ENA, Section 1.4, Exercise 4d

Time bar (total: 9.9s)

analyze22.0ms (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: 10.0ms
ival-<=: 3.0ms (30.2% of total)
ival-sub: 2.0ms (20.2% of total)
ival-mult: 2.0ms (20.2% of total)
ival-sqrt: 2.0ms (20.2% of total)
ival-and: 1.0ms (10.1% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.5s (15.5%)

Results
492.0ms2749×1valid
462.0ms4805×0valid
198.0ms702×2valid
10.0ms135×0invalid
Precisions
Click to see histograms. Total time spent on operations: 744.0ms
ival-<=: 204.0ms (27.4% of total)
ival-mult: 164.0ms (22% of total)
ival-sub: 149.0ms (20% of total)
ival-sqrt: 113.0ms (15.2% of total)
backward-pass: 63.0ms (8.5% of total)
ival-and: 31.0ms (4.2% of total)
const: 20.0ms (2.7% of total)
Bogosity

preprocess63.0ms (0.6%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02148
16046
215243
342943
4113443
5207343
6231743
7234143
067
1137
2217
3357
4587
51347
63457
75397
87177
99417
1011057
1111177
011177
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 (- (square x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- (neg x) (sqrt (- (square 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 (- (square 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)))

explain122.0ms (1.2%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1060-0-(-.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
27.0ms162×1valid
20.0ms304×0valid
10.0ms46×2valid
Compiler

Compiled 64 to 20 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-sqrt: 9.0ms (30.5% of total)
ival-sub: 9.0ms (30.5% of total)
ival-mult: 7.0ms (23.7% of total)
backward-pass: 4.0ms (13.6% 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
▶62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

simplify26.0ms (0.3%)

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
0620
11320
22120
33520
45820
513420
634520
753920
871720
994120
10110520
11111720
0111720
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

localize38.0ms (0.4%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
13.0ms152×0valid
11.0ms81×1valid
5.0ms23×2valid
Compiler

Compiled 27 to 7 computations (74.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-mult: 4.0ms (31% of total)
ival-sub: 4.0ms (31% of total)
ival-sqrt: 3.0ms (23.3% of total)
backward-pass: 2.0ms (15.5% of total)
const: 0.0ms (0% of total)

series8.0ms (0.1%)

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

21 calls:

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

rewrite329.0ms (3.3%)

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
0618
14118
232818
3408018
0835418
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) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(+.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))))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 x (/.f64 (*.f64 x x) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.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 (*.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 x x) (/.f64 x (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (pow.f64 (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 3 binary64)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(fma.f64 (/.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (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 (*.f64 x x) eps)) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) 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))))))
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(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps)))))
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(*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))) (*.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))))))
(*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)))
(*.f64 (+.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps))))
(*.f64 (+.f64 (*.f64 x x) eps) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps)))
(*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))))))
(*.f64 (+.f64 (neg.f64 (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) eps))))
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(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps)))
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(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
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(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps)) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (*.f64 eps (*.f64 (+.f64 (*.f64 x x) eps) (*.f64 eps (+.f64 (*.f64 x x) eps))))))) (+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (-.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (*.f64 x (*.f64 x (*.f64 x x)))))))
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(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (-.f64 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)))

simplify281.0ms (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
18561066
230331031
080351031
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 #s(literal 1/2 binary64) (/.f64 eps 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 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.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 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) #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 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) #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 #s(literal 1/2 binary64) (/.f64 eps 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 #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 (/.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)))))))
(* (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 (*.f64 x 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 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.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 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.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 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.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 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
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 (*.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))))) (+.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 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.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)))))))))))
(* -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)

eval48.0ms (0.5%)

Compiler

Compiled 9770 to 1039 computations (89.4% saved)

prune48.0ms (0.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New27914293
Fresh000
Picked011
Done000
Total27915294
Accuracy
99.9%
Counts
294 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
30.9%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
61.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
34.6%
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
42.0%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
▶4.0%
(-.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)))))
3.3%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶58.0%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
▶62.2%
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
4.3%
(-.f64 x x)
▶3.3%
(*.f64 x #s(literal 2 binary64))
23.4%
(*.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)))))))))
44.0%
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
Compiler

Compiled 574 to 304 computations (47% saved)

simplify187.0ms (1.9%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f64 #s(literal 0 binary64) eps)
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
✓cost-diff0
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
✓cost-diff0
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))
✓cost-diff128
(*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))
✓cost-diff128
(+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))
✓cost-diff384
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
✓cost-diff0
(/.f64 eps x)
✓cost-diff0
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
✓cost-diff0
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
✓cost-diff256
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
✓cost-diff0
(*.f64 x #s(literal 2 binary64))
✓cost-diff0
(+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))
✓cost-diff256
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
✓cost-diff256
(sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))))
✓cost-diff256
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
Rules
2118×sum3-define
1724×fnmadd-define
1598×+-lowering-+.f64
1598×+-lowering-+.f32
1378×fmsub-define
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
029166
178156
2210153
3486141
42134138
57430137
08421137
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
x
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(* eps (+ -1 (/ (* x x) eps)))
eps
(+ -1 (/ (* x x) eps))
-1
(/ (* x x) eps)
(* x x)
(* x 2)
x
2
(- x (+ x (* -1/2 (/ 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 (sqrt (- 0 eps)))
x
(sqrt (- 0 eps))
(- 0 eps)
0
eps
Outputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(* eps (+ -1 (/ (* x x) eps)))
(-.f64 (*.f64 x x) eps)
eps
(+ -1 (/ (* x x) eps))
(+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))
-1
#s(literal -1 binary64)
(/ (* x x) eps)
(/.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(- x (+ x (* -1/2 (/ eps x))))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
x
(+ x (* -1/2 (/ eps x)))
(-.f64 x (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(* -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 (-.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 (/.f64 #s(literal -1/8 binary64) x) x)))) x)
x
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))
(+.f64 x (/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 (/.f64 #s(literal -1/8 binary64) x) x)))) x))
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))
(/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (/.f64 (/.f64 #s(literal -1/8 binary64) x) x)))) x)
eps
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 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 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* eps -1/8)
(*.f64 eps #s(literal -1/8 binary64))
-1/8
#s(literal -1/8 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
(* x x)
(*.f64 x x)
(- x (sqrt (- 0 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
x
(sqrt (- 0 eps))
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
(- 0 eps)
(-.f64 #s(literal 0 binary64) eps)
0
#s(literal 0 binary64)
eps

localize150.0ms (1.5%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) eps)
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
✓accuracy100.0%
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
✓accuracy99.8%
(*.f64 x (*.f64 x x))
✓accuracy89.8%
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
✓accuracy88.8%
(*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))
✓accuracy78.7%
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
✓accuracy100.0%
(/.f64 eps x)
✓accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
✓accuracy100.0%
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
✓accuracy78.7%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
✓accuracy100.0%
(*.f64 x #s(literal 2 binary64))
✓accuracy100.0%
(sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))))
✓accuracy99.9%
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
✓accuracy83.4%
(/.f64 (*.f64 x x) eps)
✓accuracy78.7%
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
Results
47.0ms152×0valid
45.0ms51×1valid
12.0ms46×0invalid
7.0ms7×2valid
Compiler

Compiled 191 to 30 computations (84.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 54.0ms
ival-mult: 19.0ms (35.4% of total)
ival-div: 10.0ms (18.6% of total)
ival-sub: 8.0ms (14.9% of total)
ival-sqrt: 6.0ms (11.2% of total)
ival-add: 6.0ms (11.2% of total)
backward-pass: 4.0ms (7.4% of total)
const: 1.0ms (1.9% of total)

series30.0ms (0.3%)

Counts
19 → 408
Calls
Call 1
Inputs
#<alt (- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))>
#<alt (sqrt (* eps (+ -1 (/ (* x x) eps))))>
#<alt (* eps (+ -1 (/ (* x x) eps)))>
#<alt (+ -1 (/ (* x x) eps))>
#<alt (* x 2)>
#<alt (- x (+ x (* -1/2 (/ 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 (sqrt (- 0 eps)))>
#<alt (sqrt (- 0 eps))>
#<alt (- 0 eps)>
#<alt (/ (* x x) eps)>
#<alt (/ (* eps -1/8) (* x (* x x)))>
#<alt (* x (* x x))>
Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 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))))>
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#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
Calls

102 calls:

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

rewrite344.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
2626×*-lowering-*.f32
2626×*-lowering-*.f64
2586×fma-lowering-fma.f32
2586×fma-lowering-fma.f64
1896×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029141
1211131
22399125
08258125
Stop Event
1×iter limit
1×node limit
Counts
19 → 470
Calls
Call 1
Inputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(* eps (+ -1 (/ (* x x) eps)))
(+ -1 (/ (* x x) eps))
(* x 2)
(- x (+ x (* -1/2 (/ 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 (sqrt (- 0 eps)))
(sqrt (- 0 eps))
(- 0 eps)
(/ (* x x) eps)
(/ (* eps -1/8) (* x (* x x)))
(* x (* x x))
Outputs
(+.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) x)
(-.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))) (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) x)
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) (-.f64 (*.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (-.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) #s(literal 2 binary64)) (*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))))
(/.f64 (-.f64 (*.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) (+.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) #s(literal 2 binary64))) (-.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) (-.f64 (*.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) #s(literal -1 binary64))
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))))
(*.f64 (-.f64 (*.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))
(sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1 binary64))
(pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 eps) (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))))
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) (sqrt.f64 eps))
(*.f64 (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 eps) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) eps))
(exp.f64 (log.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))
(fma.f64 x (*.f64 (/.f64 x eps) eps) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 eps #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 eps (/.f64 (*.f64 x x) eps) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 #s(literal -1 binary64) eps (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 (/.f64 (*.f64 x x) eps) eps (-.f64 #s(literal 0 binary64) eps))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)) (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 eps x) (/.f64 x eps) (-.f64 #s(literal 0 binary64) eps))
(fma.f64 (*.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) eps) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)) (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) (-.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))))) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 x x) eps) (-.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))
(/.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps (*.f64 eps eps)))) eps) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 x x) eps) (-.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x)))) eps) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(pow.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 2 binary64))
(pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) eps)
(*.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 eps) (pow.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps)) (pow.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps)))
(*.f64 (pow.f64 (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))))
(*.f64 (pow.f64 (sqrt.f64 eps) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) #s(literal 1 binary64)))
(+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))
(+.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) (/.f64 (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))))
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
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(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
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(*.f64 x (*.f64 x x))
(*.f64 (*.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

simplify300.0ms (3%)

Algorithm
1×egg-herbie
Rules
5356×*-lowering-*.f32
5356×*-lowering-*.f64
3000×+-lowering-+.f64
3000×+-lowering-+.f32
1268×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03463653
111313361
239573276
084033276
Stop Event
1×iter limit
1×node limit
Counts
408 → 408
Calls
Call 1
Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (pow (sqrt -1) 3))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (pow (sqrt -1) 3)))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 eps)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(/ (pow x 2) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -1/2 (/ eps x))
(* -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 x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(/ eps x)
(* 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))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (- (* -1/8 (/ (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))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))
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))))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -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))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(* -1/8 (/ eps (pow x 3)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 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)))
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(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
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x
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
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(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
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(* (sqrt eps) (sqrt -1))
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(pow x 2)
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(pow x 2)
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-1
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(- (/ (pow x 2) eps) 1)
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(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
(* -1/8 (/ eps (pow x 3)))
(/.f64 (*.f64 eps #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))

eval153.0ms (1.5%)

Compiler

Compiled 18385 to 2204 computations (88% saved)

prune137.0ms (1.4%)

Pruning

36 alts after pruning (34 fresh and 2 done)

PrunedKeptTotal
New85127878
Fresh279
Picked415
Done011
Total85736893
Accuracy
100.0%
Counts
893 → 36
Alt Table
Click to see full alt table
StatusAccuracyProgram
30.9%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
▶61.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
57.6%
(/.f64 (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))))
7.4%
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
16.7%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
34.6%
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
42.0%
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
43.8%
(/.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
32.5%
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
40.1%
(/.f64 (*.f64 (+.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 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) x) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))))))))
44.0%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
43.7%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
3.6%
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x x))))
4.3%
(-.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 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
4.3%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))))
▶5.4%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
3.8%
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x))) x)))
7.0%
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))
7.0%
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
4.4%
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x))))
3.1%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 eps eps))))))
4.8%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)))))
▶4.4%
(-.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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
5.1%
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓62.2%
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
58.0%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
4.3%
(-.f64 x x)
43.8%
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
▶41.9%
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x)))
43.7%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
32.5%
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
15.0%
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
23.4%
(*.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)))))))))
▶3.3%
x
Compiler

Compiled 1778 to 857 computations (51.8% saved)

simplify231.0ms (2.3%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x (*.f64 x x))
✓cost-diff0
(+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))))
✓cost-diff128
(*.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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
✓cost-diff128
(-.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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
✓cost-diff0
(+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
✓cost-diff0
(/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)))))
✓cost-diff128
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
✓cost-diff0
(+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x))
✓cost-diff0
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x)
✓cost-diff0
(*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x))
✓cost-diff128
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) 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 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Rules
5094×*-lowering-*.f32
5094×*-lowering-*.f64
1816×/-lowering-/.f32
1816×/-lowering-/.f64
1798×fnmsub-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
043404
1127356
2356334
31246320
46829320
08404320
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps))))
(- (* x x) (- (* x x) eps))
(* x x)
x
(- (* x x) eps)
eps
(+ x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
x
(- 0 (* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)))
0
(* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x))
eps
(/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)
(+ -1/2 (/ (* (/ eps x) -1/8) x))
-1/2
(/ (* (/ eps x) -1/8) x)
(* (/ eps x) -1/8)
(/ eps x)
x
-1/8
(- x (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
x
(/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))
1
(/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
(+ x (* 1/2 (/ eps x)))
(* 1/2 (/ eps x))
1/2
(/ eps x)
eps
(- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))
(* x x)
(* (/ 1/4 (* x x)) (* eps eps))
(/ 1/4 (* x x))
1/4
(* eps eps)
(- x (* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
x
(* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))
(+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8)))
(* x (* x x))
(* x x)
(/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))
(* eps (* eps eps))
eps
(* eps eps)
(/ (* x (* x x)) -1/8)
-1/8
(/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))
1
(+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))
(* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))
(/ -1/2 (/ x eps))
-1/2
(/ x eps)
(- (/ -1/2 (/ x eps)) x)
Outputs
(/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(- (* x x) (- (* x x) eps))
eps
(* x x)
(*.f64 x x)
x
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
(+ x (sqrt (- (* x x) eps)))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt (- (* x x) eps))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
x
(- 0 (* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (/.f64 eps x))
0
#s(literal 0 binary64)
(* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x))
(/.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) x))) x)
eps
(/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) x)) x)
(+ -1/2 (/ (* (/ eps x) -1/8) x))
(+.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) x))
-1/2
#s(literal -1/2 binary64)
(/ (* (/ eps x) -1/8) x)
(/.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) x)
(* (/ eps x) -1/8)
(/.f64 (*.f64 eps #s(literal -1/8 binary64)) x)
(/ eps x)
(/.f64 eps x)
x
-1/8
#s(literal -1/8 binary64)
(- x (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
(+.f64 x (/.f64 (+.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps eps) x)) x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x)))
x
(/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))
(/.f64 (+.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps eps) x)) x)) (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
1
#s(literal 1 binary64)
(/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
(/.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (+.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps eps) x)) x)))
(+ x (* 1/2 (/ eps x)))
(-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(* 1/2 (/ eps x))
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
1/2
#s(literal 1/2 binary64)
(/ eps x)
(/.f64 eps x)
eps
(- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))
(+.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps eps) x)) x))
(* x x)
(*.f64 x x)
(* (/ 1/4 (* x x)) (* eps eps))
(*.f64 eps (*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps x) x)))
(/ 1/4 (* x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* eps eps)
(*.f64 eps eps)
(- x (* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
(+.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x) x))) (*.f64 x x))))
x
(* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))) (-.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x) x)))))
(+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8)))
(+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps (*.f64 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)) (/ (* x (* x x)) -1/8))
(/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x x)))
(* eps (* eps eps))
(*.f64 eps (*.f64 eps eps))
eps
(* eps eps)
(*.f64 eps eps)
(/ (* x (* x x)) -1/8)
(/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))
-1/8
#s(literal -1/8 binary64)
(/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))
(/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x) x)))))
1
#s(literal 1 binary64)
(+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))
(-.f64 (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x) x))))
(* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x)) (/.f64 x eps))
(/ -1/2 (/ x eps))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
-1/2
#s(literal -1/2 binary64)
(/ x eps)
(/.f64 x eps)
(- (/ -1/2 (/ x eps)) x)
(-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x)

localize292.0ms (2.9%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy99.2%
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))
✓accuracy77.7%
(*.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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
✓accuracy62.6%
(/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))
✓accuracy62.2%
(-.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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)))))
✓accuracy88.5%
(/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))
✓accuracy66.2%
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))
✓accuracy62.2%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
✓accuracy100.0%
(*.f64 (/.f64 eps x) #s(literal -1/8 binary64))
✓accuracy99.9%
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x)
✓accuracy99.7%
(/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)
✓accuracy88.8%
(*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x))
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓accuracy99.5%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓accuracy62.8%
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
Results
124.0ms81×1valid
64.0ms152×0valid
33.0ms23×2valid
Compiler

Compiled 449 to 44 computations (90.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 125.0ms
ival-add: 32.0ms (25.5% of total)
ival-div: 30.0ms (23.9% of total)
ival-mult: 30.0ms (23.9% of total)
backward-pass: 15.0ms (12% of total)
ival-sub: 13.0ms (10.4% of total)
ival-sqrt: 3.0ms (2.4% of total)
const: 1.0ms (0.8% of total)

series95.0ms (1%)

Counts
22 → 504
Calls
Call 1
Inputs
#<alt (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps))))>
#<alt (- (* x x) (- (* x x) eps))>
#<alt (* x x)>
#<alt (- (* x x) eps)>
#<alt (- 0 (* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)))>
#<alt (* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x))>
#<alt (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)>
#<alt (+ -1/2 (/ (* (/ eps x) -1/8) x))>
#<alt (- x (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))>
#<alt (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))>
#<alt (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))>
#<alt (+ x (* 1/2 (/ eps x)))>
#<alt (- x (* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))>
#<alt (* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))>
#<alt (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8)))>
#<alt (* x (* x x))>
#<alt (+ x (sqrt (- (* x x) eps)))>
#<alt (/ (* (/ eps x) -1/8) x)>
#<alt (* (/ eps x) -1/8)>
#<alt (* (/ 1/4 (* x x)) (* eps eps))>
#<alt (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))>
#<alt (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))>
Outputs
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* -1 (* (sqrt eps) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 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 (/ (- (* 1/2 (* 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 (* -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 (/ -1/2 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 (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ 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>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt -1/2>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
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#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (pow eps 2) (pow x 2))))))))) x))>
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#<alt (* 2 x)>
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#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* -1/8 (/ (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 (* 4 (/ (pow x 2) (pow eps 2)))>
#<alt (* (pow x 2) (+ (* -8 (/ (pow x 2) (pow eps 3))) (* 4 (/ 1 (pow eps 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* 32 (/ (pow x 4) (pow eps 5))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* (pow x 4) (+ (* -64 (/ (pow x 2) (pow eps 6))) (* 32 (/ 1 (pow eps 5))))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (+ (* -1/2 (/ eps (pow x 4))) (/ 1 (pow x 2)))>
#<alt (+ (* eps (- (* 1/8 (/ (pow eps 2) (pow x 8))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))>
#<alt (+ (* eps (- (* (pow eps 2) (+ (* -1/16 (/ eps (pow x 10))) (* 1/8 (/ 1 (pow x 8))))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))>
#<alt (* 4 (/ (pow x 2) (pow eps 2)))>
#<alt (/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -16 (pow x 6)) (* 16 (pow x 6))) (pow eps 2))) (* 4 (pow x 2))) (* 8 (/ (pow x 4) eps))) (pow eps 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -32 (pow x 8)) (* -2 (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))))) (pow eps 3))) (* 4 (pow x 2))) (+ (* -16 (/ (pow x 6) (pow eps 2))) (+ (* 8 (/ (pow x 4) eps)) (* 16 (/ (pow x 6) (pow eps 2)))))) (pow eps 2))>
#<alt (* 4 (/ (pow x 2) (pow eps 2)))>
#<alt (/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))>
#<alt (/ (+ (* -1 (/ (- (+ (* -16 (/ (pow x 6) eps)) (* 16 (/ (pow x 6) eps))) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* 2 (/ (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* 32 (/ (pow x 8) eps))) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))>
Calls

126 calls:

TimeVariablePointExpression
30.0ms
x
@inf
(- x (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
9.0ms
eps
@0
(- x (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
6.0ms
x
@0
(- x (* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
4.0ms
eps
@0
(- x (* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
3.0ms
eps
@inf
(- x (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))

rewrite398.0ms (4%)

Algorithm
1×batch-egg-rewrite
Rules
3758×*-lowering-*.f32
3758×*-lowering-*.f64
2028×pow-lowering-pow.f64
2028×pow-lowering-pow.f32
1808×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043270
1341238
23506227
08224227
Stop Event
1×iter limit
1×node limit
Counts
22 → 536
Calls
Call 1
Inputs
(/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps))))
(- (* x x) (- (* x x) eps))
(* x x)
(- (* x x) eps)
(- 0 (* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)))
(* eps (/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x))
(/ (+ -1/2 (/ (* (/ eps x) -1/8) x)) x)
(+ -1/2 (/ (* (/ eps x) -1/8) x))
(- x (/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
(/ 1 (/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))
(/ (+ x (* 1/2 (/ eps x))) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
(+ x (* 1/2 (/ eps x)))
(- x (* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
(* (+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))
(+ (* x (* x x)) (/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8)))
(* x (* x x))
(+ x (sqrt (- (* x x) eps)))
(/ (* (/ eps x) -1/8) x)
(* (/ eps x) -1/8)
(* (/ 1/4 (* x x)) (* eps eps))
(/ (* eps (* eps eps)) (/ (* x (* x x)) -1/8))
(/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))
Outputs
(+.f64 x (neg.f64 (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))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(fma.f64 (/.f64 (*.f64 x x) (+.f64 eps #s(literal 0 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))))))
(neg.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.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 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64))) (*.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (*.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 (*.f64 (+.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))) #s(literal 1 binary64)) (*.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 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (+.f64 eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(*.f64 (+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 eps #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps #s(literal 0 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 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 eps #s(literal 0 binary64)) (+.f64 eps #s(literal 0 binary64))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.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)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(*.f64 (pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (*.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 eps #s(literal 0 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
(+.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 eps #s(literal 0 binary64))
(+.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (*.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) eps)))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)) (*.f64 x x))
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(*.f64 (*.f64 eps eps) (/.f64 eps (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))
(*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))
(*.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 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
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(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))
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(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)))
(*.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))) #s(literal 1/8 binary64))
(*.f64 (/.f64 (/.f64 (*.f64 eps eps) x) (/.f64 (*.f64 x x) #s(literal -1/8 binary64))) eps)
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (/.f64 #s(literal -8 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/8 binary64))))
(*.f64 (/.f64 eps (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps eps) #s(literal -8 binary64)))
(*.f64 (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))) (/.f64 eps #s(literal -8 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 3/2 binary64)))
(*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/8 binary64))
(*.f64 (pow.f64 (/.f64 x (*.f64 eps eps)) #s(literal -1 binary64)) (pow.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal -1/8 binary64)) eps) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 x (*.f64 x x)) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -8 binary64) (*.f64 eps eps)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps eps)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -8 binary64) eps) #s(literal -1 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))))
(exp.f64 (*.f64 (log.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(pow.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
(*.f64 (pow.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps))) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))) (*.f64 x x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps))) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))) (*.f64 x x))))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) #s(literal -1 binary64)))

simplify368.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
5012×*-lowering-*.f32
5012×*-lowering-*.f64
4202×+-lowering-+.f64
4202×+-lowering-+.f32
1780×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
08175899
128004909
092014909
Stop Event
1×iter limit
1×node limit
Counts
504 → 504
Calls
Call 1
Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (- (* 1/2 (* 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))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (- (* -1/8 (/ (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))
(* -1/2 (/ 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))
(/ -1/2 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 (+ (* 1/2 (/ 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))))))
(* -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))))))
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x
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x
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x
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x
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(pow x 3)
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(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)
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(* -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)))
(* 4 (/ (pow x 2) (pow eps 2)))
(* (pow x 2) (+ (* -8 (/ (pow x 2) (pow eps 3))) (* 4 (/ 1 (pow eps 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* 32 (/ (pow x 4) (pow eps 5))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 4) (+ (* -64 (/ (pow x 2) (pow eps 6))) (* 32 (/ 1 (pow eps 5))))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))
(/ 1 (pow x 2))
(/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))
(/ 1 (pow x 2))
(+ (* -1/2 (/ eps (pow x 4))) (/ 1 (pow x 2)))
(+ (* eps (- (* 1/8 (/ (pow eps 2) (pow x 8))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(+ (* eps (- (* (pow eps 2) (+ (* -1/16 (/ eps (pow x 10))) (* 1/8 (/ 1 (pow x 8))))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(* 4 (/ (pow x 2) (pow eps 2)))
(/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))
(/ (- (+ (* -1 (/ (+ (* -16 (pow x 6)) (* 16 (pow x 6))) (pow eps 2))) (* 4 (pow x 2))) (* 8 (/ (pow x 4) eps))) (pow eps 2))
(/ (- (+ (* -1 (/ (+ (* -32 (pow x 8)) (* -2 (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))))) (pow eps 3))) (* 4 (pow x 2))) (+ (* -16 (/ (pow x 6) (pow eps 2))) (+ (* 8 (/ (pow x 4) eps)) (* 16 (/ (pow x 6) (pow eps 2)))))) (pow eps 2))
(* 4 (/ (pow x 2) (pow eps 2)))
(/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))
(/ (+ (* -1 (/ (- (+ (* -16 (/ (pow x 6) eps)) (* 16 (/ (pow x 6) eps))) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* 2 (/ (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* 32 (/ (pow x 8) eps))) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))
Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64)))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (+.f64 (/.f64 (*.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 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (+.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ (* -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 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))))
(* -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 #s(literal -1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))) (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 #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 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (*.f64 eps eps))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (/.f64 x #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 eps)))
(+ 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 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 eps))) (/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.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 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 eps))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 eps (*.f64 x x)) x) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))))) eps)) (*.f64 eps x)) eps))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (+.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(* -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)))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x x)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x x)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x x)))
(/ (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 x x)))
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(* 4 (/ (pow x 2) (pow eps 2)))
(/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 eps eps))
(/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -8 binary64)) eps) (*.f64 #s(literal 4 binary64) (*.f64 x x))) (*.f64 eps eps))
(/ (+ (* -1 (/ (- (+ (* -16 (/ (pow x 6) eps)) (* 16 (/ (pow x 6) eps))) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))
(/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -8 binary64)) eps) (*.f64 #s(literal 4 binary64) (*.f64 x x))) (*.f64 eps eps))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* 2 (/ (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* 32 (/ (pow x 8) eps))) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))
(/.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 0 binary64) eps) (/.f64 (*.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 8 binary64))) eps)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 8 binary64))) eps)) (*.f64 eps eps))

eval228.0ms (2.3%)

Compiler

Compiled 40213 to 3118 computations (92.2% saved)

prune444.0ms (4.5%)

Pruning

47 alts after pruning (45 fresh and 2 done)

PrunedKeptTotal
New1196311227
Fresh151429
Picked415
Done112
Total1216471263
Accuracy
100.0%
Counts
1263 → 47
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.3%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
5.7%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)))))
6.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
7.0%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x #s(literal 2 binary64)))
16.7%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
42.0%
(/.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))))
42.0%
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
34.6%
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
44.0%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
▶99.6%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
3.3%
(-.f64 x (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))))))
6.1%
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
5.1%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
▶2.8%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
5.0%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
6.2%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) x) x)))))
6.2%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
5.5%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))))))
6.1%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) eps)))))
5.4%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 x eps))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
3.9%
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -4 binary64) (*.f64 x x)) (*.f64 eps eps)) (/.f64 #s(literal -2 binary64) eps)))))
5.5%
(-.f64 x (-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (/.f64 (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
7.0%
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))
7.0%
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
4.4%
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x))))
4.8%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)))))
5.0%
(-.f64 x (*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
▶2.6%
(-.f64 x (*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
6.1%
(-.f64 x (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
1.9%
(-.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 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 eps eps))))
3.6%
(-.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 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
4.4%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
4.7%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 eps (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps eps) #s(literal -8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
6.1%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
5.1%
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
58.0%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶4.3%
(-.f64 x x)
43.8%
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
▶42.1%
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) (/.f64 eps x)))
41.9%
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))) (/.f64 #s(literal 1 binary64) x)))
43.9%
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
43.7%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
15.0%
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
41.9%
(*.f64 (neg.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) x)) eps)
✓3.3%
x
Compiler

Compiled 2411 to 1250 computations (48.2% saved)

simplify266.0ms (2.7%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))
✓cost-diff0
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
✓cost-diff128
(*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
✓cost-diff128
(-.f64 x (*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
✓cost-diff0
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
✓cost-diff0
(/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)))))
✓cost-diff128
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
✓cost-diff0
(/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))
✓cost-diff0
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))
✓cost-diff0
(*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) (/.f64 eps x))
✓cost-diff128
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) (/.f64 eps x)))
✓cost-diff128
(-.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
3572×*-lowering-*.f32
3572×*-lowering-*.f64
2176×/-lowering-/.f32
2176×/-lowering-/.f64
1296×fma-lowering-fma.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041321
1122309
2398297
31929286
45904286
08011286
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)
(- x x)
x
(- 0 (* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x)))
0
(* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x))
(+ -1/2 (/ -1/8 (* (/ x eps) x)))
-1/2
(/ -1/8 (* (/ x eps) x))
-1/8
(* (/ x eps) x)
(/ x eps)
x
eps
(/ eps x)
(- x (/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
x
(/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))
1
(/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
(/ (* eps 1/2) x)
(* eps 1/2)
eps
1/2
(- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))
(* x x)
(* (/ 1/4 (* x x)) (* eps eps))
(/ 1/4 (* x x))
1/4
(* eps eps)
(- x (* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
x
(* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))
(/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))
(* (* eps (* eps eps)) -1/8)
(* eps (* eps eps))
eps
(* eps eps)
-1/8
(* x (* x x))
(* x x)
(/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))
1
(+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))
(* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))
(/ -1/2 (/ x eps))
-1/2
(/ x eps)
(- (/ -1/2 (/ x eps)) x)
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)
(- x x)
#s(literal 0 binary64)
x
(- 0 (* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x)))
(/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) eps)))) x)
0
#s(literal 0 binary64)
(* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x))
(*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) eps))) (/.f64 eps x))
(+ -1/2 (/ -1/8 (* (/ x eps) x)))
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) eps)))
-1/2
#s(literal -1/2 binary64)
(/ -1/8 (* (/ x eps) x))
(/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) eps))
-1/8
#s(literal -1/8 binary64)
(* (/ x eps) x)
(/.f64 (*.f64 x x) eps)
(/ x eps)
(/.f64 x eps)
x
eps
(/ eps x)
(/.f64 eps x)
(- x (/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
(*.f64 (+.f64 (*.f64 (/.f64 #s(literal -2 binary64) eps) (+.f64 (*.f64 x x) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 x x)))) #s(literal 1 binary64)) x)
x
(/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))
(/.f64 x (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 x x)))))
1
#s(literal 1 binary64)
(/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
(/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 x x) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 x x)))) x)
(/ (* eps 1/2) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))
(+.f64 (*.f64 x x) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/4 binary64))) (*.f64 x x)))
(* x x)
(*.f64 x x)
(* (/ 1/4 (* x x)) (* eps eps))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/4 binary64))) (*.f64 x x))
(/ 1/4 (* x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* eps eps)
(*.f64 eps eps)
(- x (* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
(+.f64 x (/.f64 (/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x))) (-.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 x x))))
x
(* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))
(/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (/.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 x eps))) (/.f64 x eps)))))
(/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))
(/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(* (* eps (* eps eps)) -1/8)
(*.f64 (*.f64 eps eps) (*.f64 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 x))
(*.f64 x (*.f64 x x))
(* x x)
(*.f64 x x)
(/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 x eps))) (/.f64 x eps))))
1
#s(literal 1 binary64)
(+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))
(+.f64 (*.f64 x x) (/.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 x eps))) (/.f64 x eps)))
(* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))
(/.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 x eps))) (/.f64 x eps))
(/ -1/2 (/ x eps))
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
-1/2
#s(literal -1/2 binary64)
(/ x eps)
(/.f64 x eps)
(- (/ -1/2 (/ x eps)) x)
(-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)

localize273.0ms (2.7%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy99.5%
(*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))
✓accuracy99.2%
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))
✓accuracy72.6%
(*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
✓accuracy62.4%
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))
✓accuracy99.7%
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)))))
✓accuracy88.4%
(/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))
✓accuracy66.2%
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))
✓accuracy100.0%
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))
✓accuracy99.8%
(*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) (/.f64 eps x))
✓accuracy99.7%
(*.f64 (/.f64 x eps) x)
✓accuracy99.7%
(/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))
✓accuracy100.0%
(-.f64 x x)
✓accuracy100.0%
(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓accuracy100.0%
(-.f64 (*.f64 x x) eps)
✓accuracy100.0%
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓accuracy99.5%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Results
213.0ms256×0valid
Compiler

Compiled 383 to 42 computations (89% saved)

Precisions
Click to see histograms. Total time spent on operations: 87.0ms
ival-mult: 49.0ms (56.2% of total)
ival-div: 19.0ms (21.8% of total)
ival-sub: 12.0ms (13.8% of total)
ival-add: 4.0ms (4.6% of total)
ival-sqrt: 2.0ms (2.3% of total)
const: 1.0ms (1.1% of total)
backward-pass: 0.0ms (0% of total)

series40.0ms (0.4%)

Counts
22 → 492
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 (- x x)>
#<alt (- 0 (* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x)))>
#<alt (* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x))>
#<alt (+ -1/2 (/ -1/8 (* (/ x eps) x)))>
#<alt (/ -1/8 (* (/ x eps) x))>
#<alt (- x (/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))>
#<alt (/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))>
#<alt (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))>
#<alt (/ (* eps 1/2) x)>
#<alt (- x (* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))>
#<alt (* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))>
#<alt (/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))>
#<alt (* (* eps (* eps eps)) -1/8)>
#<alt (* (/ x eps) x)>
#<alt (* (/ 1/4 (* x x)) (* eps eps))>
#<alt (/ 1/4 (* x x))>
#<alt (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))>
#<alt (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x 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 (* 1/8 (/ (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)))))>
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#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (* 4 (/ (pow x 2) (pow eps 2)))>
#<alt (* (pow x 2) (+ (* -8 (/ (pow x 2) (pow eps 3))) (* 4 (/ 1 (pow eps 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* 32 (/ (pow x 4) (pow eps 5))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* (pow x 4) (+ (* -64 (/ (pow x 2) (pow eps 6))) (* 32 (/ 1 (pow eps 5))))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (+ (* -1/2 (/ eps (pow x 4))) (/ 1 (pow x 2)))>
#<alt (+ (* eps (- (* 1/8 (/ (pow eps 2) (pow x 8))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))>
#<alt (+ (* eps (- (* (pow eps 2) (+ (* -1/16 (/ eps (pow x 10))) (* 1/8 (/ 1 (pow x 8))))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))>
#<alt (* 4 (/ (pow x 2) (pow eps 2)))>
#<alt (/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -16 (pow x 6)) (* 16 (pow x 6))) (pow eps 2))) (* 4 (pow x 2))) (* 8 (/ (pow x 4) eps))) (pow eps 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -32 (pow x 8)) (* -2 (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))))) (pow eps 3))) (* 4 (pow x 2))) (+ (* -16 (/ (pow x 6) (pow eps 2))) (+ (* 8 (/ (pow x 4) eps)) (* 16 (/ (pow x 6) (pow eps 2)))))) (pow eps 2))>
#<alt (* 4 (/ (pow x 2) (pow eps 2)))>
#<alt (/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))>
#<alt (/ (+ (* -1 (/ (- (+ (* -16 (/ (pow x 6) eps)) (* 16 (/ (pow x 6) eps))) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* 2 (/ (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* 32 (/ (pow x 8) eps))) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 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)))))>
Calls

123 calls:

TimeVariablePointExpression
12.0ms
x
@inf
(/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
2.0ms
eps
@-inf
(- x (* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
2.0ms
x
@-inf
(/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))
1.0ms
x
@0
(/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
1.0ms
eps
@inf
(- x (* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))

rewrite348.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
3488×*-lowering-*.f32
3488×*-lowering-*.f64
2664×fma-lowering-fma.f32
2664×fma-lowering-fma.f64
1674×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041235
1307226
23067217
08660217
Stop Event
1×iter limit
1×node limit
Counts
22 → 652
Calls
Call 1
Inputs
(/ eps (+ x (sqrt (- (* x x) eps))))
(+ x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(- x x)
(- 0 (* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x)))
(* (+ -1/2 (/ -1/8 (* (/ x eps) x))) (/ eps x))
(+ -1/2 (/ -1/8 (* (/ x eps) x)))
(/ -1/8 (* (/ x eps) x))
(- x (/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))))
(/ 1 (/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps)))))
(/ (/ (* eps 1/2) x) (- (* x x) (* (/ 1/4 (* x x)) (* eps eps))))
(/ (* eps 1/2) x)
(- x (* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))))
(* (/ (* (* eps (* eps eps)) -1/8) (* x (* x x))) (/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x)))))
(/ (* (* eps (* eps eps)) -1/8) (* x (* x x)))
(* (* eps (* eps eps)) -1/8)
(* (/ x eps) x)
(* (/ 1/4 (* x x)) (* eps eps))
(/ 1/4 (* x x))
(/ 1 (+ (* x x) (* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x eps)) x))))
(* (/ -1/2 (/ x eps)) (- (/ -1/2 (/ x 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)))
(*.f64 (/.f64 eps (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 eps (-.f64 (*.f64 x x) (-.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 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x))
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
(*.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)))
(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 eps (*.f64 x x)) (-.f64 (*.f64 x x) eps))) (sqrt.f64 (+.f64 eps (*.f64 x x))))
(pow.f64 (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))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (+.f64 eps (*.f64 x x)) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x x))) #s(literal 1/2 binary64)))
(+.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps))
(+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x x))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)))
(-.f64 (*.f64 x x) eps)
(-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))) (/.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (+.f64 eps (*.f64 x x))) (/.f64 (*.f64 eps eps) (+.f64 eps (*.f64 x x))))
(sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(fma.f64 x x (-.f64 #s(literal 0 binary64) eps))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) eps))
(/.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 (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (*.f64 x x)) (*.f64 (+.f64 eps (*.f64 x x)) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x)))))
(/.f64 (*.f64 (+.f64 eps (*.f64 x x)) (-.f64 (*.f64 x x) eps)) (+.f64 eps (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 eps (*.f64 x x))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps (*.f64 x x)) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 eps (*.f64 x x))))
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(*.f64 (pow.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (-.f64 (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 x x)))))
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(fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 eps x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) x)))
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(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
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(fma.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 eps (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 eps eps) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 eps eps) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(fma.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) #s(literal -1/2 binary64)) (/.f64 eps x) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) #s(literal -1/2 binary64)) (/.f64 eps x) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(fma.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal -1/2 binary64) x)) eps (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal -1/2 binary64) x)) eps (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x eps) (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))))
(/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) (/.f64 x eps))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x x))) (*.f64 (/.f64 x eps) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x x))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x))) #s(literal -1/2 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (/.f64 x eps)))
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 #s(literal 0 binary64) (/.f64 x eps))))
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(/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 #s(literal 0 binary64) (/.f64 x eps))))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) (/.f64 x eps)))
(/.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x x))) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (*.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 (*.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 x eps)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) (-.f64 #s(literal 0 binary64) (/.f64 x eps)))
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 x x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) x) (/.f64 #s(literal 1 binary64) eps))
(pow.f64 (/.f64 (/.f64 x eps) (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))) #s(literal -1 binary64))
(*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 eps x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x eps)))
(*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(*.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) (/.f64 eps x))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 eps (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))
(*.f64 (*.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 #s(literal -1/2 binary64) x)) eps)
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) x) eps)
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) #s(literal 1 binary64)) (/.f64 eps x))
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) eps))

simplify359.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
6450×*-lowering-*.f32
6450×*-lowering-*.f64
4760×+-lowering-+.f64
4760×+-lowering-+.f32
1162×associate-*r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
09396360
132145656
090435656
Stop Event
1×iter limit
1×node limit
Counts
492 → 492
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
(* 1/8 (/ (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))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (- (* -1/8 (/ (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))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/2 (* 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))
(* -1/2 (/ 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 (/ eps (pow x 2)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(* -1/8 (/ eps (pow x 2)))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1/8 (/ eps (pow x 2)))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* -1/8 (/ eps (pow x 2)))
(* 1/2 (/ eps x))
(/ (- (pow x 2) (* -1/2 eps)) x)
(/ (- (* (pow x 2) (+ 1 (* -2 (/ (pow x 2) eps)))) (* -1/2 eps)) x)
(/ (- (* (pow x 2) (+ 1 (* -2 (/ (pow x 2) eps)))) (* -1/2 eps)) x)
(* -2 (/ (pow x 3) eps))
(* (pow x 3) (- (/ 1 (pow x 2)) (* 2 (/ 1 eps))))
(* (pow x 3) (- (+ (* 1/2 (/ eps (pow x 4))) (/ 1 (pow x 2))) (* 2 (/ 1 eps))))
(* (pow x 3) (- (+ (* 1/2 (/ eps (pow x 4))) (/ 1 (pow x 2))) (* 2 (/ 1 eps))))
(* -2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (/ 1 (pow x 2)))))
(* -2 (/ (pow x 3) eps))
(/ (- (* eps x) (* 2 (pow x 3))) eps)
(/ (- (* eps (+ x (* 1/2 (/ eps x)))) (* 2 (pow x 3))) eps)
(/ (- (* eps (+ x (* 1/2 (/ eps x)))) (* 2 (pow x 3))) eps)
(* 1/2 (/ eps x))
(* eps (+ (* 1/2 (/ 1 x)) (/ x eps)))
(* eps (+ (* -2 (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (/ 1 x)) (/ x eps))))
(* eps (+ (* -2 (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (/ 1 x)) (/ x eps))))
(* 1/2 (/ eps x))
(* -1 (* eps (- (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -2 (/ (pow x 3) eps))) eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -2 (/ (pow x 3) eps))) eps)) (* 1/2 (/ 1 x)))))
(* 2 (/ (pow x 3) eps))
(/ (+ (* -1/2 (/ (pow eps 2) x)) (* 2 (pow x 3))) eps)
(/ (+ (* -1/2 (/ (pow eps 2) x)) (* 2 (pow x 3))) eps)
(/ (+ (* -1/2 (/ (pow eps 2) x)) (* 2 (pow x 3))) eps)
(* -1/2 (/ eps x))
(* eps (- (* 2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ (pow x 3) (pow eps 2))) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (/ (pow x 4) eps))) x)
(/ (+ (* -1/2 eps) (* 2 (/ (pow x 4) eps))) x)
(/ (+ (* -1/2 eps) (* 2 (/ (pow x 4) eps))) x)
(* 2 (/ (pow x 3) eps))
(* (pow x 3) (+ (* -1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps))))
(* (pow x 3) (+ (* -1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps))))
(* (pow x 3) (+ (* -1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))
(* 1/2 (/ eps (pow x 3)))
(* eps (+ (* 1/8 (/ (pow eps 2) (pow x 7))) (* 1/2 (/ 1 (pow x 3)))))
(* eps (+ (* (pow eps 2) (+ (* 1/32 (/ (pow eps 2) (pow x 11))) (* 1/8 (/ 1 (pow x 7))))) (* 1/2 (/ 1 (pow x 3)))))
(* eps (+ (* (pow eps 2) (+ (* (pow eps 2) (+ (* 1/128 (/ (pow eps 2) (pow x 15))) (* 1/32 (/ 1 (pow x 11))))) (* 1/8 (/ 1 (pow x 7))))) (* 1/2 (/ 1 (pow x 3)))))
(* -2 (/ x eps))
(/ (+ (* -8 (/ (pow x 5) (pow eps 2))) (* -2 x)) eps)
(/ (- (+ (* -32 (/ (pow x 9) (pow eps 4))) (* -2 x)) (* 8 (/ (pow x 5) (pow eps 2)))) eps)
(/ (- (+ (* -128 (/ (pow x 13) (pow eps 6))) (* -2 x)) (+ (* 8 (/ (pow x 5) (pow eps 2))) (* 32 (/ (pow x 9) (pow eps 4))))) eps)
(* -2 (/ x eps))
(* -1 (/ (+ (* 2 x) (* 8 (/ (pow x 5) (pow eps 2)))) eps))
(* -1 (/ (- (+ (* 2 x) (* 32 (/ (pow x 9) (pow eps 4)))) (* -8 (/ (pow x 5) (pow eps 2)))) eps))
(* -1 (/ (- (+ (* 2 x) (* 128 (/ (pow x 13) (pow eps 6)))) (+ (* -32 (/ (pow x 9) (pow eps 4))) (* -8 (/ (pow x 5) (pow eps 2))))) eps))
(* -2 (/ x eps))
(* x (- (* -8 (/ (pow x 4) (pow eps 3))) (* 2 (/ 1 eps))))
(* x (- (* (pow x 4) (- (* -32 (/ (pow x 4) (pow eps 5))) (* 8 (/ 1 (pow eps 3))))) (* 2 (/ 1 eps))))
(* x (- (* (pow x 4) (- (* (pow x 4) (- (* -128 (/ (pow x 4) (pow eps 7))) (* 32 (/ 1 (pow eps 5))))) (* 8 (/ 1 (pow eps 3))))) (* 2 (/ 1 eps))))
(* 1/2 (/ eps (pow x 3)))
(/ (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (pow x 3))
(/ (+ (* 1/32 (/ (pow eps 5) (pow x 8))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))) (pow x 3))
(/ (+ (* 1/128 (/ (pow eps 7) (pow x 12))) (+ (* 1/32 (/ (pow eps 5) (pow x 8))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)))) (pow x 3))
(* 1/2 (/ eps (pow x 3)))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 4)))) (pow x 3)))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (* -1/32 (/ (pow eps 5) (pow x 8))))) (pow x 3)))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/32 (/ (pow eps 5) (pow x 8))) (* -1/128 (/ (pow eps 7) (pow x 12)))))) (pow x 3)))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ (- (* 4 (/ (pow x 6) (pow eps 2))) (* -1/2 eps)) x)
(/ (- (* (pow x 6) (+ (* -8 (/ (pow x 2) (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* -1/2 eps)) x)
(/ (- (* (pow x 6) (+ (* (pow x 2) (- (* 32 (/ (pow x 4) (pow eps 5))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2))))) (* -1/2 eps)) x)
x
(* x (+ 1 (* 1/8 (/ (pow eps 3) (pow x 6)))))
(* x (- (+ 1 (* -1/16 (/ (pow eps 4) (pow x 8)))) (* -1/8 (/ (pow eps 3) (pow x 6)))))
(* x (- (+ 1 (* -1/8 (/ (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))) (pow x 10)))) (+ (* -1/8 (/ (pow eps 3) (pow x 6))) (* 1/16 (/ (pow eps 4) (pow x 8))))))
x
(* -1 (* x (- (* -1/8 (/ (pow eps 3) (pow x 6))) 1)))
(* -1 (* x (- (* 1/16 (/ (pow eps 4) (pow x 8))) (+ 1 (* 1/8 (/ (pow eps 3) (pow x 6)))))))
(* -1 (* x (- (* 1/8 (/ (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))) (pow x 10))) (+ 1 (+ (* -1/16 (/ (pow eps 4) (pow x 8))) (* 1/8 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* 1/8 (/ (pow eps 3) (pow x 5))))
(+ x (* (pow eps 3) (+ (* -1/16 (/ eps (pow x 7))) (* 1/8 (/ 1 (pow x 5))))))
(+ x (* (pow eps 3) (+ (* eps (- (* 1/64 (/ (pow eps 2) (pow x 11))) (* 1/16 (/ 1 (pow x 7))))) (* 1/8 (/ 1 (pow x 5))))))
(* 1/2 (/ eps x))
(* eps (+ (* -1 (/ x eps)) (+ (* 1/2 (/ 1 x)) (/ x eps))))
(* eps (+ (* -1 (/ x eps)) (+ (* -1/8 (/ (+ (* -16 (pow x 3)) (* 16 (pow x 3))) (pow eps 2))) (+ (* 1/2 (/ 1 x)) (/ x eps)))))
(* eps (+ (* -1 (/ x eps)) (+ (* -1/8 (/ (+ (* -32 (pow x 5)) (* -2 (* (pow x 2) (+ (* -16 (pow x 3)) (* 16 (pow x 3)))))) (pow eps 3))) (+ (* -1/8 (/ (+ (* -16 (pow x 3)) (* 16 (pow x 3))) (pow eps 2))) (+ (* 1/2 (/ 1 x)) (/ x eps))))))
(* 1/2 (/ eps x))
(* -1 (* eps (- (* 1/8 (/ (+ (* -16 (pow x 3)) (* 16 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1/8 (/ (+ (* 2 (* (pow x 2) (+ (* -16 (pow x 3)) (* 16 (pow x 3))))) (* 32 (pow x 5))) (pow eps 3))) (+ (* -1/8 (/ (+ (* -16 (pow x 3)) (* 16 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x))))))
(* -1 (* eps (- (* -1 (/ (- (* -1/8 (/ (+ (* -4 (* (pow x 4) (+ (* -16 (pow x 3)) (* 16 (pow x 3))))) (* 2 (* (pow x 2) (+ (* 2 (* (pow x 2) (+ (* -16 (pow x 3)) (* 16 (pow x 3))))) (* 32 (pow x 5)))))) eps)) (* -1/8 (+ (* 2 (* (pow x 2) (+ (* -16 (pow x 3)) (* 16 (pow x 3))))) (* 32 (pow x 5))))) (pow eps 3))) (+ (* -1/8 (/ (+ (* -16 (pow x 3)) (* 16 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x))))))
(* -1/8 (/ (pow eps 3) (pow x 5)))
(* (pow eps 3) (- (* 1/16 (/ eps (pow x 7))) (* 1/8 (/ 1 (pow x 5)))))
(* (pow eps 3) (- (* eps (+ (* -1/64 (/ (pow eps 2) (pow x 11))) (* 1/16 (/ 1 (pow x 7))))) (* 1/8 (/ 1 (pow x 5)))))
(* (pow eps 3) (- (* eps (+ (* (pow eps 2) (- (* 1/128 (/ eps (pow x 13))) (* 1/64 (/ 1 (pow x 11))))) (* 1/16 (/ 1 (pow x 7))))) (* 1/8 (/ 1 (pow x 5)))))
(* -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 (- (* -1 (/ (+ (* -2 (* (pow x 2) (+ (* -2 (pow x 3)) (* 2 (pow x 3))))) (* 4 (pow x 5))) (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)) (* 4 (/ (pow x 5) eps))) (+ (* -2 (pow x 3)) (* 2 (pow x 3)))) eps)) (* -1 x)) eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (* (pow x 2) (+ 1 (* -4 (/ (pow x 4) (pow eps 2)))))) x)
(/ (+ (* -1/2 eps) (* (pow x 2) (+ 1 (* (pow x 4) (- (* 8 (/ (pow x 2) (pow eps 3))) (* 4 (/ 1 (pow eps 2)))))))) x)
(* -1/8 (/ (pow eps 3) (pow x 5)))
(/ (+ (* -1/8 (pow eps 3)) (* 1/16 (/ (pow eps 4) (pow x 2)))) (pow x 5))
(/ (+ (* -1/8 (pow eps 3)) (+ (* 1/16 (/ (pow eps 4) (pow x 2))) (* 1/8 (/ (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))) (pow x 4))))) (pow x 5))
(/ (+ (* -1/8 (pow eps 3)) (+ (* 1/16 (/ (pow eps 4) (pow x 2))) (+ (* 1/8 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))))) (* -1/8 (pow eps 6))) (pow x 6))) (* 1/8 (/ (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))) (pow x 4)))))) (pow x 5))
(* -1/8 (/ (pow eps 3) (pow x 5)))
(* -1 (/ (+ (* -1/16 (/ (pow eps 4) (pow x 2))) (* 1/8 (pow eps 3))) (pow x 5)))
(* -1 (/ (+ (* -1/8 (/ (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 2))) (* 1/8 (pow eps 3)))) (pow x 5)))
(* -1 (/ (+ (* -1/8 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))))) (* -1/8 (pow eps 6))) (pow x 6))) (+ (* -1/8 (/ (+ (* -1/4 (pow eps 5)) (* 1/4 (pow eps 5))) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 2))) (* 1/8 (pow eps 3))))) (pow x 5)))
(* -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)))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(* -1/8 (pow eps 3))
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(* 4 (/ (pow x 2) (pow eps 2)))
(* (pow x 2) (+ (* -8 (/ (pow x 2) (pow eps 3))) (* 4 (/ 1 (pow eps 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* 32 (/ (pow x 4) (pow eps 5))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 4) (+ (* -64 (/ (pow x 2) (pow eps 6))) (* 32 (/ 1 (pow eps 5))))) (* 8 (/ 1 (pow eps 3))))) (* 4 (/ 1 (pow eps 2)))))
(/ 1 (pow x 2))
(/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (* -1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4)))) (* 1/2 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (+ (* -1/2 (* eps (+ (* -1/4 (pow eps 2)) (* 1/4 (pow eps 2))))) (* -1/8 (pow eps 3))) (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)))))) (pow x 2))
(/ 1 (pow x 2))
(+ (* -1/2 (/ eps (pow x 4))) (/ 1 (pow x 2)))
(+ (* eps (- (* 1/8 (/ (pow eps 2) (pow x 8))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(+ (* eps (- (* (pow eps 2) (+ (* -1/16 (/ eps (pow x 10))) (* 1/8 (/ 1 (pow x 8))))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(* 4 (/ (pow x 2) (pow eps 2)))
(/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))
(/ (- (+ (* -1 (/ (+ (* -16 (pow x 6)) (* 16 (pow x 6))) (pow eps 2))) (* 4 (pow x 2))) (* 8 (/ (pow x 4) eps))) (pow eps 2))
(/ (- (+ (* -1 (/ (+ (* -32 (pow x 8)) (* -2 (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))))) (pow eps 3))) (* 4 (pow x 2))) (+ (* -16 (/ (pow x 6) (pow eps 2))) (+ (* 8 (/ (pow x 4) eps)) (* 16 (/ (pow x 6) (pow eps 2)))))) (pow eps 2))
(* 4 (/ (pow x 2) (pow eps 2)))
(/ (+ (* -8 (/ (pow x 4) eps)) (* 4 (pow x 2))) (pow eps 2))
(/ (+ (* -1 (/ (- (+ (* -16 (/ (pow x 6) eps)) (* 16 (/ (pow x 6) eps))) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* 2 (/ (* (pow x 2) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* 32 (/ (pow x 8) eps))) (+ (* -16 (pow x 6)) (* 16 (pow x 6)))) eps)) (* -8 (pow x 4))) eps)) (* 4 (pow x 2))) (pow eps 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)))))
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)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (*.f64 eps eps))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/2 binary64)) (/.f64 x #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 eps)))
(+ 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 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (*.f64 eps x)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -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 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 eps))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 eps (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.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 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64)))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))) #s(literal 1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x))) #s(literal -2 binary64))))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
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(* (sqrt eps) (sqrt -1))
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(+ x (* (sqrt eps) (sqrt -1)))
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(*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
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(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
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(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 eps)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
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(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
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(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* -1 x)
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(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
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(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
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x
(+ x (* -1/2 (/ eps x)))
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(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
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(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (sqrt.f64 eps)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
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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))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))

eval205.0ms (2.1%)

Compiler

Compiled 33782 to 3418 computations (89.9% saved)

prune181.0ms (1.8%)

Pruning

48 alts after pruning (44 fresh and 4 done)

PrunedKeptTotal
New1121231144
Fresh192140
Picked325
Done022
Total1143481191
Accuracy
100.0%
Counts
1191 → 48
Alt Table
Click to see full alt table
StatusAccuracyProgram
5.7%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) 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)))))
16.7%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
34.6%
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
44.0%
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
42.1%
(/.f64 (neg.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 x (/.f64 eps x)))))) x)
44.8%
(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
42.4%
(/.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)))))
44.8%
(/.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))))
61.5%
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))))
44.5%
(/.f64 eps (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
3.3%
(-.f64 x (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))))))
2.8%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
3.7%
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x)) eps))
5.1%
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
3.5%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
2.8%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))))))
3.4%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) (*.f64 x x)) eps)))))
2.8%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/4 binary64) x)) (*.f64 eps eps))))))
6.1%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) eps)))))
2.8%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
2.8%
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (/.f64 eps x))))
3.9%
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -4 binary64) (*.f64 x x)) (*.f64 eps eps)) (/.f64 #s(literal -2 binary64) eps)))))
7.0%
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))
7.0%
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
4.8%
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)))))
3.6%
(-.f64 x (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))) x) x) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
2.8%
(-.f64 x (*.f64 (/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 eps #s(literal 1/2 binary64))) x))
5.0%
(-.f64 x (*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
2.9%
(-.f64 x (*.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
1.4%
(-.f64 x (*.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))))
✓2.6%
(-.f64 x (*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
2.4%
(-.f64 x (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
2.8%
(-.f64 x (*.f64 (/.f64 x (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
2.6%
(-.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
6.1%
(-.f64 x (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
3.6%
(-.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 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
6.1%
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
3.3%
(-.f64 x (*.f64 (*.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) x)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
6.2%
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
5.1%
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
58.0%
(-.f64 x (sqrt.f64 (neg.f64 eps)))
43.8%
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
43.9%
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
43.7%
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
✓3.3%
x
4.3%
#s(literal 0 binary64)
Compiler

Compiled 3524 to 1072 computations (69.6% saved)

regimes121.0ms (1.2%)

Counts
96 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) 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 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.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 x #s(literal 2 binary64)))
(*.f64 (neg.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) x)) eps)
(/.f64 (neg.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 x (/.f64 eps x)))))) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x)))
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) (/.f64 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)
(/.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 #s(literal 0 binary64) eps) (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)))))
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -4 binary64) (*.f64 x x)) (*.f64 eps eps)) (/.f64 #s(literal -2 binary64) eps)))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x)) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(-.f64 x (*.f64 (/.f64 x (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
(-.f64 x (*.f64 (/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 eps #s(literal 1/2 binary64))) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 eps eps))))))
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x))) x)))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(/.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 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (/.f64 eps x))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) (*.f64 x x)) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
(-.f64 x (*.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) x) x)))))
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(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))))))
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(/.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
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(-.f64 x (*.f64 (*.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) x)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))) x) x) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(-.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(-.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 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 eps (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps eps) #s(literal -8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.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 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) x) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))))))))
(-.f64 x (*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(-.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 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
(-.f64 x (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 x (sqrt.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))))
(/.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) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (*.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(*.f64 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)))))))))
Outputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Calls

3 calls:

39.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
37.0ms
x
27.0ms
eps
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)

regimes100.0ms (1%)

Counts
90 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) 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 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.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 x #s(literal 2 binary64)))
(*.f64 (neg.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) x)) eps)
(/.f64 (neg.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 x (/.f64 eps x)))))) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x)))
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(/.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)
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(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -4 binary64) (*.f64 x x)) (*.f64 eps eps)) (/.f64 #s(literal -2 binary64) eps)))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x)) eps))
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(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(-.f64 x (*.f64 (/.f64 x (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
(-.f64 x (*.f64 (/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 eps #s(literal 1/2 binary64))) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 eps eps))))))
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(-.f64 x (/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(/.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 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (/.f64 eps x))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) (*.f64 x x)) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
(-.f64 x (*.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) x) x)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/4 binary64) x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x x))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 x eps))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))))))
(/.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) 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 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 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 eps eps))))
(-.f64 x (-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (/.f64 (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(-.f64 x (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(-.f64 x (*.f64 (*.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) x)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))) x) x) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(-.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(-.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 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 eps (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps eps) #s(literal -8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.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 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) x) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))))))))
(-.f64 x (*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(-.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 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
(-.f64 x (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

3 calls:

31.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
27.0ms
eps
25.0ms
x
Results
AccuracySegmentsBranch
91.0%2x
80.1%2eps
99.5%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes42.0ms (0.4%)

Counts
88 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) 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 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.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 x #s(literal 2 binary64)))
(*.f64 (neg.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) x)) eps)
(/.f64 (neg.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 x (/.f64 eps x)))))) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x)))
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x))) (/.f64 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)
(/.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 #s(literal 0 binary64) eps) (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 x eps) x)))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)))))
(-.f64 x (+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) x)) x))))
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -4 binary64) (*.f64 x x)) (*.f64 eps eps)) (/.f64 #s(literal -2 binary64) eps)))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x)) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(-.f64 x (*.f64 (/.f64 x (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
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(-.f64 x (/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(/.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)))))
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(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) (*.f64 x x)) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
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(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) x) x)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/4 binary64) x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))))))
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x x))))
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 x eps))) (-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))))))))
(/.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) 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 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 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 eps eps))))
(-.f64 x (-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (/.f64 (/.f64 (*.f64 eps eps) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)
(-.f64 x (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))))))
(-.f64 x (*.f64 (*.f64 (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) x)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.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 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))) x) x) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(-.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(-.f64 x (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(-.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 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x)))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 eps (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps eps) #s(literal -8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 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 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(-.f64 x (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))))
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 (+.f64 x x) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))
(/.f64 (*.f64 (+.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 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) x) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x (*.f64 x x))))))))
(-.f64 x (*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))
(-.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 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))))) (-.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))))
(-.f64 x (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (-.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (/.f64 x eps) (/.f64 x eps)) (/.f64 x eps)))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
Outputs
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

1 calls:

27.0ms
x
Results
AccuracySegmentsBranch
90.3%2x
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes54.0ms (0.5%)

Counts
86 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) 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 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(/.f64 eps (*.f64 x (+.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 x #s(literal 2 binary64)))
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Outputs
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
Calls

2 calls:

25.0ms
x
24.0ms
eps
Results
AccuracySegmentsBranch
44.8%1eps
44.8%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.2%)

Counts
13 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(-.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 x (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps)))
(-.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) x))
Outputs
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
Calls

2 calls:

14.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
44.0%1x
44.0%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

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

2 calls:

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

Compiled 6 to 4 computations (33.3% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-3.496234071307669e-155
0.0
Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch10.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
8.0ms
8.66241737742493e-90
1.60696395306489e-89
Results
4.0ms35×1valid
2.0ms29×0valid
0.0ms6×0invalid
Compiler

Compiled 103 to 70 computations (32% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 1.0ms (29.5% of total)
ival-sub: 1.0ms (29.5% of total)
ival-sqrt: 1.0ms (29.5% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify14.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02777
14077
24977
35477
45677
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 -4830671903771573/241533595188578646543459493183249209018682958106652187416077203215719946393097526533512110411370161122653976001968886073585317416315186728483931792091692546793561300926464 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(if (<=.f64 x #s(literal 5733746539975179/573374653997517877902705223825521735199141247292070280934397209846730719022121202017504638277531421638656 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
#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 -4830671903771573/241533595188578646543459493183249209018682958106652187416077203215719946393097526533512110411370161122653976001968886073585317416315186728483931792091692546793561300926464 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(if (<=.f64 x #s(literal 5733746539975179/573374653997517877902705223825521735199141247292070280934397209846730719022121202017504638277531421638656 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(if (<=.f64 x #s(literal 5733746539975179/573374653997517877902705223825521735199141247292070280934397209846730719022121202017504638277531421638656 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
#s(literal 0 binary64)

soundness1.9s (19.6%)

Rules
6450×*-lowering-*.f32
6450×*-lowering-*.f64
5012×*-lowering-*.f32
5012×*-lowering-*.f64
4906×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09396360
132145656
090435656
08175899
128004909
092014909
041235
1307226
23067217
08660217
029141
1211131
22399125
08258125
0618
14118
232818
3408018
0835418
02571162
18561066
230331031
080351031
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 277 to 133 computations (52% saved)

preprocess62.0ms (0.6%)

Compiler

Compiled 204 to 80 computations (60.8% saved)

end0.0ms (0%)

Profiling

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