 #s(literal 0 binary64) x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) x))
(/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)
(/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) x)
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) #s(literal 1 binary64))))
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(/.f64 (neg.f64 (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
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(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
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(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))
(*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x))
(*.f64 (pow.f64 (/.f64 x (*.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))

simplify302.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
4420×*-lowering-*.f32
4420×*-lowering-*.f64
2200×+-lowering-+.f64
2200×+-lowering-+.f32
1634×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05114349
117114223
261654198
080224198
Stop Event
1×iter limit
1×node limit
Counts
456 → 456
Calls
Call 1
Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* 1/8 (/ eps (pow x 2)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ 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)))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(/ (pow eps 2) (pow x 2))
(* -2 x)
(* x (- (* -8 (/ (pow x 2) eps)) 2))
(* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps)))) 2))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps)))) 2))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* 1/128 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/32 (/ (pow eps 3) (pow x 4))))) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/32 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 4) (pow x 6)))))) x))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -2 x)
(+ (* -8 (/ (pow x 3) eps)) (* -2 x))
(- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps)))
(- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2)))))
(* -2 x)
(+ (* -8 (/ (pow x 3) eps)) (* -2 x))
(+ (* -2 x) (* -1 (/ (- (* 32 (/ (pow x 5) eps)) (* -8 (pow x 3))) eps)))
(+ (* -2 x) (* -1 (/ (- (* -1 (/ (- (* -128 (/ (pow x 7) eps)) (* 32 (pow x 5))) eps)) (* -8 (pow x 3))) 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
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(* -1/2 (/ eps x))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(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)
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (pow eps 2) x)
(/ (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))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
Outputs
(* 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 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x)))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 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)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 x (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) #s(literal -1/2 binary64))) (*.f64 eps eps))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (neg.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1 binary64)) #s(literal -1/2 binary64))) x))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps))) (*.f64 eps x)) eps))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
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(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(* 1/2 (/ eps x))
(*.f64 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 1/2 binary64) eps) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
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(+ (* 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)))
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* 1/2 (/ eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/.f64 (+.f64 (*.f64 (*.f64 eps (/.f64 eps (*.f64 x x))) #s(literal -1/8 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(/.f64 (+.f64 (+.f64 (*.f64 (*.f64 eps (/.f64 eps (*.f64 x x))) #s(literal -1/8 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 (*.f64 (*.f64 eps (/.f64 eps (*.f64 x x))) #s(literal -1/8 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal -1/2 binary64) (+.f64 eps (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
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(+ (* 2 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 (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.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 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
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(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
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x
(+ x (* -1/2 (/ eps x)))
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(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
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(+ 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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(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 x #s(literal -2 binary64)) eps))))
(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)
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(/ (pow eps 2) x)
(/.f64 (*.f64 eps eps) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))
(* -1/2 (/ eps (pow x 2)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))

eval262.0ms (2.5%)

Compiler

Compiled 37028 to 3606 computations (90.3% saved)

prune450.0ms (4.3%)

Pruning

77 alts after pruning (71 fresh and 6 done)

PrunedKeptTotal
New1441501491
Fresh92130
Picked235
Done033
Total1452771529
Accuracy
100.0%
Counts
1529 → 77
Alt Table
Click to see full alt table
StatusAccuracyProgram
41.6%
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) x)
41.9%
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)))
9.4%
(/.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 eps eps) (*.f64 #s(literal 0 binary64) eps)))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
19.1%
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))
19.0%
(/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
8.0%
(/.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))))
7.3%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))) (*.f64 x #s(literal 1 binary64))) (*.f64 x (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (*.f64 x (-.f64 (*.f64 x x) eps))) (*.f64 x (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))
3.5%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 x (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
4.1%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))) (*.f64 x (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) (*.f64 x (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))))
4.4%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) x) (*.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))) (*.f64 x x))
3.4%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
6.4%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))
3.9%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
4.9%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))))
2.8%
(/.f64 (-.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
5.8%
(/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
4.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))) (+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))))
5.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 (-.f64 #s(literal 4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 x x))) x) (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))
5.7%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
7.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))))
7.2%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
7.2%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))))
6.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
6.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 eps (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))))))
5.7%
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
19.0%
(/.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))))
25.0%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
18.0%
(/.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))))
42.0%
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
16.8%
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
16.6%
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (/.f64 (-.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) x)))
17.5%
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (/.f64 (-.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) x)))
16.7%
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x)))) (/.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))))
20.8%
(/.f64 (*.f64 (/.f64 (*.f64 (/.f64 eps x) eps) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
19.1%
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))) x)
19.0%
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal -1/4 binary64) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
20.8%
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))
30.3%
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))
25.7%
(/.f64 (*.f64 (*.f64 eps (/.f64 (/.f64 eps x) x)) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
17.3%
(/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
42.0%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
40.5%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
42.0%
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
✓99.5%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
41.1%
(/.f64 eps (+.f64 x x))
41.9%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
41.7%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
41.8%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps #s(literal 0 binary64))))
99.3%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps))
41.8%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (/.f64 (+.f64 eps #s(literal 0 binary64)) x)))
41.0%
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
5.4%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
5.4%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
4.3%
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
✓7.2%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
4.5%
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
6.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
6.9%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
6.3%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
✓65.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
61.2%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
39.7%
(*.f64 (/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (-.f64 #s(literal 4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 x x)))) (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)))
26.3%
(*.f64 (/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (+.f64 #s(literal 8 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (+.f64 #s(literal 4 binary64) (/.f64 (-.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x) #s(literal 2 binary64)) (/.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))))
19.0%
(*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) #s(literal 1/2 binary64)) (/.f64 x eps))
8.0%
(*.f64 (/.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))))
41.9%
(*.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))
19.0%
(*.f64 (/.f64 (*.f64 eps eps) x) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
41.9%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (+.f64 eps #s(literal 0 binary64)))
18.9%
(*.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) eps))
40.9%
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
✓3.4%
(*.f64 x #s(literal 2 binary64))
5.5%
(*.f64 x #s(literal -2 binary64))
✓38.8%
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
41.0%
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
19.0%
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) (/.f64 eps x)))
✓4.1%
#s(literal 0 binary64)
Compiler

Compiled 5004 to 1544 computations (69.1% saved)

regimes136.0ms (1.3%)

Counts
112 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 eps (+.f64 x x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) (/.f64 eps x)))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))) x)
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(*.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) eps))
(*.f64 (/.f64 (*.f64 eps eps) x) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) #s(literal 1/2 binary64)) (/.f64 x eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(/.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 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) (/.f64 eps x))
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)))
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) x)
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (+.f64 eps #s(literal 0 binary64)))
(*.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (/.f64 (+.f64 eps #s(literal 0 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 eps (/.f64 (/.f64 eps x) x)) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal -1/4 binary64) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (*.f64 (/.f64 eps x) eps) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
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(/.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))))))
(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))))))))
Outputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Calls

3 calls:

55.0ms
x
33.0ms
eps
30.0ms
(-.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)

regimes139.0ms (1.3%)

Counts
104 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 eps (+.f64 x x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) (/.f64 eps x)))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
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(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
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(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))) x)
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(*.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) eps))
(*.f64 (/.f64 (*.f64 eps eps) x) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
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(/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(/.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 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
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(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (+.f64 eps #s(literal 0 binary64)))
(*.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (/.f64 (+.f64 eps #s(literal 0 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 eps (/.f64 (/.f64 eps x) x)) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal -1/4 binary64) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (*.f64 (/.f64 eps x) eps) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (*.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 #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) x) (*.f64 eps 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)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) 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))))
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(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))) (*.f64 x (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 eps (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))))))
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(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))))
(/.f64 (neg.f64 (/.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))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.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 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x)))) (/.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))))
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) x) (*.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))) (*.f64 x x))
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (*.f64 x (-.f64 (*.f64 x x) eps))) (*.f64 x (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))
(*.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 eps (/.f64 x #s(literal 1/2 binary64))))) (/.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 #s(literal 1 binary64) (/.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 (+.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 eps (/.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))) (*.f64 x #s(literal 1 binary64))) (*.f64 x (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))) (*.f64 x (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) (*.f64 x (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))) (+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 x (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
(/.f64 (-.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
Calls

3 calls:

49.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
42.0ms
eps
28.0ms
x
Results
AccuracySegmentsBranch
88.0%2x
82.5%2eps
99.2%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes52.0ms (0.5%)

Counts
103 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 eps (+.f64 x x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) (/.f64 eps x)))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))) x)
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(*.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) eps))
(*.f64 (/.f64 (*.f64 eps eps) x) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) #s(literal 1/2 binary64)) (/.f64 x eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(/.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 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) (/.f64 eps x))
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)))
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) x)
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (+.f64 eps #s(literal 0 binary64)))
(*.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (/.f64 (+.f64 eps #s(literal 0 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 eps (/.f64 (/.f64 eps x) x)) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal -1/4 binary64) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (*.f64 (/.f64 eps x) eps) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (*.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 #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) x) (*.f64 eps 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)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) 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 #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 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.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 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))) (*.f64 x (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 eps (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))))
(/.f64 (neg.f64 (/.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))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.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 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 #s(literal 0 binary64) (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x)))) (/.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (/.f64 (+.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 eps eps) (*.f64 #s(literal 0 binary64) eps)))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(*.f64 (/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (-.f64 #s(literal 4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 x x)))) (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (/.f64 (-.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) 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)
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x))))
(*.f64 (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.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))))
(*.f64 (/.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))))
(/.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 0 binary64) (+.f64 (*.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 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 (-.f64 #s(literal 4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (*.f64 x x))) x) (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) x) (*.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))))) (*.f64 x x))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(/.f64 (*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) #s(literal -1/4 binary64)) (/.f64 (-.f64 (*.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) x)))
(*.f64 (/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) x) (+.f64 #s(literal 8 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (+.f64 #s(literal 4 binary64) (/.f64 (-.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x) #s(literal 2 binary64)) (/.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (*.f64 x (-.f64 (*.f64 x x) eps))) (*.f64 x (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))
(*.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 eps (/.f64 x #s(literal 1/2 binary64))))) (/.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 #s(literal 1 binary64) (/.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 (+.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 eps (/.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))) (*.f64 x #s(literal 1 binary64))) (*.f64 x (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))) (*.f64 x (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) (*.f64 x (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)) (*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))) (+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 eps (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 x (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
(/.f64 (-.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
Outputs
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

1 calls:

31.0ms
x
Results
AccuracySegmentsBranch
86.6%2x
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes68.0ms (0.7%)

Counts
102 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 eps (+.f64 x x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) (/.f64 eps x)))
(*.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))) x)
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(*.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 (/.f64 (/.f64 (*.f64 eps eps) x) x) eps))
(*.f64 (/.f64 (*.f64 eps eps) x) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) #s(literal 1/2 binary64)) (/.f64 x eps))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))))
(/.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 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 (*.f64 eps eps) x))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
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(/.f64 (-.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (*.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))))
Outputs
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

2 calls:

32.0ms
eps
30.0ms
x
Results
AccuracySegmentsBranch
42.0%1eps
42.0%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts
12 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 eps (+.f64 x x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
Outputs
(/.f64 eps (+.f64 x x))
Calls

2 calls:

5.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
41.1%1x
41.1%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0.1%)

Counts
6 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.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
41.0%1x
41.0%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

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

2 calls:

2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
5.5%1x
5.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
Outputs
#s(literal 0 binary64)
Calls

2 calls:

1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
4.1%1eps
4.1%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch26.0ms (0.3%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.3400197833610262e-154
0.0
Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch9.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
7.0ms
5.118351179111484e-116
7.893707823329584e-116
Results
3.0ms51×0valid
1.0ms13×1valid
1.0ms10×0invalid
Compiler

Compiled 107 to 74 computations (30.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 1.0ms (39.3% of total)
ival-sub: 1.0ms (39.3% of total)
ival-sqrt: 1.0ms (39.3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03585
15185
26185
36685
46885
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(if (<=.f64 x #s(literal 3460291778262777/44362715105933037753254626946289339254982993206013065202727673289833940924890009968639590497666233249558259375382457149263586525184 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 x x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal -2 binary64))
#s(literal 0 binary64)
Outputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(if (<=.f64 x #s(literal 3460291778262777/44362715105933037753254626946289339254982993206013065202727673289833940924890009968639590497666233249558259375382457149263586525184 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 x x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal -2 binary64))
#s(literal 0 binary64)

soundness2.0s (19%)

Rules
4906×*-lowering-*.f32
4906×*-lowering-*.f64
4670×*-lowering-*.f32
4670×*-lowering-*.f64
4420×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05114349
117114223
261654198
080224198
05264310
117584177
264454173
080494173
04634784
115364617
254714582
080814582
02571162
18561135
230301098
080341098
037178
1281162
22819153
08632153
0619
14019
232419
3405519
0821819
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 390 to 201 computations (48.5% saved)

preprocess61.0ms (0.6%)

Compiler

Compiled 220 to 96 computations (56.4% saved)

end0.0ms (0%)

Profiling

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