ENA, Section 1.4, Exercise 4d

Time bar (total: 5.6s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze19.0ms (0.3%)

Memory
-10.2MiB live, 34.2MiB allocated; 7ms collecting garbage
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 24 to 18 computations (25% saved)

sample1.5s (27.7%)

Memory
45.5MiB live, 1 538.7MiB allocated; 338ms collecting garbage
Samples
497.0ms4 828×0valid
458.0ms2 774×1valid
115.0ms654×2valid
31.0ms155×0invalid
Precisions
Click to see histograms. Total time spent on operations: 768.0ms
ival-mult: 216.0ms (28.1% of total)
ival-sub: 164.0ms (21.3% of total)
ival-sqrt: 133.0ms (17.3% of total)
adjust: 119.0ms (15.5% of total)
ival-<=: 92.0ms (12% of total)
ival-and: 23.0ms (3% of total)
exact: 18.0ms (2.3% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

explain104.0ms (1.9%)

Memory
-19.8MiB live, 158.6MiB allocated; 23ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1091(3.317328434341291e-53 1.0805286610062134e-107)0-(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
00-0-eps
00-0-(sqrt.f64 (-.f64 (*.f64 x x) eps))
00-0-(-.f64 (*.f64 x x) eps)
00-0-(*.f64 x x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))cancellation1100
Confusion
Predicted +Predicted -
+1090
-1146
Precision
0.990909090909091
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+10900
-10146
Precision?
0.990909090909091
Recall?
1.0
Freqs
test
numberfreq
0146
1110
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
21.0ms172×1valid
15.0ms300×0valid
7.0ms40×2valid
Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-sub: 8.0ms (29.9% of total)
adjust: 7.0ms (26.2% of total)
ival-sqrt: 6.0ms (22.4% of total)
ival-mult: 6.0ms (22.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess16.0ms (0.3%)

Memory
-6.9MiB live, 37.9MiB allocated; 5ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01846
13246
26146
38846
411246
068
0108
1148
2278
3468
4588
0588
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.4MiB live, 1.4MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Memory
13.3MiB live, 13.3MiB allocated; 0ms collecting garbage
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)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0624
01024
11424
22724
34624
45824
05824
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps

localize28.0ms (0.5%)

Memory
3.0MiB live, 49.5MiB allocated; 2ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.0078125
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.015625
(-.f64 (*.f64 x x) eps)
accuracy24.194933043325374
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Samples
10.0ms86×1valid
8.0ms150×0valid
5.0ms20×2valid
Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-sqrt: 4.0ms (29% of total)
ival-sub: 4.0ms (29% of total)
adjust: 3.0ms (21.8% of total)
ival-mult: 3.0ms (21.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory
14.6MiB live, 14.6MiB allocated; 0ms collecting garbage
Counts
4 → 49
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
Outputs
(* -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)))
(* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 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)
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)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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 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))))))))
(* 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))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (+ 1 (* -1 (/ (pow x 2) eps)))))
Calls

6 calls:

TimeVariablePointExpression
2.0ms
eps
@inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
2.0ms
x
@inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms
x
@0
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms
eps
@-inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms
eps
@0
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))

simplify175.0ms (3.1%)

Memory
-12.2MiB live, 171.2MiB allocated; 27ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02571067
18071053
233631038
08415979
Stop Event
1×iter limit
1×node limit
Counts
49 → 48
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)))
(* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 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)
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)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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 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))))))))
(* 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))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (+ 1 (* -1 (/ (pow x 2) eps)))))
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* 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)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64))) (*.f64 x x) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))
(fma.f64 (fma.f64 (*.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/8 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64))) (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps (*.f64 #s(literal -1/8 binary64) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) eps))))
(/ (- (* 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 (fma.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) (/.f64 eps x) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) 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)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) eps) eps) (pow.f64 x #s(literal 4 binary64))))) x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64) #s(literal -2 binary64)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))))
(* -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 (neg.f64 x) (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(* -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))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) eps) eps) (pow.f64 x #s(literal 4 binary64))))) x x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* 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 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 eps x) #s(literal -1/2 binary64)) x) eps x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 5 binary64))) eps (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal -1/2 binary64) x)) eps x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.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 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) 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)))))
(*.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* 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 (fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(fma.f64 (/.f64 x eps) eps (*.f64 (*.f64 eps (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 (neg.f64 eps) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal -1/2 binary64) (neg.f64 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 (neg.f64 eps) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps) x) eps)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64)) (fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)

rewrite80.0ms (1.4%)

Memory
-30.2MiB live, 32.1MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0622
01022
14222
032022
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
4 → 41
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
Outputs
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (neg.f64 (fma.f64 x x eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (fma.f64 x x eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))
(sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval11.0ms (0.2%)

Memory
13.5MiB live, 13.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 993 to 440 computations (77.9% saved)

prune10.0ms (0.2%)

Memory
14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New751186
Fresh000
Picked011
Done000
Total751287
Accuracy
99.4%
Counts
87 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
47.1%
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))
▶61.9%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
47.0%
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
▶61.8%
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
7.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
25.4%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (fma.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) (/.f64 eps x) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x))
▶30.3%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
38.8%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶44.1%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Compiler

Compiled 532 to 294 computations (44.7% saved)

simplify98.0ms (1.8%)

Memory
-2.9MiB live, 85.6MiB allocated; 10ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
cost-diff0
(fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff0
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff0
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff17
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
cost-diff0
(/.f64 #s(literal 1/2 binary64) x)
cost-diff0
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
cost-diff0
(neg.f64 x)
cost-diff0
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
cost-diff0
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff8
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
034278
057261
179249
2184245
3583245
43537245
08137245
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
(*.f64 x x)
x
(-.f64 (*.f64 x x) eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
x
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
eps
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
eps
(pow.f64 x #s(literal 5 binary64))
x
#s(literal 5 binary64)
#s(literal 1/16 binary64)
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
Outputs
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
eps
(*.f64 x x)
x
(-.f64 (*.f64 x x) eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
x
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
eps
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
(fma.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
eps
(pow.f64 x #s(literal 5 binary64))
x
#s(literal 5 binary64)
#s(literal 1/16 binary64)
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

localize175.0ms (3.2%)

Memory
-13.1MiB live, 130.5MiB allocated; 21ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy7.055815180336951
(fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy7.280097819541601
(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
accuracy31.917708664605904
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
accuracy35.53315662023681
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy0.015625
(-.f64 (*.f64 x x) eps)
accuracy0.34994125976844204
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy5.849423618635148
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy24.153878048733475
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
accuracy0.0
(/.f64 #s(literal 1/2 binary64) x)
accuracy0.33203125
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy35.62063415817835
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy0.0
(neg.f64 x)
accuracy24.194933043325374
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy62.411527461044514
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy0.01171875
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.015625
(-.f64 (*.f64 x x) eps)
accuracy0.296875
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy23.826351796708263
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
Samples
71.0ms86×1valid
55.0ms150×0valid
13.0ms20×2valid
Compiler

Compiled 253 to 31 computations (87.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 117.0ms
ival-pow: 39.0ms (33.4% of total)
ival-mult: 36.0ms (30.8% of total)
ival-div: 13.0ms (11.1% of total)
adjust: 12.0ms (10.3% of total)
ival-sub: 7.0ms (6% of total)
ival-add: 5.0ms (4.3% of total)
ival-sqrt: 3.0ms (2.6% of total)
exact: 1.0ms (0.9% of total)
ival-neg: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series52.0ms (0.9%)

Memory
1.7MiB live, 89.8MiB allocated; 12ms collecting garbage
Counts
19 → 153
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
Outputs
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))))
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (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)))))))))
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(+ 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)))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/16 (/ (pow eps 2) (pow x 5)))
(/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))
(* 1/16 (/ eps (pow x 5)))
(/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(/ eps (pow x 5))
(/ (+ (* 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)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 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)
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)))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(* 2 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)))))))
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)
(/ 1/8 (pow x 3))
(/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))
(* x (- (+ 1/2 (* -1/2 (/ eps (pow x 2)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))) (pow x 4))) (* -1/2 (/ eps (pow x 2))))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))))))) (pow x 6))) (* -1/2 (/ eps (pow x 2))))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4)))))))
(* -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 (* 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 (* 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))))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* -1 (/ (+ (* -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))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x))
(* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))
(* -1 (* (pow x 3) (- (* 5/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 5/8 eps)) (pow x 4))) (* 5/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2)))) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 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 eps) (pow x 2))
(+ 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)))))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
(+ (* -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)))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))
(+ (* -3/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (- (* eps (- (* -3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -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)))))
(* eps (- (/ (pow x 2) eps) 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)))))
(* 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 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
(* 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)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(+ 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)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
Calls

6 calls:

TimeVariablePointExpression
16.0ms
x
@-inf
((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)) (/ eps (pow x 5)))
7.0ms
eps
@inf
((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)) (/ eps (pow x 5)))
7.0ms
eps
@-inf
((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)) (/ eps (pow x 5)))
6.0ms
x
@0
((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)) (/ eps (pow x 5)))
6.0ms
eps
@0
((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)) (/ eps (pow x 5)))

simplify232.0ms (4.2%)

Memory
-21.8MiB live, 272.0MiB allocated; 59ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08544132
129963867
083073668
Stop Event
1×iter limit
1×node limit
Counts
153 → 151
Calls
Call 1
Inputs
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))))
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (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)))))))))
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(+ 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)))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/16 (/ (pow eps 2) (pow x 5)))
(/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))
(* 1/16 (/ eps (pow x 5)))
(/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(/ eps (pow x 5))
(/ (+ (* 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)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 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)
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)))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(* 2 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)))))))
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)
(/ 1/8 (pow x 3))
(/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))
(* x (- (+ 1/2 (* -1/2 (/ eps (pow x 2)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))) (pow x 4))) (* -1/2 (/ eps (pow x 2))))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))))))) (pow x 6))) (* -1/2 (/ eps (pow x 2))))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4)))))))
(* -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 (* 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 (* 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))))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* -1 (/ (+ (* -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))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x))
(* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))
(* -1 (* (pow x 3) (- (* 5/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 5/8 eps)) (pow x 4))) (* 5/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2)))) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 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 eps) (pow x 2))
(+ 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)))))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
(+ (* -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)))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))
(+ (* -3/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (- (* eps (- (* -3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -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)))))
(* eps (- (/ (pow x 2) eps) 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)))))
(* 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 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
(* 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)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(+ 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)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
Outputs
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 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (*.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) x (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) #s(literal 1 binary64)) x (*.f64 (neg.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)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64))) (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 x)
(neg.f64 x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (+.f64 (/.f64 x eps) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1 binary64) (neg.f64 eps))) x (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x) (/.f64 #s(literal 1 binary64) (neg.f64 eps))) x (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)) (*.f64 x x) (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(/.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) (*.f64 x x) (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ (pow eps 2) (pow x 5)))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/8 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ eps (pow x 5)))
(*.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64))
(/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))
(/.f64 (fma.f64 #s(literal 1/16 binary64) eps (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(/.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(fma.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64) (/.f64 x #s(literal -1 binary64)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(fma.f64 (fma.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) x #s(literal -1 binary64)) x (/.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))))) x #s(literal -1 binary64)) x (/.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64))))
(/ eps (pow x 5))
(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x)
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(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
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(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -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 (neg.f64 eps) (-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) eps)) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (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 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (/.f64 (fma.f64 (neg.f64 x) eps (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) eps)) (neg.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (/.f64 (neg.f64 (fma.f64 eps x (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (neg.f64 (*.f64 (sqrt.f64 eps) x)) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 eps))) eps))) (neg.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (neg.f64 eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (/.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)) #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (neg.f64 eps))) (neg.f64 eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(/.f64 (fma.f64 (*.f64 (sqrt.f64 eps) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 (fma.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x)) (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 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 (*.f64 (pow.f64 x #s(literal 5 binary64)) eps) (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) eps) #s(literal -1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (neg.f64 eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (neg.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) (neg.f64 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 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) eps)) (neg.f64 eps))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps)
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x)) (neg.f64 eps)))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 #s(literal 3/2 binary64) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)) (fma.f64 (*.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps x))) (neg.f64 eps)))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (/.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x)) (sqrt.f64 #s(literal -1 binary64)))))) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x)) (sqrt.f64 #s(literal -1 binary64))))))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x))) (neg.f64 eps)))

rewrite67.0ms (1.2%)

Memory
11.4MiB live, 58.2MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
034221
057212
1203186
01660186
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
19 → 229
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
Outputs
(*.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (fabs.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 eps eps) (*.f64 #s(literal 0 binary64) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (*.f64 x x) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) (fma.f64 x x (-.f64 (*.f64 x x) eps)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64))) (fma.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 x x (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (-.f64 (*.f64 x x) eps))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (fma.f64 x x (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 eps #s(literal 0 binary64))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
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(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (neg.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))) eps))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))))
(+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps) #s(literal 2 binary64)))))
(+.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps) (/.f64 #s(literal 1/2 binary64) x))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) eps))
(/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64))) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))) (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) eps) (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/8 binary64))) (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))))
(/.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) eps) (pow.f64 x #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64))) (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) eps))) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (pow.f64 x #s(literal 5 binary64))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) eps))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 5 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))))
(/.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))))))
(/.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))) (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64))))
(fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/2 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))))
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5/2 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5/2 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))
(fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))))
(fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))))
(fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))) (/.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))))
(-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))))
(-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 (neg.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64)))
(+.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))) (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64)))) (/.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))) (pow.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)))
(+.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (*.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))) (fma.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) x (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (fma.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) eps)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (*.f64 (fma.f64 x x eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(neg.f64 (/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (/.f64 eps (pow.f64 x #s(literal 5/2 binary64))) (pow.f64 x #s(literal 5/2 binary64)))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64)))))
(/.f64 (neg.f64 eps) (neg.f64 (pow.f64 x #s(literal 5 binary64))))
(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
(neg.f64 (/.f64 (neg.f64 eps) (pow.f64 x #s(literal 5 binary64))))
(neg.f64 (/.f64 eps (neg.f64 (pow.f64 x #s(literal 5 binary64)))))

eval112.0ms (2%)

Memory
-38.2MiB live, 105.1MiB allocated; 13ms collecting garbage
Compiler

Compiled 21 366 to 2 123 computations (90.1% saved)

prune45.0ms (0.8%)

Memory
-4.8MiB live, 42.3MiB allocated; 4ms collecting garbage
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New5736579
Fresh426
Picked325
Done011
Total58011591
Accuracy
100.0%
Counts
591 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶47.4%
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶99.5%
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶7.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶81.4%
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
44.3%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
31.5%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 #s(approx (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/.f64 (fma.f64 #s(literal 1/16 binary64) eps (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
✓44.1%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
42.6%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
Compiler

Compiled 401 to 272 computations (32.2% saved)

simplify163.0ms (2.9%)

Memory
15.8MiB live, 158.2MiB allocated; 14ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
cost-diff0
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
cost-diff1
(fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))
cost-diff2
(+.f64 #s(literal 0 binary64) eps)
cost-diff0
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff1
(-.f64 #s(literal 0 binary64) eps)
cost-diff1
(-.f64 #s(literal 0 binary64) (*.f64 eps eps))
cost-diff6
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
cost-diff0
(/.f64 eps x)
cost-diff0
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
cost-diff0
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
cost-diff0
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
cost-diff0
(neg.f64 eps)
cost-diff0
#s(approx (- (* x x) eps) (neg.f64 eps))
cost-diff0
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff0
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff0
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff0
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff2
(+.f64 eps #s(literal 0 binary64))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036287
064259
1113257
2313257
31075257
45433257
08458257
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
x
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps eps))
#s(literal 0 binary64)
(*.f64 eps eps)
eps
(-.f64 #s(literal 0 binary64) eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
(+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
#s(literal 3/2 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
Outputs
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
x
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
eps
(-.f64 #s(literal 0 binary64) (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
#s(literal 0 binary64)
(*.f64 eps eps)
eps
(-.f64 #s(literal 0 binary64) eps)
(neg.f64 eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(*.f64 (fma.f64 (-.f64 (+.f64 x x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) x (neg.f64 eps)) (/.f64 eps (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 eps (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
(+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
#s(literal 3/2 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))
(fma.f64 (-.f64 (+.f64 x x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) x (neg.f64 eps))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))

localize280.0ms (5%)

Memory
9.1MiB live, 248.3MiB allocated; 26ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.16796875
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))
accuracy0.35384750976844204
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
accuracy11.52512599647902
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
accuracy24.194933043325374
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy0.01171875
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.015625
(-.f64 (*.f64 x x) eps)
accuracy0.296875
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy32.8291713591133
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
accuracy0.0
(/.f64 eps x)
accuracy0.00390625
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy24.194933043325374
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy34.807088202915715
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy0.0
(neg.f64 eps)
accuracy0.0078125
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy24.194933043325374
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy26.477864152244837
#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy0.0078125
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.01171875
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.015625
(-.f64 (*.f64 x x) eps)
accuracy0.296875
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Samples
135.0ms86×1valid
105.0ms150×0valid
14.0ms20×2valid
Compiler

Compiled 269 to 32 computations (88.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 142.0ms
ival-pow: 69.0ms (48.7% of total)
ival-add: 26.0ms (18.3% of total)
adjust: 12.0ms (8.5% of total)
ival-div: 11.0ms (7.8% of total)
ival-mult: 11.0ms (7.8% of total)
ival-sub: 6.0ms (4.2% of total)
ival-sqrt: 3.0ms (2.1% of total)
exact: 1.0ms (0.7% of total)
ival-neg: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series58.0ms (1%)

Memory
5.2MiB live, 48.5MiB allocated; 12ms collecting garbage
Counts
23 → 175
Calls
Call 1
Inputs
(+.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps eps))
(-.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 #s(literal 0 binary64) eps)
(fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))
Outputs
(* (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))))
(* (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 (* (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)))))))))
(* -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 eps)
(- (pow x 2) eps)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(- (* -1 (* (sqrt eps) (* x (sqrt -1)))) eps)
(- (* x (+ (* -1 (* (sqrt eps) (sqrt -1))) (* 2 x))) eps)
(- (* x (+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 2 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))) eps)
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 x) (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (- (* x (- (* 2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))) 1)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (- (* x (- (+ (* 2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2)))) (* -1/2 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (* (pow eps 3) (pow (sqrt -1) 2))))))) (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))) 1)))
(* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(+ (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* (pow x 2) (- (* -1 (/ x (* (pow eps 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))))
(+ (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* (pow x 2) (- (* x (- (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow eps 13))) (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (pow (sqrt -1) 5)))) (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (pow (sqrt -1) 3))))))) (/ 1 (* (pow eps 2) (pow (sqrt -1) 2))))) (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))))
(* (sqrt (pow eps 3)) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))))
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- 1 (* 1/2 (/ (* (+ (* 2 (pow eps 2)) (pow eps 2)) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (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)
(* 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)))))))
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)))))))
(/ (- (* 1/8 (/ (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)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1/2 eps)) (pow x 2)))))
(* (pow x 2) (- (+ 1 (* 1/8 (/ (pow eps 2) (pow x 4)))) (+ (* -1/2 (/ eps (pow x 2))) (/ eps (pow x 2)))))
(* (pow x 2) (- (+ 1 (* 1/16 (/ (pow eps 3) (pow x 6)))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (/ eps (pow x 2))))))
(/ (- (+ (* -1/2 (/ (* eps (+ eps (* -1/2 eps))) (pow x 2))) (* 1/2 eps)) (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2)))) x)
(/ (- (+ (* -1/2 (/ (* eps (+ eps (* -1/2 eps))) (pow x 2))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))) (+ (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (+ (* 1/8 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4))) (* 1/4 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps)))))) (pow x 4)))))) x)
(/ (- (+ (* -1/2 (/ (* eps (+ eps (* -1/2 eps))) (pow x 2))) (+ (* 1/32 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)))) (+ (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (+ (* 1/8 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow x 6))) (+ (* 1/8 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4))) (+ (* 1/4 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps)))))) (pow x 4))) (+ (* 1/4 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/16 (pow eps 3)) (+ (* 1/8 (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))) (* 1/4 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps)))))))))) (pow x 6))) (* 1/4 (/ (* (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps))))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 6))))))))) x)
(* 1/2 (/ eps (pow x 3)))
(/ (+ (* -1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (* 1/2 eps)) (pow x 3))
(/ (- (+ (* -1 (/ (+ (* -1/32 (* eps (pow (+ (* -2 eps) (* -1 eps)) 2))) (* 1/8 (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* 1/2 eps)) (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2)))) (pow x 3))
(/ (- (+ (* -1 (/ (+ (* -1/4 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/32 (* eps (pow (+ (* -2 eps) (* -1 eps)) 2))) (* 1/8 (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))) (+ (* -1/32 (* eps (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (* 1/8 (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))))) (pow x 6))) (* 1/2 eps)) (+ (* -1/32 (/ (* eps (pow (+ (* -2 eps) (* -1 eps)) 2)) (pow x 4))) (+ (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (* 1/8 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4)))))) (pow x 3))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))
(* -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 (/ (+ (* -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))
(* -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))))))))
(* -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 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* 3 (pow x 2))
(* (pow x 2) (- (+ 3 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2))))
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2))))
(* -6 (/ (* eps x) (+ (* -2 eps) (* -1 eps))))
(* -1 (* x (- (+ (* 2 (/ (* eps (- (* -1/2 eps) eps)) (* (pow x 2) (+ (* -2 eps) (* -1 eps))))) (* 6 (/ eps (+ (* -2 eps) (* -1 eps))))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))))))
(* -1 (* x (- (+ (* -1/4 (/ (pow eps 3) (* (pow x 4) (+ (* -2 eps) (* -1 eps))))) (+ (* 2 (/ (* eps (- (* -1/2 eps) eps)) (* (pow x 2) (+ (* -2 eps) (* -1 eps))))) (* 6 (/ eps (+ (* -2 eps) (* -1 eps)))))) (+ (* 6 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (/ (* (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 4) (+ (* -2 eps) (* -1 eps)))))))))
(* -1 (* x (- (+ (* -1/4 (/ (pow eps 3) (* (pow x 4) (+ (* -2 eps) (* -1 eps))))) (+ (* -1/8 (/ (pow eps 4) (* (pow x 6) (+ (* -2 eps) (* -1 eps))))) (+ (* 2 (/ (* eps (- (* -1/2 eps) eps)) (* (pow x 2) (+ (* -2 eps) (* -1 eps))))) (* 6 (/ eps (+ (* -2 eps) (* -1 eps))))))) (+ (* -6 (/ (* eps (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))))) (* (pow x 6) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 6 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (/ (* (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2))))) (* (pow x 6) (+ (* -2 eps) (* -1 eps)))) (+ (/ (* (- (* -1/4 (/ (pow eps 3) (+ (* -2 eps) (* -1 eps)))) (+ (* 6 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow (+ (* -2 eps) (* -1 eps)) 2))) (/ (* (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* -2 eps) (* -1 eps))))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 6) (+ (* -2 eps) (* -1 eps)))) (/ (* (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 4) (+ (* -2 eps) (* -1 eps))))))))))))
(* -2 (/ eps (* x (+ (* -2 eps) (* -1 eps)))))
(* -1 (/ (+ (* -2 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* 2 (/ eps (+ (* -2 eps) (* -1 eps))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* -2 (/ (* eps (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (pow (+ (* -2 eps) (* -1 eps)) 3))) (* 2 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4))) (* 2 (/ eps (+ (* -2 eps) (* -1 eps))))) (* 2 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* -2 (/ (* eps (* (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))) (pow (+ (* -2 eps) (* -1 eps)) 3))) (+ (* -2 (/ (* eps (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))))) (pow (+ (* -2 eps) (* -1 eps)) 2))) (* -1 (/ (* (+ (* -2 (/ (* eps (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (pow (+ (* -2 eps) (* -1 eps)) 3))) (* 2 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* -2 eps) (* -1 eps)))))) (pow x 6))) (* 2 (/ eps (+ (* -2 eps) (* -1 eps))))) (+ (* -2 (/ (* eps (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 3)))) (+ (* 2 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* 2 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2))))))) x))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))))
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))
eps
(* 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))))
(+ (* -1/2 (/ 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)))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(* -1 (pow eps 2))
(+ (* -1/2 eps) (pow x 2))
(+ (* eps (- (* 1/8 (/ eps (pow x 2))) 1/2)) (pow x 2))
(+ (* eps (- (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 1/2)) (pow x 2))
(* eps (+ (* -1 (* eps (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (- (* eps (- (* 1/16 (/ 1 (pow x 5))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (- (* eps (- (+ (* 1/16 (/ 1 (pow x 5))) (* eps (- (* 1/32 (/ 1 (pow x 7))) (+ (* -1/4 (/ (* (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))) (+ (* -1/8 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 7))) (* 1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (* 1/16 (/ 1 (pow x 5))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (pow x 6)))))))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(* eps (+ (* -1/8 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 9))) (* 1/2 (/ 1 (pow x 3)))))
(* eps (+ (* eps (- (* -1 (* eps (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9)))))) (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 9))))) (* 1/2 (/ 1 (pow x 3)))))
(* eps (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9))))) (pow x 6))) (+ (* -1/8 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 9))) (* -1/32 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 15))))))) (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9)))))) (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 9))))) (* 1/2 (/ 1 (pow x 3)))))
(+ (* 1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) (pow x 3))
(+ (* eps (+ (* 1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) (pow x 3))
(+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3))
(- (+ (* -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)))))
(* 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)))))
(* 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))))))
(* 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)))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1))
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (* 2 (/ (pow x 2) eps))) 1))
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (* 2 (/ (pow x 2) eps)))) 1))
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (* 2 (/ (pow x 2) eps))))) 1))
(* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1)))
(+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1))))
(- (+ (* -1/2 (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1))))) (/ (* (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)) (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) (* eps (pow (sqrt -1) 2))))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) (pow (sqrt -1) 3)))) (* 2 (/ (* eps (* (pow x 2) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* -1/2 (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1)))))) (/ (* (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)) (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) (* eps (pow (sqrt -1) 2))))
(/ (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (/ (* eps (pow x 3)) (pow (sqrt -1) 2))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) eps)
(/ (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)) (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (/ (* eps (pow x 3)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (pow (sqrt -1) 3))))) (pow eps 4))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) eps)
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 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)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))
(* -1 (* eps (+ 1 (+ (* -2 (/ (pow x 2) eps)) (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
(* -1 (* eps (+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps))))))
(* -1 (* eps (+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1))))) eps)) (* 2 (pow x 2))) eps))))))
(* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
(+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))) (* 2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))))
(+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))) (* -1 (/ (- (+ (* -2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/2 (pow x 3))) (* -1 (* (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3))))) eps)))
(+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))) (* -1 (/ (+ (* -2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (/ (+ (* -1 (- (* 1/2 (* eps (pow x 3))) (* -1 (* eps (* (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3))))))) (* -1 (/ (+ (* -2 (* eps (* (pow x 2) (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3))))) (* 1/2 (* (sqrt (pow eps 3)) (* (sqrt -1) (* (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* 2 (pow x 4)) (pow x 4))))))) eps))) eps))) eps)))
(* (sqrt (/ 1 eps)) (sqrt -1))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) eps))) eps))
(* -1 (/ (- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (/ (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) eps)) eps))
(* -1 (/ (- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* (sqrt eps) (* (sqrt -1) (pow (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) 2)))) (* -1/2 (* (sqrt (pow eps 3)) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3)))) (/ (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) eps)) eps))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
Calls

6 calls:

TimeVariablePointExpression
19.0ms
eps
@0
((+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (/ (- 0 (* eps eps)) (- 0 eps)) (- 0 (* eps eps)) (- 0 eps) (/ (/ (- 0 (* eps eps)) (- 0 eps)) (+ (sqrt (- (* x x) eps)) x)) (+ 0 eps) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps)) (* (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps))) (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (pow (- (* x x) eps) 3/2))
8.0ms
x
@-inf
((+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (/ (- 0 (* eps eps)) (- 0 eps)) (- 0 (* eps eps)) (- 0 eps) (/ (/ (- 0 (* eps eps)) (- 0 eps)) (+ (sqrt (- (* x x) eps)) x)) (+ 0 eps) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps)) (* (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps))) (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (pow (- (* x x) eps) 3/2))
7.0ms
x
@inf
((+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (/ (- 0 (* eps eps)) (- 0 eps)) (- 0 (* eps eps)) (- 0 eps) (/ (/ (- 0 (* eps eps)) (- 0 eps)) (+ (sqrt (- (* x x) eps)) x)) (+ 0 eps) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps)) (* (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps))) (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (pow (- (* x x) eps) 3/2))
7.0ms
eps
@inf
((+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (/ (- 0 (* eps eps)) (- 0 eps)) (- 0 (* eps eps)) (- 0 eps) (/ (/ (- 0 (* eps eps)) (- 0 eps)) (+ (sqrt (- (* x x) eps)) x)) (+ 0 eps) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps)) (* (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps))) (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (pow (- (* x x) eps) 3/2))
7.0ms
eps
@-inf
((+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (/ (- 0 (* eps eps)) (- 0 eps)) (- 0 (* eps eps)) (- 0 eps) (/ (/ (- 0 (* eps eps)) (- 0 eps)) (+ (sqrt (- (* x x) eps)) x)) (+ 0 eps) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps)) (* (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (+ (* x (- x (sqrt (- (* x x) eps)))) (- (* x x) eps))) (/ (+ 0 eps) (+ (pow (- (* x x) eps) 3/2) (pow x 3))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (pow (- (* x x) eps) 3/2))

simplify200.0ms (3.6%)

Memory
-7.4MiB live, 131.0MiB allocated; 31ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011447128
140676857
080616503
Stop Event
1×iter limit
1×node limit
Counts
175 → 173
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))))
(* (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 (* (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)))))))))
(* -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 eps)
(- (pow x 2) eps)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(- (* -1 (* (sqrt eps) (* x (sqrt -1)))) eps)
(- (* x (+ (* -1 (* (sqrt eps) (sqrt -1))) (* 2 x))) eps)
(- (* x (+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 2 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))) eps)
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 x) (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (- (* x (- (* 2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))) 1)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (- (* x (- (+ (* 2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2)))) (* -1/2 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (* (pow eps 3) (pow (sqrt -1) 2))))))) (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))) 1)))
(* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(+ (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* (pow x 2) (- (* -1 (/ x (* (pow eps 2) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))))
(+ (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* (pow x 2) (- (* x (- (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow eps 13))) (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (pow (sqrt -1) 5)))) (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (pow (sqrt -1) 3))))))) (/ 1 (* (pow eps 2) (pow (sqrt -1) 2))))) (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow (sqrt -1) 3)))))))
(* (sqrt (pow eps 3)) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))))
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- 1 (* 1/2 (/ (* (+ (* 2 (pow eps 2)) (pow eps 2)) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (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)
(* 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)))))))
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)))))))
(/ (- (* 1/8 (/ (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)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ eps (* -1/2 eps)) (pow x 2)))))
(* (pow x 2) (- (+ 1 (* 1/8 (/ (pow eps 2) (pow x 4)))) (+ (* -1/2 (/ eps (pow x 2))) (/ eps (pow x 2)))))
(* (pow x 2) (- (+ 1 (* 1/16 (/ (pow eps 3) (pow x 6)))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (/ eps (pow x 2))))))
(/ (- (+ (* -1/2 (/ (* eps (+ eps (* -1/2 eps))) (pow x 2))) (* 1/2 eps)) (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2)))) x)
(/ (- (+ (* -1/2 (/ (* eps (+ eps (* -1/2 eps))) (pow x 2))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))) (+ (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (+ (* 1/8 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4))) (* 1/4 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps)))))) (pow x 4)))))) x)
(/ (- (+ (* -1/2 (/ (* eps (+ eps (* -1/2 eps))) (pow x 2))) (+ (* 1/32 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)))) (+ (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (+ (* 1/8 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow x 6))) (+ (* 1/8 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4))) (+ (* 1/4 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps)))))) (pow x 4))) (+ (* 1/4 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/16 (pow eps 3)) (+ (* 1/8 (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))) (* 1/4 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps)))))))))) (pow x 6))) (* 1/4 (/ (* (- (* -1/2 (* eps (+ eps (* -1/2 eps)))) (* 1/8 (* eps (+ (* -2 eps) (* -1 eps))))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 6))))))))) x)
(* 1/2 (/ eps (pow x 3)))
(/ (+ (* -1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (* 1/2 eps)) (pow x 3))
(/ (- (+ (* -1 (/ (+ (* -1/32 (* eps (pow (+ (* -2 eps) (* -1 eps)) 2))) (* 1/8 (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* 1/2 eps)) (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2)))) (pow x 3))
(/ (- (+ (* -1 (/ (+ (* -1/4 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/32 (* eps (pow (+ (* -2 eps) (* -1 eps)) 2))) (* 1/8 (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))) (+ (* -1/32 (* eps (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (* 1/8 (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))))) (pow x 6))) (* 1/2 eps)) (+ (* -1/32 (/ (* eps (pow (+ (* -2 eps) (* -1 eps)) 2)) (pow x 4))) (+ (* 1/8 (/ (* eps (+ (* -2 eps) (* -1 eps))) (pow x 2))) (* 1/8 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4)))))) (pow x 3))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))
(* -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 (/ (+ (* -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))
(* -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))))))))
(* -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 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* 3 (pow x 2))
(* (pow x 2) (- (+ 3 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2))))
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2))))
(* -6 (/ (* eps x) (+ (* -2 eps) (* -1 eps))))
(* -1 (* x (- (+ (* 2 (/ (* eps (- (* -1/2 eps) eps)) (* (pow x 2) (+ (* -2 eps) (* -1 eps))))) (* 6 (/ eps (+ (* -2 eps) (* -1 eps))))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))))))
(* -1 (* x (- (+ (* -1/4 (/ (pow eps 3) (* (pow x 4) (+ (* -2 eps) (* -1 eps))))) (+ (* 2 (/ (* eps (- (* -1/2 eps) eps)) (* (pow x 2) (+ (* -2 eps) (* -1 eps))))) (* 6 (/ eps (+ (* -2 eps) (* -1 eps)))))) (+ (* 6 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (/ (* (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 4) (+ (* -2 eps) (* -1 eps)))))))))
(* -1 (* x (- (+ (* -1/4 (/ (pow eps 3) (* (pow x 4) (+ (* -2 eps) (* -1 eps))))) (+ (* -1/8 (/ (pow eps 4) (* (pow x 6) (+ (* -2 eps) (* -1 eps))))) (+ (* 2 (/ (* eps (- (* -1/2 eps) eps)) (* (pow x 2) (+ (* -2 eps) (* -1 eps))))) (* 6 (/ eps (+ (* -2 eps) (* -1 eps))))))) (+ (* -6 (/ (* eps (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))))) (* (pow x 6) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 6 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (/ (* (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2))))) (* (pow x 6) (+ (* -2 eps) (* -1 eps)))) (+ (/ (* (- (* -1/4 (/ (pow eps 3) (+ (* -2 eps) (* -1 eps)))) (+ (* 6 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow (+ (* -2 eps) (* -1 eps)) 2))) (/ (* (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* -2 eps) (* -1 eps))))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 6) (+ (* -2 eps) (* -1 eps)))) (/ (* (- (* 2 (/ (* eps (- (* -1/2 eps) eps)) (+ (* -2 eps) (* -1 eps)))) (* 6 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 4) (+ (* -2 eps) (* -1 eps))))))))))))
(* -2 (/ eps (* x (+ (* -2 eps) (* -1 eps)))))
(* -1 (/ (+ (* -2 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* 2 (/ eps (+ (* -2 eps) (* -1 eps))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* -2 (/ (* eps (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (pow (+ (* -2 eps) (* -1 eps)) 3))) (* 2 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (pow x 4))) (* 2 (/ eps (+ (* -2 eps) (* -1 eps))))) (* 2 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* -2 (/ (* eps (* (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))) (pow (+ (* -2 eps) (* -1 eps)) 3))) (+ (* -2 (/ (* eps (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))))))) (pow (+ (* -2 eps) (* -1 eps)) 2))) (* -1 (/ (* (+ (* -2 (/ (* eps (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (pow (+ (* -2 eps) (* -1 eps)) 3))) (* 2 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* -2 eps) (* -1 eps)))))) (pow x 6))) (* 2 (/ eps (+ (* -2 eps) (* -1 eps))))) (+ (* -2 (/ (* eps (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 3)))) (+ (* 2 (/ (* eps (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (* (pow x 4) (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* 2 (/ (* eps (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* (pow x 2) (pow (+ (* -2 eps) (* -1 eps)) 2))))))) x))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))))
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))
eps
(* 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))))
(+ (* -1/2 (/ 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)))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(* -1 (pow eps 2))
(+ (* -1/2 eps) (pow x 2))
(+ (* eps (- (* 1/8 (/ eps (pow x 2))) 1/2)) (pow x 2))
(+ (* eps (- (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 1/2)) (pow x 2))
(* eps (+ (* -1 (* eps (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (- (* eps (- (* 1/16 (/ 1 (pow x 5))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (- (* eps (- (+ (* 1/16 (/ 1 (pow x 5))) (* eps (- (* 1/32 (/ 1 (pow x 7))) (+ (* -1/4 (/ (* (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))) (+ (* -1/8 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 7))) (* 1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (* 1/16 (/ 1 (pow x 5))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (pow x 6)))))))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
(* eps (+ (* -1/8 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 9))) (* 1/2 (/ 1 (pow x 3)))))
(* eps (+ (* eps (- (* -1 (* eps (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9)))))) (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 9))))) (* 1/2 (/ 1 (pow x 3)))))
(* eps (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9))))) (pow x 6))) (+ (* -1/8 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 9))) (* -1/32 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 15))))))) (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9)))))) (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 9))))) (* 1/2 (/ 1 (pow x 3)))))
(+ (* 1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) (pow x 3))
(+ (* eps (+ (* 1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) (pow x 3))
(+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3))
(- (+ (* -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)))))
(* 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)))))
(* 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))))))
(* 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)))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1))
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (* 2 (/ (pow x 2) eps))) 1))
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (* 2 (/ (pow x 2) eps)))) 1))
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (* 2 (/ (pow x 2) eps))))) 1))
(* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1)))
(+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1))))
(- (+ (* -1/2 (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1))))) (/ (* (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)) (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) (* eps (pow (sqrt -1) 2))))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) (pow (sqrt -1) 3)))) (* 2 (/ (* eps (* (pow x 2) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* -1/2 (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (/ (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1) (sqrt -1)))))) (/ (* (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)) (- (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) (* eps (pow (sqrt -1) 2))))
(/ (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (/ (* eps (pow x 3)) (pow (sqrt -1) 2))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) eps)
(/ (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (pow x 3)) (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (/ (* eps (pow x 3)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (pow (sqrt -1) 3))))) (pow eps 4))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) eps)
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 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)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))
(* -1 (* eps (+ 1 (+ (* -2 (/ (pow x 2) eps)) (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
(* -1 (* eps (+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps))))))
(* -1 (* eps (+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1))))) eps)) (* 2 (pow x 2))) eps))))))
(* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
(+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))) (* 2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))))
(+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))) (* -1 (/ (- (+ (* -2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/2 (pow x 3))) (* -1 (* (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3))))) eps)))
(+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))) (* -1 (/ (+ (* -2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (/ (+ (* -1 (- (* 1/2 (* eps (pow x 3))) (* -1 (* eps (* (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3))))))) (* -1 (/ (+ (* -2 (* eps (* (pow x 2) (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3))))) (* 1/2 (* (sqrt (pow eps 3)) (* (sqrt -1) (* (+ 1 (* -1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* 2 (pow x 4)) (pow x 4))))))) eps))) eps))) eps)))
(* (sqrt (/ 1 eps)) (sqrt -1))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) eps))) eps))
(* -1 (/ (- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (/ (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) eps)) eps))
(* -1 (/ (- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* (sqrt eps) (* (sqrt -1) (pow (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) 2)))) (* -1/2 (* (sqrt (pow eps 3)) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3)))) (/ (+ (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (pow x 3)) eps)) eps))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (/.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))))
(fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) x) #s(literal -1 binary64)) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(+ (* 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))))
(fma.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (*.f64 (neg.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) #s(literal -1/2 binary64))) x) #s(literal -1 binary64)) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))))) x #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
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x
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(* eps (+ (* eps (- (* eps (- (+ (* 1/16 (/ 1 (pow x 5))) (* eps (- (* 1/32 (/ 1 (pow x 7))) (+ (* -1/4 (/ (* (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))) (+ (* -1/8 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 7))) (* 1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (* 1/16 (/ 1 (pow x 5))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (pow x 6)))))))) (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3))))) (pow x 6))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 7)))))) (+ (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 7))) (* 1/4 (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))
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(* eps (+ (* -1/8 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 9))) (* 1/2 (/ 1 (pow x 3)))))
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(* eps (+ (* eps (- (* -1 (* eps (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9)))))) (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 9))))) (* 1/2 (/ 1 (pow x 3)))))
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(* eps (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1/4 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9))))) (pow x 6))) (+ (* -1/8 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 9))) (* -1/32 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 15))))))) (+ (* -1/32 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 15))) (* 1/8 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 9)))))) (* 1/8 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 9))))) (* 1/2 (/ 1 (pow x 3)))))
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(+ (* 1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) (pow x 3))
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(+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3))
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(* eps (- (/ (pow x 2) eps) 1))
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(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
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(* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 2 binary64)) eps) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 eps eps))

rewrite233.0ms (4.2%)

Memory
29.9MiB live, 175.7MiB allocated; 15ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036215
064166
1262165
22580161
08808161
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
23 → 1 111
Calls
Call 1
Inputs
(+.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps eps))
(-.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 #s(literal 0 binary64) eps)
(fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))
Outputs
(*.f64 (fabs.f64 (/.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 eps eps))
(*.f64 (fabs.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps))) eps)
(*.f64 (sqrt.f64 eps) (sqrt.f64 eps))
(*.f64 (pow.f64 (/.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 eps eps))
(*.f64 (pow.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1 binary64)) eps)
(*.f64 (pow.f64 eps #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)))
(*.f64 (/.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(*.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) eps)
(*.f64 eps (/.f64 eps eps))
(*.f64 eps (fabs.f64 (/.f64 eps eps)))
(pow.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (fabs.f64 (pow.f64 eps #s(literal 6 binary64))) (fabs.f64 (pow.f64 eps #s(literal 5 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 0 binary64))) (*.f64 eps eps))
(/.f64 (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 6 binary64)))) (*.f64 eps eps))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 0 binary64))) (*.f64 eps eps))
(/.f64 (sqrt.f64 (pow.f64 eps #s(literal 5 binary64))) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 eps))
(/.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 eps #s(literal 3 binary64)))
(/.f64 (pow.f64 eps #s(literal 6 binary64)) (neg.f64 (pow.f64 eps #s(literal 5 binary64))))
(/.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 eps #s(literal 5 binary64)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(neg.f64 eps)
(fma.f64 (fabs.f64 (/.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (fabs.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps))) eps #s(literal 0 binary64))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 eps) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1 binary64)) eps #s(literal 0 binary64))
(fma.f64 (pow.f64 eps #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) eps #s(literal 0 binary64))
(fma.f64 eps (/.f64 eps eps) #s(literal 0 binary64))
(fma.f64 eps (fabs.f64 (/.f64 eps eps)) #s(literal 0 binary64))
(sqrt.f64 (*.f64 eps eps))
(-.f64 (/.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 5 binary64))) eps)
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 4 binary64))) eps) eps)
(-.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(fabs.f64 eps)
(exp.f64 (-.f64 (*.f64 (log.f64 eps) #s(literal 3 binary64)) (*.f64 (log.f64 eps) #s(literal 2 binary64))))
(exp.f64 (/.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 eps #s(literal 0 binary64))
eps
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps) (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 9/2 binary64)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64))))
(*.f64 (/.f64 eps (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps))
(*.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(*.f64 eps (/.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (fma.f64 eps (-.f64 (*.f64 x x) eps) (*.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) eps)) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (fma.f64 eps (-.f64 (*.f64 x x) eps) (*.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) eps)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (fma.f64 (-.f64 (*.f64 x x) eps) eps (*.f64 eps (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (fma.f64 (-.f64 (*.f64 x x) eps) eps (*.f64 eps (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (fma.f64 eps (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) (*.f64 (-.f64 (*.f64 x x) eps) eps)) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (fma.f64 eps (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) (*.f64 (-.f64 (*.f64 x x) eps) eps)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (fma.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) eps (*.f64 eps (-.f64 (*.f64 x x) eps))) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (fma.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) eps (*.f64 eps (-.f64 (*.f64 x x) eps))) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (+.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps)) #s(literal 0 binary64)) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (fma.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps #s(literal 0 binary64)) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (fma.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps #s(literal 0 binary64)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (neg.f64 (*.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps))) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps)) (neg.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps) eps)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) #s(literal 2 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (neg.f64 (fma.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) eps)))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) #s(literal 3 binary64))) (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (neg.f64 (fma.f64 (-.f64 (*.f64 x x) eps) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) (pow.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (pow.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) #s(literal 2 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))))) (neg.f64 (fma.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) eps)))
(/.f64 (neg.f64 (*.f64 (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (-.f64 (*.f64 x x) eps) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) (pow.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64)))) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 2 binary64)) #s(literal 0 binary64))) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (*.f64 x x) eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (*.f64 (/.f64 eps (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (*.f64 x x) eps)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64)) #s(literal 0 binary64))) (neg.f64 (+.f64 (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 0 binary64))))))
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(/.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fabs.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (*.f64 x x) eps))) (hypot.f64 (sqrt.f64 eps) x))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (-.f64 (*.f64 x x) eps))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (hypot.f64 (sqrt.f64 eps) x))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (sqrt.f64 (*.f64 (fma.f64 x x eps) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (sqrt.f64 (*.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x eps))))
(/.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (exp.f64 (log.f64 (fma.f64 x x eps))))
(/.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (exp.f64 (log.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (neg.f64 (fma.f64 x x eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (fma.f64 x x eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (-.f64 (*.f64 x x) #s(literal 0 binary64)) eps)
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (-.f64 (*.f64 x x) eps) #s(literal 0 binary64))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 eps (-.f64 (*.f64 x x) #s(literal 0 binary64))))
(fabs.f64 (-.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps))))
(fabs.f64 (-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(fabs.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)))
(fabs.f64 (-.f64 eps (*.f64 x x)))
(fabs.f64 (neg.f64 (-.f64 (*.f64 x x) eps)))
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.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 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (cosh.f64 (log.f64 (-.f64 (*.f64 x x) eps))) (sinh.f64 (log.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (-.f64 (*.f64 x x) #s(literal 0 binary64)) eps)
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (*.f64 x (+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) eps))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(*.f64 (neg.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)))))
(*.f64 (pow.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) #s(literal 3/4 binary64)) (pow.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)))
(*.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64))) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64))))
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))
(*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (exp.f64 #s(literal 3/2 binary64)) (log.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #s(literal 3/4 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 3 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))
(/.f64 (pow.f64 (hypot.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 (hypot.f64 (sqrt.f64 eps) x) #s(literal 3 binary64)))
(/.f64 (pow.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)))
(fabs.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))
(fabs.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))
(exp.f64 (fma.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 3/4 binary64) (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 3/4 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) #s(literal 3/4 binary64)))
(exp.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))

eval258.0ms (4.6%)

Memory
-24.7MiB live, 156.6MiB allocated; 25ms collecting garbage
Compiler

Compiled 44 939 to 4 016 computations (91.1% saved)

prune76.0ms (1.4%)

Memory
10.2MiB live, 57.6MiB allocated; 2ms collecting garbage
Pruning

14 alts after pruning (9 fresh and 5 done)

PrunedKeptTotal
New1 13481 142
Fresh213
Picked325
Done033
Total1 139141 153
Accuracy
100.0%
Counts
1 153 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
35.0%
(/.f64 (fma.f64 (*.f64 eps eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps) #s(literal 0 binary64))) (*.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
47.4%
(/.f64 (/.f64 (*.f64 eps eps) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶99.3%
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
45.7%
(/.f64 (+.f64 eps #s(literal 0 binary64)) #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))))
▶99.5%
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶62.2%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶1.3%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
✓7.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
44.3%
#s(approx (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
✓44.1%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
▶42.6%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
Compiler

Compiled 443 to 266 computations (40% saved)

simplify89.0ms (1.6%)

Memory
0.3MiB live, 91.1MiB allocated; 6ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff0
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
cost-diff2
(+.f64 eps #s(literal 0 binary64))
cost-diff8
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
cost-diff0
(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
cost-diff0
(*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
cost-diff0
(fma.f64 x x (neg.f64 eps))
cost-diff0
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
cost-diff0
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
cost-diff0
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
cost-diff0
#s(approx (- (* x x) eps) eps)
cost-diff0
(sqrt.f64 #s(approx (- (* x x) eps) eps))
cost-diff0
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff0
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff0
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044303
066283
198283
2236283
3756283
43657283
08046277
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
x
(sqrt.f64 #s(approx (- (* x x) eps) eps))
#s(approx (- (* x x) eps) eps)
eps
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 eps (*.f64 x x))
eps
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
x
(sqrt.f64 #s(approx (- (* x x) eps) eps))
#s(approx (- (* x x) eps) eps)
eps
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps)))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
(fma.f64 x x (neg.f64 eps))
(-.f64 (*.f64 x x) eps)
(neg.f64 eps)
eps
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 eps (*.f64 x x))
eps
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x

localize147.0ms (2.6%)

Memory
-1.7MiB live, 241.2MiB allocated; 48ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.015625
(-.f64 (*.f64 x x) eps)
accuracy0.0859375
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy0.296875
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
accuracy0.3639450195368841
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
accuracy4.396372179135785
(*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
accuracy10.642534688645465
(/.f64 eps (*.f64 x x))
accuracy35.53315662023681
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
accuracy36.95812918523611
#s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
accuracy0.0
(neg.f64 eps)
accuracy0.0
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
accuracy0.0078125
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
accuracy24.194933043325374
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
accuracy0.0078125
(sqrt.f64 #s(approx (- (* x x) eps) eps))
accuracy24.194933043325374
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
accuracy61.37498360209479
#s(approx (- (* x x) eps) eps)
accuracy0.0078125
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.01171875
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.015625
(-.f64 (*.f64 x x) eps)
accuracy0.296875
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Samples
46.0ms86×1valid
37.0ms150×0valid
37.0ms20×2valid
Compiler

Compiled 231 to 37 computations (84% saved)

Precisions
Click to see histograms. Total time spent on operations: 88.0ms
adjust: 29.0ms (32.8% of total)
ival-div: 17.0ms (19.2% of total)
ival-mult: 13.0ms (14.7% of total)
ival-add: 11.0ms (12.4% of total)
ival-pow: 7.0ms (7.9% of total)
ival-sqrt: 5.0ms (5.7% of total)
ival-sub: 4.0ms (4.5% of total)
exact: 1.0ms (1.1% of total)
ival-neg: 1.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series24.0ms (0.4%)

Memory
17.0MiB live, 61.8MiB allocated; 5ms collecting garbage
Counts
21 → 127
Calls
Call 1
Inputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(sqrt.f64 #s(approx (- (* x x) eps) eps))
#s(approx (- (* x x) eps) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(neg.f64 eps)
(/.f64 eps (*.f64 x x))
Outputs
(* (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))))
(* (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 (* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/16 (/ (pow eps 2) (pow x 5)))
(/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(/ eps (pow x 2))
(* 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)
(* 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)))))))
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)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 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)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* -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 (/ (+ (* -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))
(* -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))))))))
(* -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 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* 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))))
(+ (* -1/2 (/ 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)))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
eps
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(- (+ (* -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)))))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 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)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(+ 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)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
Calls

6 calls:

TimeVariablePointExpression
4.0ms
eps
@inf
((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x) (+ eps 0) (/ (+ eps 0) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x)) (sqrt (sqrt (- (* x x) eps))) (neg eps) (/ eps (* x x)))
4.0ms
eps
@-inf
((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x) (+ eps 0) (/ (+ eps 0) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x)) (sqrt (sqrt (- (* x x) eps))) (neg eps) (/ eps (* x x)))
3.0ms
x
@0
((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x) (+ eps 0) (/ (+ eps 0) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x)) (sqrt (sqrt (- (* x x) eps))) (neg eps) (/ eps (* x x)))
3.0ms
x
@inf
((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x) (+ eps 0) (/ (+ eps 0) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x)) (sqrt (sqrt (- (* x x) eps))) (neg eps) (/ eps (* x x)))
3.0ms
eps
@0
((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x) (+ eps 0) (/ (+ eps 0) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x)) (sqrt (sqrt (- (* x x) eps))) (neg eps) (/ eps (* x x)))

simplify200.0ms (3.6%)

Memory
26.8MiB live, 289.0MiB allocated; 83ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06413009
121962872
083642719
Stop Event
1×iter limit
1×node limit
Counts
127 → 125
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))))
(* (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 (* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/16 (/ (pow eps 2) (pow x 5)))
(/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(/ eps (pow x 2))
(* 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)
(* 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)))))))
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)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 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)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* -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 (/ (+ (* -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))
(* -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))))))))
(* -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 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* 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))))
(+ (* -1/2 (/ 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)))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
eps
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(- (+ (* -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)))))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 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)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(+ 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)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* 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 (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
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 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (*.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) x (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/8 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))
(fma.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/8 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64))) (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(- (* 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)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)) x) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(/.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) x) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 5 binary64)))
(* 1/16 (/ (pow eps 2) (pow x 5)))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/8 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))
(/.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) eps)) x) x (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 5 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64)) x) x (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (*.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -7/128 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 11 binary64))) #s(literal 1/4 binary64))) x) x (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64))) (*.f64 x x) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (*.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(* 1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) eps))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) eps)))) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64))) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(*.f64 (-.f64 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) 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)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) eps))) 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 (fma.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal -1/8 binary64) x) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) eps))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))) x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
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(* (pow 1 1/4) (sqrt x))
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(* eps (- (/ (pow x 2) eps) 1))
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(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
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(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(*.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 eps eps))
(* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(*.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps))) (*.f64 eps eps))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x eps)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(fma.f64 (/.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64)))) (*.f64 x x)) eps) #s(literal -1/4 binary64) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64)))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) eps) (/.f64 #s(literal -3/32 binary64) eps)) (fma.f64 (/.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64)))) (*.f64 x x)) eps) #s(literal -1/4 binary64) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) eps) (/.f64 #s(literal -3/32 binary64) eps) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (/.f64 (*.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64)))) (*.f64 x x)) eps) #s(literal -1/4 binary64) (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (+.f64 (log.f64 eps) (log.f64 #s(literal -1 binary64))))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(+ (* -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)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (*.f64 (neg.f64 x) eps)) 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)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (-.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) eps) (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x))))) (neg.f64 eps)) (*.f64 x eps)) eps)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (neg.f64 x) eps)))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal -1/2 binary64) x) (neg.f64 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 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64))) eps)) (neg.f64 eps))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) x) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -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 (neg.f64 eps) (-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) eps)) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x eps)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 (neg.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -3/32 binary64))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (*.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -3/32 binary64) (*.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)))) (neg.f64 eps))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))

rewrite92.0ms (1.6%)

Memory
-11.0MiB live, 92.1MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044262
066242
1247242
02018236
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
21 → 235
Calls
Call 1
Inputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(sqrt.f64 #s(approx (- (* x x) eps) eps))
#s(approx (- (* x x) eps) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(neg.f64 eps)
(/.f64 eps (*.f64 x x))
Outputs
(*.f64 (/.f64 eps (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (/.f64 eps (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(/.f64 (-.f64 (*.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) #s(literal 0 binary64)) (-.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 0 binary64)))))
(/.f64 (fma.f64 (neg.f64 eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 0 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (fma.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 0 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (*.f64 eps eps) (*.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (*.f64 eps eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 eps) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(neg.f64 (/.f64 (neg.f64 eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(neg.f64 (/.f64 eps (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(fma.f64 (/.f64 eps (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)) #s(literal 0 binary64))
(+.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 0 binary64))
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eps
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eval57.0ms (1%)

Memory
16.0MiB live, 106.3MiB allocated; 7ms collecting garbage
Compiler

Compiled 16 143 to 1 893 computations (88.3% saved)

prune73.0ms (1.3%)

Memory
12.6MiB live, 59.5MiB allocated; 55ms collecting garbage
Pruning

16 alts after pruning (7 fresh and 9 done)

PrunedKeptTotal
New4736479
Fresh314
Picked145
Done055
Total47716493
Accuracy
100.0%
Counts
493 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
75.4%
(/.f64 (fma.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 0 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
47.4%
(/.f64 (/.f64 (*.f64 eps eps) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓99.5%
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
66.5%
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x))
60.5%
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
45.7%
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))
45.7%
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))))
44.3%
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)))
✓62.2%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓62.2%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓1.3%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
✓7.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓44.1%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
✓42.6%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
Compiler

Compiled 973 to 337 computations (65.4% saved)

regimes32.0ms (0.6%)

Memory
-6.8MiB live, 40.8MiB allocated; 11ms collecting garbage
Counts
32 → 1
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 eps #s(literal 0 binary64)) #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (/.f64 (*.f64 eps eps) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (fma.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 0 binary64))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (fma.f64 (*.f64 eps eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps) #s(literal 0 binary64))) (*.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 #s(approx (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/.f64 (fma.f64 #s(literal 1/16 binary64) eps (*.f64 #s(literal 1/8 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (fma.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/8 binary64)) (/.f64 eps x) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x))
Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Calls

3 calls:

14.0ms
eps
8.0ms
x
8.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.5%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
99.5%1x
99.5%1eps
Compiler

Compiled 10 to 10 computations (0% saved)

regimes15.0ms (0.3%)

Memory
-24.7MiB live, 20.0MiB allocated; 5ms collecting garbage
Counts
12 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))
Calls

3 calls:

7.0ms
x
4.0ms
eps
4.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
98.6%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
89.8%2x
79.5%2eps
Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory
6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Counts
11 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
98.0%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes4.0ms (0.1%)

Memory
6.1MiB live, 6.2MiB allocated; 0ms collecting garbage
Counts
9 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
98.0%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory
5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Counts
8 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
96.1%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory
4.0MiB live, 4.0MiB allocated; 0ms collecting garbage
Counts
4 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Calls

1 calls:

2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
95.9%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory
10.4MiB live, 10.4MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
Calls

3 calls:

2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
57.1%1eps
57.1%1x
57.1%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes7.0ms (0.1%)

Memory
-35.4MiB live, 9.8MiB allocated; 4ms collecting garbage
Accuracy

Total -1.4b remaining (-2.3%)

Threshold costs -1.4b (-2.3%)

Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) eps)))
Outputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
Calls

3 calls:

4.0ms
eps
1.0ms
x
1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
3.5%1x
3.5%1eps
3.5%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.323219036088085e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.323219036088085e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.323219036088085e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.323219036088085e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.323219036088085e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

simplify13.0ms (0.2%)

Memory
28.4MiB live, 28.4MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043212
163212
290212
3113212
4125212
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

derivations613.0ms (11%)

Memory
-6.3MiB live, 553.7MiB allocated; 122ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036215
064166
1262165
22580161
08808161
011447128
140676857
080616503
02571067
18071053
233631038
08415979
034221
057212
1203186
01660186
0622
01022
14222
032022
06413009
121962872
083642719
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 212 to 43 computations (79.7% saved)

preprocess136.0ms (2.4%)

Memory
-20.7MiB live, 145.4MiB allocated; 106ms collecting garbage
Compiler

Compiled 460 to 112 computations (75.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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