ENA, Section 1.4, Exercise 4d

Time bar (total: 10.8s)

analyze24.0ms (0.2%)

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-mult: 5.0ms (38.8% of total)
ival-<=: 3.0ms (23.3% of total)
ival-sub: 2.0ms (15.5% of total)
ival-sqrt: 2.0ms (15.5% of total)
ival-and: 1.0ms (7.8% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.5s (13.5%)

Results
470.0ms4869×0valid
384.0ms2682×1valid
179.0ms705×2valid
17.0ms170×0invalid
Precisions
Click to see histograms. Total time spent on operations: 680.0ms
ival-mult: 159.0ms (23.4% of total)
ival-<=: 158.0ms (23.3% of total)
ival-sub: 147.0ms (21.6% of total)
ival-sqrt: 109.0ms (16% of total)
backward-pass: 64.0ms (9.4% of total)
ival-and: 26.0ms (3.8% of total)
const: 18.0ms (2.6% of total)
Bogosity

preprocess87.0ms (0.8%)

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)))

explain110.0ms (1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1210-0-(-.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
39.0ms274×0valid
29.0ms196×1valid
11.0ms42×2valid
Compiler

Compiled 64 to 20 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-sub: 8.0ms (27.5% of total)
backward-pass: 7.0ms (24.1% of total)
ival-mult: 7.0ms (24.1% of total)
ival-sqrt: 6.0ms (20.6% of total)
const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶56.6%
(-.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

localize39.0ms (0.4%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓accuracy56.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
13.0ms98×1valid
10.0ms137×0valid
7.0ms21×2valid
Compiler

Compiled 27 to 7 computations (74.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-sub: 4.0ms (30.8% of total)
ival-mult: 4.0ms (30.8% of total)
ival-sqrt: 3.0ms (23.1% of total)
backward-pass: 2.0ms (15.4% of total)
const: 0.0ms (0% of total)

series11.0ms (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
4.0ms
eps
@inf
(- (* x x) eps)
1.0ms
x
@inf
(- x (sqrt (- (* x x) eps)))
1.0ms
eps
@inf
(- x (sqrt (- (* x x) eps)))
1.0ms
eps
@0
(- x (sqrt (- (* x x) eps)))
1.0ms
x
@0
(- x (sqrt (- (* x x) eps)))

rewrite297.0ms (2.8%)

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)))

simplify298.0ms (2.8%)

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)

eval41.0ms (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
99.8%
Counts
294 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶56.5%
(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))))
56.2%
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
56.2%
(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))))))
▶56.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
39.0%
(/.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)
47.7%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
49.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
▶3.8%
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
▶7.0%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓56.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
51.7%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
4.2%
(-.f64 x x)
▶3.5%
(*.f64 x #s(literal 2 binary64))
33.5%
(*.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 510 to 276 computations (45.9% saved)

simplify254.0ms (2.4%)

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 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 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
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
✓cost-diff0
(-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓cost-diff64
(pow.f64 x #s(literal 1/2 binary64))
✓cost-diff19456
(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))))
Rules
2998×*-lowering-*.f32
2998×*-lowering-*.f64
2192×--lowering--.f32
2192×--lowering--.f64
1438×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
030183
187166
2238161
3716160
44294160
08162160
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(+ (* (pow x 1/2) (pow x 1/2)) (- 0 (pow (- (* x x) eps) 1/2)))
(pow x 1/2)
x
1/2
(- 0 (pow (- (* x x) eps) 1/2))
0
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(* x x)
eps
(* x 2)
x
2
(- x (+ x (* -1/2 (/ eps x))))
x
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
-1/2
(/ eps x)
eps
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
x
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
eps
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))
(/ -1/2 x)
-1/2
(/ (* eps -1/8) (* x (* x x)))
(* eps -1/8)
-1/8
(* x (* x x))
(* x x)
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
(- (* x x) (- (* x x) eps))
(* x x)
x
(- (* x x) eps)
eps
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
1/2
Outputs
(+ (* (pow x 1/2) (pow x 1/2)) (- 0 (pow (- (* x x) eps) 1/2)))
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(pow x 1/2)
(sqrt.f64 x)
x
1/2
#s(literal 1/2 binary64)
(- 0 (pow (- (* x x) eps) 1/2))
(-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
0
#s(literal 0 binary64)
(pow (- (* x x) eps) 1/2)
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(- x (+ x (* -1/2 (/ eps x))))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
x
(+ x (* -1/2 (/ eps x)))
(+.f64 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
#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 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
x
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))
(+.f64 x (*.f64 (/.f64 eps x) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/8 binary64) x)) x))))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
(*.f64 (/.f64 eps x) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/8 binary64) x)) x)))
eps
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/8 binary64) x)) x) x))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(/ (* eps -1/8) (* x (* x x)))
(/.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/8 binary64) x)) x) x)
(* eps -1/8)
(*.f64 eps #s(literal -1/8 binary64))
-1/8
#s(literal -1/8 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
(* x x)
(*.f64 x x)
(/ (- (* x 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)

localize374.0ms (3.5%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓accuracy99.9%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
✓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))))
✓accuracy100.0%
(*.f64 x (*.f64 x x))
✓accuracy99.9%
(-.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)))))))
✓accuracy90.4%
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
✓accuracy89.0%
(*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))
✓accuracy100.0%
(/.f64 eps x)
✓accuracy100.0%
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
✓accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
✓accuracy99.9%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
✓accuracy100.0%
(*.f64 x #s(literal 2 binary64))
✓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)
✓accuracy99.8%
(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))))
Results
232.0ms119×5exit
64.0ms137×0valid
Compiler

Compiled 228 to 30 computations (86.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 164.0ms
ival-pow: 39.0ms (23.8% of total)
ival-mult: 38.0ms (23.1% of total)
backward-pass: 38.0ms (23.1% of total)
ival-div: 14.0ms (8.5% of total)
ival-sub: 12.0ms (7.3% of total)
ival-add: 12.0ms (7.3% of total)
compiled-spec: 10.0ms (6.1% of total)
const: 2.0ms (1.2% of total)

series35.0ms (0.3%)

Counts
20 → 432
Calls
Call 1
Inputs
#<alt (+ (* (pow x 1/2) (pow x 1/2)) (- 0 (pow (- (* x x) eps) 1/2)))>
#<alt (pow x 1/2)>
#<alt (- 0 (pow (- (* x x) eps) 1/2))>
#<alt (pow (- (* x x) eps) 1/2)>
#<alt (* x 2)>
#<alt (- x (+ x (* -1/2 (/ eps x))))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ eps x)>
#<alt (- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))>
#<alt (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))>
#<alt (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))>
#<alt (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))>
#<alt (/ (- (* x 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 (/ (* eps -1/8) (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) 1)))>
#<alt (* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -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 x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* (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)))>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 (/ eps (pow x 2))) 1))>
#<alt (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 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 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* -1 x)>
#<alt (- (* 1/2 (/ eps x)) x)>
#<alt (- (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) x)>
#<alt (- (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) x)>
#<alt (* -1 (* (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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -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 (* (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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -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 (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (/ eps x)>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (- (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))>
#<alt (* -1 (/ (- (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))>
#<alt (* -1 (/ (- (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))>
#<alt (* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))>
#<alt (* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (/ -1/2 x)>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* -1 (* (sqrt eps) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1/8 (/ 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 (* (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)))))>
Calls

108 calls:

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

rewrite330.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
2498×*-lowering-*.f32
2498×*-lowering-*.f64
1980×fma-lowering-fma.f32
1980×fma-lowering-fma.f64
1962×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
030151
1239128
22721126
08527126
Stop Event
1×iter limit
1×node limit
Counts
20 → 696
Calls
Call 1
Inputs
(+ (* (pow x 1/2) (pow x 1/2)) (- 0 (pow (- (* x x) eps) 1/2)))
(pow x 1/2)
(- 0 (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(* x 2)
(- x (+ x (* -1/2 (/ eps x))))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(/ eps x)
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))
(- (* x x) (- (* x x) eps))
(* x x)
(- (* x x) eps)
(/ (* eps -1/8) (* x (* x x)))
(* x (* x x))
(+ x (pow (- (* x x) eps) 1/2))
Outputs
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) #s(literal -1 binary64)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fma.f64 (-.f64 (*.f64 x x) eps) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) x)
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) 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)
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) x)
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(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 #s(literal 0 binary64) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fma.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 #s(literal 0 binary64) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (+.f64 #s(literal 0 binary64) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (*.f64 (+.f64 (*.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 #s(literal 0 binary64) eps)) (*.f64 x (*.f64 x (-.f64 (*.f64 x x) eps)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 #s(literal 0 binary64) eps)) (*.f64 x (*.f64 x (-.f64 (*.f64 x x) eps))))))
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(/.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 #s(literal 0 binary64) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (*.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 #s(literal 0 binary64) eps)) (*.f64 x (*.f64 x (-.f64 (*.f64 x x) eps)))) (+.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) (+.f64 (*.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 #s(literal 0 binary64) eps)) (*.f64 x (*.f64 x (-.f64 (*.f64 x x) eps)))))
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(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)) #s(literal -1 binary64))
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(*.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 0 binary64) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (+.f64 #s(literal 0 binary64) eps))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (+.f64 #s(literal 0 binary64) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 #s(literal 0 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
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(*.f64 (pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 #s(literal 0 binary64) eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) eps)))

simplify397.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
5036×*-lowering-*.f32
5036×*-lowering-*.f64
2530×+-lowering-+.f64
2530×+-lowering-+.f32
1234×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05454795
118904486
272454485
082234485
Stop Event
1×iter limit
1×node limit
Counts
432 → 432
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)))
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(/ (- (* 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)
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x
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x
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* eps (+ (* 1/2 (* (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))))))
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(* 2 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
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(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(* -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 (/ eps (pow x 3)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ -1/2 x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (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)))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* -1/8 (/ eps (pow x 3)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* (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)))))
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64)))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (sqrt.f64 #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (+.f64 (/.f64 (*.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 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))) x)
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal -2 binary64))))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -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 x (*.f64 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))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(*.f64 (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x (*.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 (*.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)))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (+.f64 (/.f64 x eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (/.f64 x eps) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (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)))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (-.f64 (/.f64 x (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (-.f64 (/.f64 (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (-.f64 (/.f64 (-.f64 x (/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 eps) (*.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64)))) eps)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
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(* 2 x)
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(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (*.f64 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 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(* -1/8 (/ eps (pow x 3)))
(*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) #s(literal -1/8 binary64))))))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))))
(* 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 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 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 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) x)
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) (*.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 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64)))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x)) (*.f64 x #s(literal 2 binary64)))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 (*.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))) (*.f64 x #s(literal 2 binary64)))
(* (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 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)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(*.f64 eps (+.f64 (/.f64 x 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)) (/ x eps)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 x eps) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (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)))))))
(* -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 #s(literal 0 binary64) eps) (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (+.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 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 (sqrt.f64 eps) (*.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64))) (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (*.f64 x (*.f64 x x))))))) eps)) eps))))

eval315.0ms (2.9%)

Compiler

Compiled 37761 to 3433 computations (90.9% saved)

prune197.0ms (1.8%)

Pruning

27 alts after pruning (25 fresh and 2 done)

PrunedKeptTotal
New1506211527
Fresh549
Picked415
Done011
Total1515271542
Accuracy
100.0%
Counts
1542 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64))))
5.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x)) (*.f64 x #s(literal 2 binary64))))
▶7.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #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 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
47.7%
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
49.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
▶99.6%
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
39.1%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
▶49.5%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
5.3%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
6.2%
(-.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))))
7.0%
(-.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
7.0%
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
4.5%
(-.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))))
5.5%
(-.f64 x (*.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
4.1%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))))))
▶6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
6.9%
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
✓56.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
51.7%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
▶4.2%
(-.f64 x x)
43.7%
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (+.f64 #s(literal 0 binary64) eps))
39.2%
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))))
49.5%
(*.f64 (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
✓3.5%
(*.f64 x #s(literal 2 binary64))
34.9%
(*.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 1085 to 562 computations (48.2% saved)

simplify185.0ms (1.7%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
✓cost-diff384
(*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
✓cost-diff1408
(/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))
✓cost-diff1536
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
✓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 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
✓cost-diff0
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))
✓cost-diff256
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓cost-diff512
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓cost-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
2516×*-lowering-*.f32
2516×*-lowering-*.f64
2072×fma-lowering-fma.f32
2072×fma-lowering-fma.f64
1368×fmm-def
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
030240
192202
2243192
31162165
47774165
08425165
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)
(/ (- (* x x) (- (* x x) eps)) (+ x (+ x (/ (* eps -1/2) x))))
(- (* x x) (- (* x x) eps))
(* x x)
x
(- (* x x) eps)
eps
(+ x (+ x (/ (* eps -1/2) x)))
(+ x (/ (* eps -1/2) x))
(/ (* eps -1/2) x)
(* eps -1/2)
-1/2
(/ 1 (/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))))
1
(/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x)))))
(+ x (+ x (* -1/2 (/ eps x))))
x
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
-1/2
(/ eps x)
eps
(* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))
(- 0 (* -1/2 (/ eps x)))
0
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 (*.f64 eps #s(literal 1/2 binary64)) x)
x
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ 1 (/ (* eps -1/2) (* x x)))
(+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
1
#s(literal 1 binary64)
(/ (* eps -1/2) (* x x))
(/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
(/ (- (* x x) (- (* x x) eps)) (+ x (+ x (/ (* eps -1/2) x))))
(/.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.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 (+ x (/ (* eps -1/2) x)))
(+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64)))
(+ x (/ (* eps -1/2) x))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/ (* eps -1/2) x)
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ 1 (/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x)))))
(/.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (+ x (* -1/2 (/ eps x))))
(+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64)))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 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
#s(literal -1/2 binary64)
(/ eps x)
(/.f64 eps x)
eps
(* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))
(-.f64 eps (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))
(- 0 (* -1/2 (/ eps x)))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
0
#s(literal 0 binary64)

localize210.0ms (2%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
✓accuracy99.6%
(*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
✓accuracy99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
✓accuracy93.1%
(/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
✓accuracy99.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
✓accuracy57.2%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))
✓accuracy85.6%
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
✓accuracy84.6%
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓accuracy56.6%
(-.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%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
✓accuracy100.0%
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓accuracy99.6%
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
Results
83.0ms103×1valid
45.0ms137×0valid
28.0ms16×2valid
Compiler

Compiled 267 to 31 computations (88.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 94.0ms
ival-mult: 23.0ms (24.5% of total)
ival-pow: 20.0ms (21.3% of total)
ival-div: 19.0ms (20.2% of total)
ival-add: 11.0ms (11.7% of total)
backward-pass: 10.0ms (10.6% of total)
ival-sub: 9.0ms (9.6% of total)
const: 1.0ms (1.1% of total)

series42.0ms (0.4%)

Counts
18 → 408
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 (/ (- (* x x) (- (* x x) eps)) (+ x (+ x (/ (* eps -1/2) x))))>
#<alt (- (* x x) (- (* x x) eps))>
#<alt (* x x)>
#<alt (/ 1 (/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))))>
#<alt (/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x)))))>
#<alt (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))>
#<alt (- 0 (* -1/2 (/ eps x)))>
#<alt (+ x (+ x (/ (* eps -1/2) x)))>
#<alt (+ x (+ x (* -1/2 (/ eps 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 (* -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) (* -1/32 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1/2 eps) (* -1/128 (/ (pow eps 4) (pow x 6)))) (+ (* 1/32 (/ (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 (+ (* 1/32 (/ 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 (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* 2 (/ x eps))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))>
#<alt eps>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt eps>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt (+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1/2 (/ 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 (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
Calls

102 calls:

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

rewrite465.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
4720×*-lowering-*.f32
4720×*-lowering-*.f64
2746×/-lowering-/.f32
2746×/-lowering-/.f64
2558×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
030179
1265135
22312112
010632112
Stop Event
1×iter limit
1×node limit
Counts
18 → 918
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))
(/ (- (* x x) (- (* x x) eps)) (+ x (+ x (/ (* eps -1/2) x))))
(- (* x x) (- (* x x) eps))
(* x x)
(/ 1 (/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))))
(/ (+ x (+ x (* -1/2 (/ eps x)))) (* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x)))))
(* (+ x (+ x (* -1/2 (/ eps x)))) (- 0 (* -1/2 (/ eps x))))
(- 0 (* -1/2 (/ eps x)))
(+ x (+ x (/ (* eps -1/2) x)))
(+ x (+ x (* -1/2 (/ eps 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)))
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(/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))))
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x))) (/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) #s(literal -1 binary64))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x))) (/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x)))))
(*.f64 (*.f64 (/.f64 (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)) #s(literal 1 binary64)) x)

simplify439.0ms (4.1%)

Algorithm
1×egg-herbie
Rules
4442×*-lowering-*.f32
4442×*-lowering-*.f64
2224×+-lowering-+.f64
2224×+-lowering-+.f32
1658×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05093838
117203692
262583667
082343667
Stop Event
1×iter limit
1×node limit
Counts
408 → 408
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)))))
0
0
0
0
0
0
0
0
0
0
0
0
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
1
(+ 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)))
(* 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))))
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(* -1/2 (/ eps (pow x 2)))
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(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
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(* -1/2 (/ eps (pow x 2)))
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(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (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))
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(* -1 (/ (- (+ (* -1/2 eps) (* -1/32 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1/2 eps) (* -1/128 (/ (pow eps 4) (pow x 6)))) (+ (* 1/32 (/ (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 (+ (* 1/32 (/ 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
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(pow x 2)
(pow x 2)
(pow x 2)
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(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
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(* -1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
(/ (+ (* -1/4 (pow eps 2)) (* eps (pow x 2))) (pow x 2))
eps
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
eps
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
(+ eps (* -1/4 (/ (pow eps 2) (pow x 2))))
eps
(* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))
(* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))
(* eps (+ 1 (* -1/4 (/ eps (pow x 2)))))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -1/2 (/ 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)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(* -1/2 (/ eps x))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
Outputs
(* 1/2 (/ eps x))
(*.f64 #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 eps (/.f64 #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 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.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)))
(-.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 (neg.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 eps (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)))))) 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 x (*.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)))))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))))))))
(* 1/2 (/ eps x))
(*.f64 #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 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (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 #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 (*.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))))) 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))) (neg.f64 (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 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) eps) (+.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/4 binary64)))) #s(literal -1/8 binary64)) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) eps)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (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 eps #s(literal -1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 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 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) eps))) (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)))))
(*.f64 eps (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) eps))) (sqrt.f64 #s(literal -1 binary64)))) (*.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)))
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(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(/.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 x x))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* (pow eps 2) (- (/ 1 eps) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 x x)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* 1/2 (/ 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 (- (* 1/2 (/ 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))
(* 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 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x 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))))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (*.f64 x #s(literal 2 binary64)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 x x)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* 1/2 (/ 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 (- (* 1/2 (/ 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))
(* 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 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x 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))))

eval311.0ms (2.9%)

Compiler

Compiled 45102 to 3593 computations (92% saved)

prune232.0ms (2.1%)

Pruning

51 alts after pruning (49 fresh and 2 done)

PrunedKeptTotal
New1531441575
Fresh15520
Picked505
Done022
Total1551511602
Accuracy
100.0%
Counts
1602 → 51
Alt Table
Click to see full alt table
StatusAccuracyProgram
19.3%
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
8.9%
(/.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 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
4.1%
(/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.7%
(/.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 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.1%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (-.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 x x)) (-.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x)))
3.6%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
4.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))))
2.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))))
7.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x))
5.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x)) (*.f64 x #s(literal 2 binary64))))
▶7.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
3.9%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.8%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x x))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.7%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
7.3%
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
33.0%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
49.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
50.4%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
45.5%
(/.f64 eps (+.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)))))
50.4%
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
▶99.6%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶50.1%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
32.6%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 x x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 x x))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
32.9%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))))
5.7%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
6.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
43.5%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
5.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
48.8%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/4 binary64)) (*.f64 x x))))))
50.2%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) eps))
49.0%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
49.5%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
31.1%
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
49.5%
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
7.0%
(-.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) x)
▶4.1%
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
5.3%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
4.1%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
4.6%
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
6.7%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 x eps)))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))))
6.7%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x eps) x)))))
✓56.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
51.7%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
32.9%
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
✓3.5%
(*.f64 x #s(literal 2 binary64))
5.5%
(*.f64 x #s(literal -2 binary64))
43.3%
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))))
34.9%
(*.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)))))
49.5%
(*.f64 eps (neg.f64 (/.f64 #s(literal -1/2 binary64) x)))
▶4.2%
#s(literal 0 binary64)
Compiler

Compiled 2675 to 1350 computations (49.5% saved)

simplify252.0ms (2.3%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
✓cost-diff128
(+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
✓cost-diff128
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
✓cost-diff128
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
✓cost-diff0
(*.f64 x x)
✓cost-diff128
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) 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 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
✓cost-diff0
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
✓cost-diff0
(+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))
✓cost-diff128
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓cost-diff128
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.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)))
✓cost-diff0
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Rules
2996×*-lowering-*.f32
2996×*-lowering-*.f64
1840×fnmadd-define
1648×--lowering--.f32
1648×--lowering--.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
036293
1109280
2300272
3805268
44545254
08056254
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 (* x (+ 2 (/ (* eps -1/2) (* x x)))))
eps
(* x (+ 2 (/ (* eps -1/2) (* x x))))
x
(+ 2 (/ (* eps -1/2) (* x x)))
2
(/ (* eps -1/2) (* x x))
(* eps -1/2)
-1/2
(* x x)
(/ (- (* x x) (- (* x x) eps)) (* eps (+ (* 2 (/ x eps)) (/ -1/2 x))))
(- (* x x) (- (* x x) eps))
(* x x)
x
(- (* x x) eps)
eps
(* eps (+ (* 2 (/ x eps)) (/ -1/2 x)))
(+ (* 2 (/ x eps)) (/ -1/2 x))
(* 2 (/ x eps))
2
(/ x eps)
(/ -1/2 x)
-1/2
(- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))
x
(/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))))
(+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))))
(* x (* x x))
(* x x)
(/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))
(* (* eps (* eps eps)) -1/8)
(* eps (* eps eps))
eps
(* eps eps)
-1/8
(+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))
(/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))
(- (/ -1/2 (/ x eps)) x)
(/ -1/2 (/ x eps))
-1/2
(/ x eps)
(/ x (* eps -1/2))
(* eps -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 (* x (+ 2 (/ (* eps -1/2) (* x x)))))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
eps
(* x (+ 2 (/ (* eps -1/2) (* x x))))
(+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64)))
x
(+ 2 (/ (* eps -1/2) (* x x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) eps)))
2
#s(literal 2 binary64)
(/ (* eps -1/2) (* x x))
(/.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) eps))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
(/ (- (* x x) (- (* x x) eps)) (* eps (+ (* 2 (/ x eps)) (/ -1/2 x))))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x)))
(- (* x x) (- (* x x) eps))
eps
(* x x)
(*.f64 x x)
x
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
(* eps (+ (* 2 (/ x eps)) (/ -1/2 x)))
(+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64)))
(+ (* 2 (/ x eps)) (/ -1/2 x))
(+.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal -1/2 binary64) x))
(* 2 (/ x eps))
(/.f64 (*.f64 x #s(literal 2 binary64)) eps)
2
#s(literal 2 binary64)
(/ x eps)
(/.f64 x eps)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))
(+.f64 x (/.f64 (-.f64 (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))))))
x
(/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)))))
(+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))))
(+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x))))
(* x (* x x))
(*.f64 x (*.f64 x x))
(* x x)
(*.f64 x x)
(/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))
(/.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(* (* eps (* eps eps)) -1/8)
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)))
(* eps (* eps eps))
(*.f64 eps (*.f64 eps eps))
eps
(* eps eps)
(*.f64 eps eps)
-1/8
#s(literal -1/8 binary64)
(+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))
(+.f64 (*.f64 x x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))))
(/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)))
(- (/ -1/2 (/ x eps)) x)
(-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x)
(/ -1/2 (/ x eps))
(/.f64 eps (/.f64 x #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(/ x eps)
(/.f64 x eps)
(/ x (* eps -1/2))
(/.f64 (/.f64 x eps) #s(literal -1/2 binary64))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))

localize287.0ms (2.7%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy99.5%
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
✓accuracy80.1%
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
✓accuracy59.8%
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
✓accuracy56.6%
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
✓accuracy100.0%
(+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))
✓accuracy99.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
✓accuracy99.6%
(*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))
✓accuracy57.2%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
✓accuracy100.0%
(*.f64 eps #s(literal -1/2 binary64))
✓accuracy99.9%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓accuracy85.6%
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))
✓accuracy84.5%
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(sqrt.f64 (-.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
78.0ms98×1valid
71.0ms137×0valid
26.0ms21×2valid
Compiler

Compiled 349 to 37 computations (89.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 98.0ms
ival-div: 36.0ms (36.9% of total)
ival-mult: 27.0ms (27.7% of total)
backward-pass: 11.0ms (11.3% of total)
ival-sub: 9.0ms (9.2% of total)
ival-add: 9.0ms (9.2% of total)
ival-sqrt: 3.0ms (3.1% of total)
const: 1.0ms (1% of total)

series38.0ms (0.4%)

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 (* x (+ 2 (/ (* eps -1/2) (* x x)))))>
#<alt (* x (+ 2 (/ (* eps -1/2) (* x x))))>
#<alt (+ 2 (/ (* eps -1/2) (* x x)))>
#<alt (/ (* eps -1/2) (* x x))>
#<alt (/ (- (* x x) (- (* x x) eps)) (* eps (+ (* 2 (/ x eps)) (/ -1/2 x))))>
#<alt (- (* x x) (- (* x x) eps))>
#<alt (* eps (+ (* 2 (/ x eps)) (/ -1/2 x)))>
#<alt (* x x)>
#<alt (- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))>
#<alt (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))))>
#<alt (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))>
#<alt (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))>
#<alt (* eps -1/2)>
#<alt (+ (* 2 (/ x eps)) (/ -1/2 x))>
#<alt (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))>
#<alt (/ -1/2 (/ x eps))>
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 (+ (* 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 (* -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 (/ (+ (* -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 2>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* eps (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* eps (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* eps (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt 2>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 2 (* -1/2 (/ eps (pow x 2))))>
#<alt (+ 2 (* -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 (* -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) (* -1/32 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1/2 eps) (* -1/128 (/ (pow eps 4) (pow x 6)))) (+ (* 1/32 (/ (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 (+ (* 1/32 (/ 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 (* 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 (* -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 (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)>
#<alt (/ (+ (* -1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))) x)>
#<alt (/ (- (+ (* -1/2 (/ (* eps (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3)))) (pow x 6))) (+ (* -1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (* (pow eps 2) (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))))) (* 1/16 (/ (pow eps 4) (pow x 6)))) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 2))) (* 1/2 eps)) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (+ (* -1/8 (pow eps 3)) (* 1/8 (pow eps 3)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))))) (+ (* -1/4 (* (pow eps 2) (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/16 (pow eps 4)))) (pow x 6))) (+ (* -1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))))) x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (+ (* -1 (/ (+ (* -4 (pow x 5)) (+ (* -2 (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3))))) (* 4 (pow x 5)))) (pow eps 3))) (* 1/2 (/ 1 x))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (* 2 (/ (pow x 3) (pow eps 2))))))>
#<alt (* eps (- (+ (* 8 (/ (pow x 7) (pow eps 4))) (* 1/2 (/ 1 x))) (+ (* -4 (/ (* (pow x 4) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) (pow eps 4))) (+ (* -4 (/ (pow x 5) (pow eps 3))) (+ (* -2 (/ (* (pow x 2) (+ (* -4 (pow x 5)) (* -2 (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3))))))) (pow eps 4))) (+ (* -2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) (pow eps 3))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (+ (* 2 (/ (pow x 3) (pow eps 2))) (* 4 (/ (pow x 5) (pow eps 3)))))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) eps)))) eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (+ (* -2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)))) eps)) (* 1/2 (/ 1 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 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6)))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))))>
#<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 (- (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* eps (- (* 2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) (pow eps 3))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (+ (* -1 (/ x eps)) (+ (* 2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x)))))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (+ (* -2 (/ (pow x 3) eps)) (* 2 (/ (pow x 3) eps))) (* -1 x)) eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* -1 (/ (- (* 2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)) (* -1 x)) eps)) (* 1/2 (/ 1 x)))))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* 1/2 eps) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* 1/2 eps) (pow x 2)))) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))>
#<alt (pow x 2)>
#<alt (+ (* 1/2 eps) (pow x 2))>
#<alt (+ (* eps (+ 1/2 (* 1/4 (/ eps (pow x 2))))) (pow x 2))>
#<alt (+ (* eps (+ 1/2 (* 1/4 (/ eps (pow x 2))))) (pow x 2))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow x 2) eps)) 1/2) eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow x 2) eps)) 1/2) eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* 1/4 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1/2 (* 1/4 (/ eps (pow x 2)))))>
#<alt (* eps (+ 1/2 (* 1/4 (/ eps (pow x 2)))))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (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 x)>
#<alt (/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)>
#<alt (/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)>
#<alt (/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)>
#<alt (* 2 (/ x eps))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 2 (/ x eps))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* 2 (/ x eps))>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ -1/2 x)>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (/ -1/2 x)>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/8 (/ (pow eps 3) (pow x 3)))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1/2 (/ eps x))>
Calls

114 calls:

TimeVariablePointExpression
5.0ms
eps
@0
(- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))
5.0ms
x
@0
(- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))
3.0ms
eps
@-inf
(/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))
1.0ms
x
@inf
(- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))
1.0ms
eps
@inf
(- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))

rewrite331.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
3260×*-lowering-*.f32
3260×*-lowering-*.f64
2586×/-lowering-/.f32
2586×/-lowering-/.f64
2398×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035219
1278198
23053192
08494192
Stop Event
1×iter limit
1×node limit
Counts
20 → 609
Calls
Call 1
Inputs
(/ eps (+ x (sqrt (- (* x x) eps))))
(+ x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(/ eps (* x (+ 2 (/ (* eps -1/2) (* x x)))))
(* x (+ 2 (/ (* eps -1/2) (* x x))))
(+ 2 (/ (* eps -1/2) (* x x)))
(/ (* eps -1/2) (* x x))
(/ (- (* x x) (- (* x x) eps)) (* eps (+ (* 2 (/ x eps)) (/ -1/2 x))))
(- (* x x) (- (* x x) eps))
(* eps (+ (* 2 (/ x eps)) (/ -1/2 x)))
(* x x)
(- x (/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))))
(/ (+ (* x (* x x)) (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))) (+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))))
(+ (* x x) (/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2))))
(/ (- (/ -1/2 (/ x eps)) x) (/ x (* eps -1/2)))
(* eps -1/2)
(+ (* 2 (/ x eps)) (/ -1/2 x))
(/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))
(/ -1/2 (/ x eps))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(*.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) eps)
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(*.f64 (/.f64 eps (+.f64 eps #s(literal 0 binary64))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 eps (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
(/.f64 (+.f64 eps #s(literal 0 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 eps #s(literal 0 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 x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(pow.f64 (/.f64 (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 eps #s(literal 0 binary64))) #s(literal -1 binary64))
(*.f64 (+.f64 eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 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)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
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(*.f64 (/.f64 eps x) (pow.f64 (/.f64 (*.f64 x x) (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) x))
(*.f64 (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 x (*.f64 x x)))
(*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) x))
(*.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))))
(*.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) x) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))
(*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) #s(literal -1/8 binary64))
(*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 3 binary64)))
(*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))) #s(literal 3 binary64)))
(*.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) x))
(*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) x))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x x)))
(*.f64 (pow.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) #s(literal 3/2 binary64)) (pow.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))
(*.f64 (pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 x (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 x x) (*.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 x x) (*.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)) (pow.f64 (/.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))
(*.f64 (pow.f64 (*.f64 x (/.f64 eps x)) #s(literal 3 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 eps (/.f64 x #s(literal -1/2 binary64)))
(/.f64 x (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps)))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 x (/.f64 (/.f64 x #s(literal -1/2 binary64)) eps)) x)
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal -1/2 binary64)) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) eps) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -2 binary64) eps))
(/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) eps) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (*.f64 x (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x x))
(/.f64 (*.f64 x (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x x))
(/.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))
(pow.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 eps (/.f64 #s(literal -1/2 binary64) x))
(*.f64 eps (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))
(*.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 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))) x)
(*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x eps))))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(*.f64 (/.f64 eps x) (*.f64 (/.f64 #s(literal -1/2 binary64) x) x))
(*.f64 #s(literal 1 binary64) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))
(*.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 -2 binary64) eps) #s(literal -1 binary64)))
(*.f64 (*.f64 x eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 x (*.f64 eps #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(*.f64 (*.f64 x (/.f64 eps x)) (/.f64 #s(literal -1/2 binary64) x))
(*.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 -2 binary64) eps) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))

simplify320.0ms (3%)

Algorithm
1×egg-herbie
Rules
5834×*-lowering-*.f32
5834×*-lowering-*.f64
4042×+-lowering-+.f64
4042×+-lowering-+.f32
1748×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07225421
125344984
090274984
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 (+ (* 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)))
(* -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))
(/ (+ (* -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)))))
2
(+ 2 (* -1/2 (/ eps (pow x 2))))
(+ 2 (* -1/2 (/ eps (pow x 2))))
(+ 2 (* -1/2 (/ eps (pow x 2))))
(* -1/2 (/ eps (pow x 2)))
(* eps (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ eps (pow x 2)))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1/2 (/ eps (pow x 2)))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) (pow x 2))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) (pow x 2))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) (pow x 2))
2
(+ 2 (* -1/2 (/ eps (pow x 2))))
(+ 2 (* -1/2 (/ eps (pow x 2))))
(+ 2 (* -1/2 (/ eps (pow x 2))))
2
(+ 2 (* -1/2 (/ eps (pow x 2))))
(+ 2 (* -1/2 (/ eps (pow x 2))))
(+ 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 (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) (* -1/32 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1/2 eps) (* -1/128 (/ (pow eps 4) (pow x 6)))) (+ (* 1/32 (/ (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 (+ (* 1/32 (/ 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
(* 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)))))
(* -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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* -1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))) x)
(/ (- (+ (* -1/2 (/ (* eps (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3)))) (pow x 6))) (+ (* -1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (* (pow eps 2) (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))))) (* 1/16 (/ (pow eps 4) (pow x 6)))) x)
(* 1/2 (/ eps x))
(* -1 (/ (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 2))) (* 1/2 eps)) x))
(* -1 (/ (- (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (+ (* -1/8 (pow eps 3)) (* 1/8 (pow eps 3)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))) x))
(* -1 (/ (- (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))))) (+ (* -1/4 (* (pow eps 2) (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/16 (pow eps 4)))) (pow x 6))) (+ (* -1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 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))
(* eps (+ (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x))))
(* eps (- (+ (* -1 (/ (+ (* -4 (pow x 5)) (+ (* -2 (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3))))) (* 4 (pow x 5)))) (pow eps 3))) (* 1/2 (/ 1 x))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (* 2 (/ (pow x 3) (pow eps 2))))))
(* eps (- (+ (* 8 (/ (pow x 7) (pow eps 4))) (* 1/2 (/ 1 x))) (+ (* -4 (/ (* (pow x 4) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) (pow eps 4))) (+ (* -4 (/ (pow x 5) (pow eps 3))) (+ (* -2 (/ (* (pow x 2) (+ (* -4 (pow x 5)) (* -2 (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3))))))) (pow eps 4))) (+ (* -2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) (pow eps 3))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (+ (* 2 (/ (pow x 3) (pow eps 2))) (* 4 (/ (pow x 5) (pow eps 3)))))))))))
(* 1/2 (/ eps x))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) eps)))) eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (+ (* -2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)))) eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6)))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/2 (/ (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* eps (- (* 2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) (pow eps 3))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (+ (* -1 (/ x eps)) (+ (* 2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x)))))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ (- (+ (* -2 (/ (pow x 3) eps)) (* 2 (/ (pow x 3) eps))) (* -1 x)) eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ (- (* -1 (/ (- (* 2 (/ (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)) (* -1 x)) eps)) (* 1/2 (/ 1 x)))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* 1/2 eps) (pow x 2)))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* 1/2 eps) (pow x 2)))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))
(* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))
(* (pow x 2) (+ 1 (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))))
(pow x 2)
(+ (* 1/2 eps) (pow x 2))
(+ (* eps (+ 1/2 (* 1/4 (/ eps (pow x 2))))) (pow x 2))
(+ (* eps (+ 1/2 (* 1/4 (/ eps (pow x 2))))) (pow x 2))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow x 2) eps)) 1/2) eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow x 2) eps)) 1/2) eps)) (* 1/4 (/ 1 (pow x 2)))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(* 1/2 eps)
(+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(* 1/2 eps)
(+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (* 1/4 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* 1/4 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* 1/4 (/ eps (pow x 2)))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (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 x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(* 2 (/ x eps))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* 2 (/ x eps))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* 2 (/ x eps))
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ -1/2 x)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(/ -1/2 x)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
Outputs
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) eps) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 5/128 binary64) eps) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
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(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
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(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
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(/.f64 (*.f64 #s(literal 1/2 binary64) 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 (*.f64 eps eps) #s(literal 1/16 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps))) 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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(*.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)))))))
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(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
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(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
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(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
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(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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x
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2
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(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) eps) #s(literal -1/2 binary64)) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) eps) #s(literal -1/2 binary64)) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) eps) #s(literal -1/2 binary64)) x)
(* 2 (/ x eps))
(*.f64 #s(literal 2 binary64) (/.f64 x eps))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(* 2 (/ x eps))
(*.f64 #s(literal 2 binary64) (/.f64 x eps))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal -2 binary64) eps)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal -2 binary64) eps)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal -2 binary64) eps)))
(* 2 (/ x eps))
(*.f64 #s(literal 2 binary64) (/.f64 x eps))
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* -1/8 (/ (pow eps 3) (pow x 3)))
(/.f64 (*.f64 eps (*.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 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)

eval178.0ms (1.7%)

Compiler

Compiled 39085 to 3339 computations (91.5% saved)

prune218.0ms (2%)

Pruning

73 alts after pruning (69 fresh and 4 done)

PrunedKeptTotal
New1208331241
Fresh83644
Picked325
Done022
Total1219731292
Accuracy
100.0%
Counts
1292 → 73
Alt Table
Click to see full alt table
StatusAccuracyProgram
19.3%
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
23.4%
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) eps)
8.9%
(/.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 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
8.9%
(/.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 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
50.1%
(/.f64 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
6.4%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))) (*.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 (*.f64 x x) eps))) (*.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))))
4.1%
(/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.7%
(/.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 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.7%
(/.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 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
5.1%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (-.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 x x)) (-.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x)))
3.6%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
4.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))))
6.7%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) eps) (-.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
2.6%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 8 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x)))) eps) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))))
7.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x))
5.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x)) (*.f64 x #s(literal 2 binary64))))
2.6%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 x #s(literal -1/2 binary64))))))))
6.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (/.f64 (+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) x) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))))
6.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
5.8%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x x))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
5.7%
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
33.0%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
22.5%
(/.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 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
22.6%
(/.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 (/.f64 #s(literal 1 binary64) eps) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))
31.0%
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))
49.7%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
5.5%
(/.f64 eps (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
50.4%
(/.f64 eps (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64))))
45.5%
(/.f64 eps (+.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)))))
50.4%
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
✓99.6%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
27.9%
(/.f64 eps (*.f64 x (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (+.f64 (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 x x)) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))))))
5.2%
(/.f64 eps (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
50.3%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x))))
50.1%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))))
50.3%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))))
50.0%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (*.f64 eps #s(literal -1/2 binary64))))))
50.3%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
50.1%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
48.4%
(/.f64 eps (*.f64 x (*.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))))
50.3%
(/.f64 eps (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
32.9%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))))
50.2%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64))) eps))
5.7%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
6.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
43.5%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
5.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
48.8%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/4 binary64)) (*.f64 x x))))))
49.0%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
49.5%
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
31.1%
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
49.5%
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
7.0%
(-.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) x)
4.5%
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
4.8%
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
5.3%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
4.1%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
4.6%
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
6.7%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 x eps)))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))))
6.7%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x eps) x)))))
✓56.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
51.7%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
48.4%
(*.f64 (/.f64 (/.f64 eps x) (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 x x)))) (-.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
50.1%
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 eps #s(literal 0 binary64)))
50.1%
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
50.2%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64)))) eps)
32.9%
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
50.2%
(*.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 0 binary64) eps))))
✓3.5%
(*.f64 x #s(literal 2 binary64))
5.5%
(*.f64 x #s(literal -2 binary64))
49.5%
(*.f64 eps (neg.f64 (/.f64 #s(literal -1/2 binary64) x)))
✓4.2%
#s(literal 0 binary64)
Compiler

Compiled 4744 to 1480 computations (68.8% saved)

regimes195.0ms (1.8%)

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

3 calls:

66.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
60.0ms
eps
48.0ms
x
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
99.6%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes118.0ms (1.1%)

Counts
105 → 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 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(*.f64 eps (neg.f64 (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 eps (/.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 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(-.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) x)
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (*.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 eps (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64)))) eps)
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x eps) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64))) eps))
(/.f64 eps (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
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(/.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 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) 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 (*.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 (/.f64 #s(literal 1 binary64) eps) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) 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 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
(-.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 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
Calls

3 calls:

41.0ms
eps
29.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
29.0ms
x
Results
AccuracySegmentsBranch
87.9%2x
81.0%4eps
98.9%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes47.0ms (0.4%)

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 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(*.f64 eps (neg.f64 (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 eps (/.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 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(-.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) x)
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (*.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 eps (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64)))) eps)
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x eps) x)))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 x #s(literal 2 binary64))) eps))
(/.f64 eps (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) eps))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) 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 eps (/.f64 x #s(literal -1/2 binary64))) x))))
(/.f64 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))))))
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 x eps)))))
(-.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (*.f64 eps #s(literal -1/2 binary64))))))
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))))
(/.f64 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 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) eps)
(*.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 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (+.f64 eps #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 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 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 0 binary64) eps))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 eps (+.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)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x 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 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/4 binary64)) (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (*.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (/.f64 (+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) x) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x)) (*.f64 x #s(literal 2 binary64))))
(/.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 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(*.f64 (/.f64 (/.f64 eps x) (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 x x)))) (-.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps 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 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 eps (*.f64 x (*.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x 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 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x x))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.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 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.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 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) eps) (-.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (-.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 x x)) (-.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) x)))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))))) (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (*.f64 x (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (+.f64 (/.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 x x)) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 x x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 x x))) (*.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 8 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x)))) eps) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (+.f64 (*.f64 x x) #s(literal 0 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))) (*.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 (*.f64 x x) eps))) (*.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x))) (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 eps (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 x #s(literal -1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (*.f64 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) x)) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.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 (*.f64 eps (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) 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 (*.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 (/.f64 #s(literal 1 binary64) eps) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 x eps)) (/.f64 #s(literal -1/2 binary64) 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 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x)))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps x) (/.f64 eps x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) (/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
Outputs
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
Calls

1 calls:

28.0ms
x
Results
AccuracySegmentsBranch
86.8%2x
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes103.0ms (1%)

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

2 calls:

51.0ms
eps
46.0ms
x
Results
AccuracySegmentsBranch
50.4%1eps
50.4%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (0.2%)

Counts
17 → 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 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(*.f64 eps (neg.f64 (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 eps (/.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 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(-.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) x)
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (*.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))))
Outputs
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

2 calls:

15.0ms
x
5.0ms
eps
Results
AccuracySegmentsBranch
50.4%1x
50.4%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts
16 → 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 #s(literal 1/2 binary64) (/.f64 x eps))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(*.f64 eps (neg.f64 (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(/.f64 eps (/.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 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(-.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) x)
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (*.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
Outputs
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
Calls

2 calls:

5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
49.7%1x
49.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
5 → 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 #s(literal 1/2 binary64) (/.f64 x eps))
Outputs
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
Calls

2 calls:

2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
49.5%1x
49.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

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:

7.0ms
eps
2.0ms
x
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
eps
1.0ms
x
Results
AccuracySegmentsBranch
4.2%1x
4.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-4.9504167048607757e-154
-6.780516674269231e-156
Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch17.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
16.0ms
5.0459097812721e-124
2.843940838612873e-123
Results
7.0ms22×1valid
4.0ms74×0valid
1.0ms15×0invalid
Compiler

Compiled 165 to 118 computations (28.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-sub: 6.0ms (69.9% of total)
ival-mult: 1.0ms (11.7% of total)
ival-sqrt: 1.0ms (11.7% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
040100
158100
268100
373100
475100
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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(if (<=.f64 x #s(literal 520997997575091/186070713419675363980626894819329160794532188335953423432061490990243657757029868371504908982723472783555205531204141550984858016925351936 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(*.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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(if (<=.f64 x #s(literal 520997997575091/186070713419675363980626894819329160794532188335953423432061490990243657757029868371504908982723472783555205531204141550984858016925351936 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 (/.f64 eps x) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(*.f64 x #s(literal -2 binary64))
#s(literal 0 binary64)

soundness2.3s (21.5%)

Rules
5036×*-lowering-*.f32
5036×*-lowering-*.f64
4906×*-lowering-*.f32
4906×*-lowering-*.f64
4720×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030179
1265135
22312112
010632112
035219
1278198
23053192
08494192
05093838
117203692
262583667
082343667
05454795
118904486
272454485
082234485
0619
14019
232419
3405519
0821819
02571162
18561135
230301098
080341098
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 463 to 245 computations (47.1% saved)

preprocess76.0ms (0.7%)

Compiler

Compiled 250 to 106 computations (57.6% saved)

end0.0ms (0%)

Profiling

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