ENA, Section 1.4, Exercise 4d

Time bar (total: 6.0s)

start0.0ms (0%)

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

analyze19.0ms (0.3%)

Memory
-8.7MiB live, 38.7MiB allocated; 5ms 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)

sample1.6s (27.3%)

Memory
32.8MiB live, 2 082.9MiB allocated; 399ms collecting garbage
Samples
484.0ms2 673×1valid
483.0ms4 848×0valid
177.0ms735×2valid
31.0ms187×0invalid
Precisions
Click to see histograms. Total time spent on operations: 695.0ms
adjust: 194.0ms (27.9% of total)
ival-sub: 126.0ms (18.1% of total)
ival-mult: 114.0ms (16.4% of total)
ival-<=: 114.0ms (16.4% of total)
ival-sqrt: 102.0ms (14.7% of total)
ival-and: 24.0ms (3.5% of total)
exact: 18.0ms (2.6% of total)
ival-assert: 4.0ms (0.6% of total)
Bogosity

explain203.0ms (3.4%)

Memory
-13.3MiB live, 127.5MiB allocated; 9ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
980-0-(-.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)))cancellation980
Confusion
Predicted +Predicted -
+980
-0158
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+9800
-00158
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0158
198
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
51.0ms142×1valid
16.0ms318×0valid
9.0ms52×2valid
Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-sub: 7.0ms (28.1% of total)
adjust: 6.0ms (24.1% of total)
ival-mult: 5.0ms (20.1% of total)
ival-sqrt: 5.0ms (20.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess14.0ms (0.2%)

Memory
8.9MiB live, 8.9MiB allocated; 0ms 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
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶64.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Memory
1.5MiB live, 1.5MiB 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

localize26.0ms (0.4%)

Memory
13.5MiB live, 13.5MiB allocated; 0ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.00390625
(-.f64 (*.f64 x x) eps)
accuracy0.0078125
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy22.640234965027545
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Samples
8.0ms159×0valid
8.0ms71×1valid
4.0ms26×2valid
Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
adjust: 3.0ms (24.6% of total)
ival-mult: 3.0ms (24.6% of total)
ival-sqrt: 3.0ms (24.6% of total)
ival-sub: 3.0ms (24.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB 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
eps
@-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
@0
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))

simplify164.0ms (2.7%)

Memory
-5.6MiB live, 85.6MiB allocated; 19ms 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)

rewrite48.0ms (0.8%)

Memory
0.4MiB live, 45.5MiB allocated; 8ms 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
21.2MiB live, 21.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 993 to 440 computations (77.9% saved)

prune17.0ms (0.3%)

Memory
-29.7MiB live, 16.0MiB allocated; 6ms collecting garbage
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New79786
Fresh000
Picked011
Done000
Total79887
Accuracy
99.6%
Counts
87 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶64.2%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓64.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶61.4%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶6.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶3.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
23.9%
#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))
35.2%
#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))
▶41.3%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Compiler

Compiled 276 to 182 computations (34.1% saved)

simplify117.0ms (1.9%)

Memory
5.2MiB live, 76.6MiB allocated; 12ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
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
(/.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 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
(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
028171
047163
163157
2137155
3366155
42099155
08388155
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)
(-.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
#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 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)
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)
(-.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
#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 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)

localize108.0ms (1.8%)

Memory
12.1MiB live, 104.6MiB allocated; 4ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(/.f64 eps x)
accuracy0.00390625
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy22.640234965027545
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy37.20276864740273
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy0.0
(/.f64 #s(literal 1/2 binary64) x)
accuracy0.4923724132973225
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy37.452603692687845
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy0.0
(neg.f64 eps)
accuracy0.0078125
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy22.640234965027545
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy23.843731952616675
#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy0.0
(neg.f64 x)
accuracy22.640234965027545
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy62.425635588846895
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy0.0078125
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.01953125
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.28515625
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy22.25222568160574
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
Samples
41.0ms26×2valid
31.0ms71×1valid
21.0ms159×0valid
Compiler

Compiled 139 to 20 computations (85.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
adjust: 7.0ms (21.6% of total)
ival-div: 6.0ms (18.5% of total)
ival-mult: 6.0ms (18.5% of total)
ival-sub: 5.0ms (15.4% of total)
ival-sqrt: 3.0ms (9.3% of total)
ival-add: 3.0ms (9.3% of total)
ival-neg: 2.0ms (6.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series60.0ms (1%)

Memory
-27.5MiB live, 15.5MiB allocated; 15ms collecting garbage
Counts
20 → 89
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)
(-.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)
#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 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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
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)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(+ 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)))
(/ (+ (* 1/8 (/ (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)))))))
(* 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 (* 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))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -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))
(* 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)))))
(+ (* -1/2 (/ 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 (/ (+ (* -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))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* 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)))))
(+ 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 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -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)))))
Calls

6 calls:

TimeVariablePointExpression
46.0ms
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))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms
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))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms
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))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms
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))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms
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))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))

simplify208.0ms (3.5%)

Memory
33.7MiB live, 126.9MiB allocated; 25ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04412056
114711959
265441955
080101844
Stop Event
1×iter limit
1×node limit
Counts
89 → 87
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)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(+ 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)))
(/ (+ (* 1/8 (/ (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)))))))
(* 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 (* 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))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -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))
(* 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)))))
(+ (* -1/2 (/ 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 (/ (+ (* -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))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* 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)))))
(+ 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 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
Outputs
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* 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 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/2 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 (fma.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 #s(literal -1/2 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))) x (*.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 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 #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 (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 (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 (/.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 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* (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)))))))
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(+ (* (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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(* 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 #s(literal 1/16 binary64) (/.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)))) (fma.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) #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 (- (/ x eps) (* 1/2 (/ 1 x))))
(*.f64 (-.f64 (/.f64 x eps) (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)) eps)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(*.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)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(*.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) #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)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))) eps)
(+ 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 (fma.f64 (neg.f64 eps) x (/.f64 (fma.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 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) #s(literal -1 binary64)))))) (neg.f64 eps))) eps)))
(* -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) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #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 (neg.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 (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)) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (*.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (*.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (*.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 (/ x eps)) (* 1/2 (/ 1 x)))))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* -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 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #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 (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)) (neg.f64 eps))))

rewrite57.0ms (0.9%)

Memory
-23.4MiB live, 67.8MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
028160
047160
1155144
01182144
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
20 → 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)
(-.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)
#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 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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
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))
(*.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 (*.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))) (fma.f64 x (/.f64 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 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (fma.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.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 (*.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 (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 (neg.f64 (+.f64 #s(literal 0 binary64) (neg.f64 eps))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) (*.f64 (fma.f64 x x (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64))) (*.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 (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 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(neg.f64 (/.f64 (+.f64 #s(literal 0 binary64) (neg.f64 eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(neg.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (neg.f64 (+.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 (/.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 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (/.f64 #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 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.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)))
(*.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 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #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 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.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 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(literal 2 binary64))) (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(literal 3 binary64))) (fma.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x) (*.f64 x x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x)) (/.f64 (pow.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(literal 2 binary64)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x) (*.f64 x x))) (/.f64 (pow.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) x) (*.f64 x x))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps)))) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x #s(approx (- (* x x) eps) (neg.f64 eps))))))
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x #s(approx (- (* x x) eps) (neg.f64 eps)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x #s(approx (- (* x x) eps) (neg.f64 eps))))) (/.f64 (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x #s(approx (- (* x x) eps) (neg.f64 eps))))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(*.f64 (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)))
(pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
(exp.f64 (*.f64 (log.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(*.f64 (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(pow.f64 (*.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 2 binary64))
(pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1 binary64))
#s(approx (- (* x x) eps) (neg.f64 eps))
(sqrt.f64 (*.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(approx (- (* x x) eps) (neg.f64 eps))))
(neg.f64 eps)
#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) (/.f64 eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(/.f64 (*.f64 #s(literal -1/2 binary64) eps) (neg.f64 x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 x))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1/2 binary64) x)
(neg.f64 (/.f64 #s(literal -1/2 binary64) x))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 x)))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) #s(literal 2 binary64))) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) #s(literal 3 binary64))) (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x) (*.f64 x x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)) (/.f64 (pow.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) #s(literal 2 binary64)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x) (*.f64 x x))) (/.f64 (pow.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x) (*.f64 x x))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64))) (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)) (*.f64 x x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x)))
(-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(-.f64 x (*.f64 (neg.f64 (/.f64 eps x)) #s(literal -1/2 binary64)))
(+.f64 (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x)
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps x)
(neg.f64 (/.f64 (neg.f64 eps) x))
(neg.f64 (/.f64 eps (neg.f64 x)))
(/.f64 (neg.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (+.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 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (+.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 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
(-.f64 (/.f64 (-.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 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))) (/.f64 (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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(+.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)))

eval56.0ms (0.9%)

Memory
22.5MiB live, 74.6MiB allocated; 8ms collecting garbage
Compiler

Compiled 8 239 to 1 130 computations (86.3% saved)

prune8.0ms (0.1%)

Memory
-24.1MiB live, 21.9MiB allocated; 3ms collecting garbage
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New2833286
Fresh202
Picked235
Done011
Total2877294
Accuracy
100.0%
Counts
294 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶52.5%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.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))
✓64.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓61.4%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓6.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶41.5%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
Compiler

Compiled 116 to 62 computations (46.6% saved)

simplify184.0ms (3.1%)

Memory
52.9MiB live, 271.6MiB allocated; 48ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))
cost-diff18
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
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))
cost-diff0
(/.f64 eps x)
cost-diff0
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
022204
035165
174156
2272156
31466148
47082148
08545148
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
#s(literal 1/2 binary64)
(/.f64 eps x)
eps
x
(/.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 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))
(*.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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 eps x)
eps
x
(/.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 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.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 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))
(*.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 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x 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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

localize173.0ms (2.9%)

Memory
-43.3MiB live, 152.1MiB allocated; 67ms collecting garbage
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy0.27734375
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
accuracy0.3046875
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy12.875259693824011
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
accuracy16.940164185513467
(-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))
accuracy0.00390625
(-.f64 (*.f64 x x) eps)
accuracy0.0078125
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.01953125
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.28515625
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy0.0
(/.f64 eps x)
accuracy0.0
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
accuracy37.452603692687845
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
Samples
82.0ms26×2valid
35.0ms159×0valid
24.0ms71×1valid
Compiler

Compiled 200 to 20 computations (90% saved)

Precisions
Click to see histograms. Total time spent on operations: 64.0ms
ival-mult: 24.0ms (37.7% of total)
ival-div: 18.0ms (28.3% of total)
adjust: 8.0ms (12.6% of total)
ival-sub: 6.0ms (9.4% of total)
ival-sqrt: 3.0ms (4.7% of total)
ival-add: 3.0ms (4.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series35.0ms (0.6%)

Memory
10.0MiB live, 54.1MiB allocated; 8ms collecting garbage
Counts
14 → 180
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 eps x)
(+.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 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))
(*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
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)))
(* 1/2 (/ eps x))
(/ eps x)
(* (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)))))))))
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* x (- (/ 1 (* eps (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 eps)) (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1))))))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* (sqrt (pow eps 3)) (sqrt -1))
(- (* eps x) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* x (- (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(* (sqrt eps) (* (pow x 2) (sqrt -1)))
(* (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* 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))))
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(* eps (pow (sqrt -1) 2))
(+ (* 2 (* (sqrt eps) (* x (sqrt -1)))) (* eps (pow (sqrt -1) 2)))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 x) (* 2 (* (sqrt eps) (sqrt -1))))))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 (* (sqrt eps) (sqrt -1))) (* x (+ 2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))))))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* -1 (* eps x)) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1))))))))
(/ (- (* 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)
(/ (+ (* 1/8 (/ (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)) (* -1/4 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4)))))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/64 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/2 (/ (* eps (- (* -1/32 (pow eps 3)) (+ (* -1/2 (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2))))) (* 1/8 (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))))))) (pow x 6))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* 1/8 (/ (* eps (+ (* -1/4 (pow eps 3)) (* 1/8 (pow eps 3)))) (pow x 6))) (* 1/4 (/ (* (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2))) (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 6))))))))) x)
(* 2 (* eps x))
(* x (- (* -1/2 (/ (pow eps 2) (pow x 2))) (* -2 eps)))
(* x (- (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -2 eps) (* 1/2 (/ (pow eps 2) (pow x 2))))))
(* x (- (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* -2 eps) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* 2 (pow x 3))
(* (pow x 3) (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 3) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* (pow x 3) (+ 2 (+ (* -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)))))
(* 4 (pow x 2))
(* (pow x 2) (+ 4 (* -2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/4 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))))
(* -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 (/ (+ (* -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 (- (* -1/2 (/ eps (pow x 2))) (+ 2 (* -1 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4)))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -1 (/ eps (pow x 2))) (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4)))))))))
(* -1 (* x (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))) (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4))))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -8 (/ (+ (* 1/64 (pow eps 5)) (* 1/2 (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))))) (* (pow eps 2) (pow x 6)))) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/2 (/ (* eps (- (* -1/4 (pow eps 2)) (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (* 1/2 (* eps (- (* -1/2 eps) (* -1 eps))))))) (pow x 6))) (* 4 (/ (* (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (- (* -1/2 eps) (* -1 eps))) (* (pow eps 2) (pow x 6)))))))))))))
(* 1/2 (/ (pow eps 2) x))
(* -1 (/ (- (* -1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2)))) x))
(* -1 (/ (- (* -1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))))) x))
(* 1/2 (* eps x))
(* -1 (* x (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))))
(* -1 (* x (+ (* -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))))))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/64 (/ (pow eps 5) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (+ (* 1/4 (pow eps 2)) (* 1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6)))))))) (pow x 2))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))
(* -1 (* x (+ (* -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))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))))
(* 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))))
eps
(+ (* -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)))))
(* eps (- (* -1/2 (/ eps x)) (* -2 x)))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (* -2 x)))
(* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (* -2 x)))
(+ (* -1/2 (* eps x)) (* 2 (pow x 3)))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* -1/8 (/ eps x)))))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))))
(+ (* -1 eps) (pow x 2))
(+ (* -2 eps) (* 4 (pow x 2)))
(+ (* 4 (pow x 2)) (* eps (- (* -1/4 (/ eps (pow x 2))) 2)))
(+ (* 4 (pow x 2)) (* eps (- (* eps (- (* -1/8 (/ eps (pow x 4))) (* 1/4 (/ 1 (pow x 2))))) 2)))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (* -1/2 x))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* 3/8 (/ eps x))))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x))))))))
(* 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)))))
(- (+ (* -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))))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))) (* 2 (/ x (pow (sqrt -1) 2))))
(- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(- (+ (* -1 (/ (+ (* 2 (* (sqrt eps) (/ (* x (- (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt eps) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))))) (sqrt -1)))) (+ (* 2 (/ (* eps (* (pow x 2) (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(* (pow eps 2) (- (/ x eps) (* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (- (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* (pow eps 2) (- (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1))))))))
(* eps (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 6) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))))
(* eps (- (/ (pow x 2) eps) 1))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ (pow (sqrt -1) 2) eps)))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (/ (pow (sqrt -1) 2) eps))))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 3) (sqrt -1))) (/ (pow (sqrt -1) 2) eps)))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2)))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2))))))))
(* -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)))))
(+ 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 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* eps x) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (* (pow x 2) (- (* eps x) (* 2 (* eps x))))) (+ (* -1 (* eps (pow x 3))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x)))))))))))))))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(* (pow eps 2) (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* -1 (* (sqrt eps) (* (pow x 2) (sqrt -1))))
(* -1 (* eps (+ (* -1 (/ (pow x 3) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 6) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) eps)) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* (pow eps 2) (- (* -2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ (pow x 2) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3))) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
Calls

6 calls:

TimeVariablePointExpression
10.0ms
eps
@-inf
((- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) (/ eps x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
6.0ms
x
@inf
((- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) (/ eps x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
5.0ms
eps
@inf
((- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) (/ eps x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
4.0ms
x
@-inf
((- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) (/ eps x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
4.0ms
x
@0
((- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) (/ eps x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))

simplify240.0ms (4%)

Memory
13.1MiB live, 247.9MiB allocated; 58ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09715381
134155213
083964928
Stop Event
1×iter limit
1×node limit
Counts
180 → 178
Calls
Call 1
Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ eps x)
(* (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)))))))))
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* x (- (/ 1 (* eps (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 eps)) (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1))))))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* (sqrt (pow eps 3)) (sqrt -1))
(- (* eps x) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* x (- (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(* (sqrt eps) (* (pow x 2) (sqrt -1)))
(* (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* 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))))
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(* eps (pow (sqrt -1) 2))
(+ (* 2 (* (sqrt eps) (* x (sqrt -1)))) (* eps (pow (sqrt -1) 2)))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 x) (* 2 (* (sqrt eps) (sqrt -1))))))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 (* (sqrt eps) (sqrt -1))) (* x (+ 2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))))))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* -1 (* eps x)) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1))))))))
(/ (- (* 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)
(/ (+ (* 1/8 (/ (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)) (* -1/4 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4)))))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/64 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/2 (/ (* eps (- (* -1/32 (pow eps 3)) (+ (* -1/2 (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2))))) (* 1/8 (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))))))) (pow x 6))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* 1/8 (/ (* eps (+ (* -1/4 (pow eps 3)) (* 1/8 (pow eps 3)))) (pow x 6))) (* 1/4 (/ (* (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2))) (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 6))))))))) x)
(* 2 (* eps x))
(* x (- (* -1/2 (/ (pow eps 2) (pow x 2))) (* -2 eps)))
(* x (- (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -2 eps) (* 1/2 (/ (pow eps 2) (pow x 2))))))
(* x (- (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* -2 eps) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* 2 (pow x 3))
(* (pow x 3) (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 3) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* (pow x 3) (+ 2 (+ (* -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)))))
(* 4 (pow x 2))
(* (pow x 2) (+ 4 (* -2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/4 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))))
(* -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 (/ (+ (* -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 (- (* -1/2 (/ eps (pow x 2))) (+ 2 (* -1 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4)))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -1 (/ eps (pow x 2))) (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4)))))))))
(* -1 (* x (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))) (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4))))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -8 (/ (+ (* 1/64 (pow eps 5)) (* 1/2 (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))))) (* (pow eps 2) (pow x 6)))) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/2 (/ (* eps (- (* -1/4 (pow eps 2)) (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (* 1/2 (* eps (- (* -1/2 eps) (* -1 eps))))))) (pow x 6))) (* 4 (/ (* (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (- (* -1/2 eps) (* -1 eps))) (* (pow eps 2) (pow x 6)))))))))))))
(* 1/2 (/ (pow eps 2) x))
(* -1 (/ (- (* -1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2)))) x))
(* -1 (/ (- (* -1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))))) x))
(* 1/2 (* eps x))
(* -1 (* x (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))))
(* -1 (* x (+ (* -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))))))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/64 (/ (pow eps 5) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (+ (* 1/4 (pow eps 2)) (* 1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6)))))))) (pow x 2))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))
(* -1 (* x (+ (* -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))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))))
(* 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))))
eps
(+ (* -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)))))
(* eps (- (* -1/2 (/ eps x)) (* -2 x)))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (* -2 x)))
(* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (* -2 x)))
(+ (* -1/2 (* eps x)) (* 2 (pow x 3)))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* -1/8 (/ eps x)))))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))))
(+ (* -1 eps) (pow x 2))
(+ (* -2 eps) (* 4 (pow x 2)))
(+ (* 4 (pow x 2)) (* eps (- (* -1/4 (/ eps (pow x 2))) 2)))
(+ (* 4 (pow x 2)) (* eps (- (* eps (- (* -1/8 (/ eps (pow x 4))) (* 1/4 (/ 1 (pow x 2))))) 2)))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (* -1/2 x))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* 3/8 (/ eps x))))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x))))))))
(* 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)))))
(- (+ (* -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))))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))) (* 2 (/ x (pow (sqrt -1) 2))))
(- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(- (+ (* -1 (/ (+ (* 2 (* (sqrt eps) (/ (* x (- (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt eps) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))))) (sqrt -1)))) (+ (* 2 (/ (* eps (* (pow x 2) (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(* (pow eps 2) (- (/ x eps) (* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (- (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* (pow eps 2) (- (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1))))))))
(* eps (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 6) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))))
(* eps (- (/ (pow x 2) eps) 1))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ (pow (sqrt -1) 2) eps)))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (/ (pow (sqrt -1) 2) eps))))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 3) (sqrt -1))) (/ (pow (sqrt -1) 2) eps)))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2)))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2))))))))
(* -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)))))
(+ 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 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* eps x) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (* (pow x 2) (- (* eps x) (* 2 (* eps x))))) (+ (* -1 (* eps (pow x 3))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x)))))))))))))))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(* (pow eps 2) (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* -1 (* (sqrt eps) (* (pow x 2) (sqrt -1))))
(* -1 (* eps (+ (* -1 (/ (pow x 3) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 6) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) eps)) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* (pow eps 2) (- (* -2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ (pow x 2) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3))) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
Outputs
(* -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 (/.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 #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 #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* 1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/ eps x)
(/.f64 eps x)
(* (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 (*.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)))
(+ (* 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 (*.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)) (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 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #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 #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #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 #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #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)))))))))
(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 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64))) (*.f64 x x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (*.f64 (-.f64 (*.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)) (*.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 0 binary64))) x) #s(literal -1 binary64)) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(+ (* x (- (* x (- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* x (- (/ 1 (* eps (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 eps)) (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1))))))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (-.f64 (*.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)) (*.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 0 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 0 binary64)))) x) #s(literal -1 binary64)) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* (sqrt (pow eps 3)) (sqrt -1))
(*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(- (* eps x) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(fma.f64 eps x (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
(- (* x (- (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1 binary64) eps)) x) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))))
(- (* x (- (* x (- (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) x (*.f64 #s(literal 1 binary64) eps)) x (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt eps) (* (pow x 2) (sqrt -1)))
(*.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(* (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x) (*.f64 x x))
(* (pow x 2) (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) (*.f64 x x))
(* (pow x 2) (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))))
(*.f64 (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 #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(* eps (pow (sqrt -1) 2))
(neg.f64 eps)
(+ (* 2 (* (sqrt eps) (* x (sqrt -1)))) (* eps (pow (sqrt -1) 2)))
(fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (neg.f64 eps))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 x) (* 2 (* (sqrt eps) (sqrt -1))))))
(fma.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)) x (neg.f64 eps))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 (* (sqrt eps) (sqrt -1))) (* x (+ 2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64)) x)) x (neg.f64 eps))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))))
(+ (* -1 (* eps x)) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(neg.f64 (fma.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)) (*.f64 eps x)))
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(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
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(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* (pow eps 2) (- (/ x eps) (* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (pow eps 2) (- (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
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(* (pow eps 2) (- (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1))))))))
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(* eps (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))
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(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 6) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))))
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(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ (pow (sqrt -1) 2) eps)))
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(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (/ (pow (sqrt -1) 2) eps))))
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(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 3) (sqrt -1))) (/ (pow (sqrt -1) 2) eps)))))
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(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))))))
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(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2)))))))
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(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2))))))))
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(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(+ x (* -1 (* (sqrt eps) (sqrt -1))))
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(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 x x) (sqrt.f64 #s(literal -1 binary64))) (*.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 (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 1/2 binary64) (*.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)))))) (neg.f64 eps)) (*.f64 eps x)) 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 (fma.f64 (/.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) #s(literal -1 binary64) x) (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)))) (*.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 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* eps x) (* 2 (* eps x))) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 eps x (*.f64 (*.f64 #s(literal -2 binary64) eps) x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (/.f64 (-.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)))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (fma.f64 eps x (*.f64 (*.f64 #s(literal -2 binary64) eps) x)))))) eps) #s(literal -1 binary64) (fma.f64 eps x (*.f64 (*.f64 #s(literal -2 binary64) eps) x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (* (pow x 2) (- (* eps x) (* 2 (* eps x))))) (+ (* -1 (* eps (pow x 3))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x)))))))))))))))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (*.f64 x x)) (fma.f64 eps x (*.f64 (*.f64 #s(literal -2 binary64) eps) x)) (fma.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) eps (fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) 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)))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (fma.f64 eps x (*.f64 (*.f64 #s(literal -2 binary64) eps) x))))))) (*.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))))))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (fma.f64 eps x (*.f64 (*.f64 #s(literal -2 binary64) eps) x)))))) eps) #s(literal -1 binary64) (fma.f64 eps x (*.f64 (*.f64 #s(literal -2 binary64) eps) x))) eps)))
(* (pow eps 2) (- (/ 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)))) (*.f64 eps eps))
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (-.f64 (/.f64 (-.f64 (*.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)))) (*.f64 eps eps))
(* (pow eps 2) (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (-.f64 (/.f64 (-.f64 (/.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))))) (neg.f64 eps)) x) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps eps))
(* -1 (* (sqrt eps) (* (pow x 2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 eps) (*.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ (pow x 3) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 eps))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64))) (neg.f64 eps))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 6) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) eps)) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))))) eps) #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)))
(* (pow eps 2) (- (* -2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ 1 eps)))
(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ (pow x 2) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(*.f64 (-.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 2 binary64) (*.f64 (/.f64 (*.f64 x x) eps) #s(literal -2 binary64))) (neg.f64 eps)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(*.f64 (-.f64 (/.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (/.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 2 binary64))) (neg.f64 eps))) (neg.f64 eps)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) x) (neg.f64 eps))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64))) (neg.f64 eps))) x) (neg.f64 eps))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3))) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (/.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 -1/2 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 eps))) x) (neg.f64 eps))) (*.f64 eps eps))

rewrite866.0ms (14.4%)

Memory
-117.8MiB live, 226.6MiB allocated; 1.2s collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
022174
035145
1141127
21321104
08873104
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
14 → 731
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 eps x)
(+.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 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))
(*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(*.f64 eps (/.f64 eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (fma.f64 eps (neg.f64 (neg.f64 x)) (*.f64 x eps)) (*.f64 x (neg.f64 (neg.f64 x))))
(/.f64 (fma.f64 eps (*.f64 eps x) (*.f64 x eps)) (*.f64 x (*.f64 eps x)))
(/.f64 (fma.f64 eps (neg.f64 x) (*.f64 x eps)) (*.f64 x x))
(/.f64 (fma.f64 eps x (*.f64 (neg.f64 (neg.f64 x)) eps)) (*.f64 (neg.f64 (neg.f64 x)) x))
(/.f64 (fma.f64 eps x (*.f64 (*.f64 eps x) eps)) (*.f64 (*.f64 eps x) x))
(/.f64 (fma.f64 eps x (*.f64 (neg.f64 x) eps)) (*.f64 (neg.f64 x) x))
(/.f64 (fma.f64 eps x (*.f64 x eps)) (*.f64 x x))
(/.f64 eps (neg.f64 (*.f64 eps x)))
(/.f64 eps (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 eps (*.f64 eps x))
(/.f64 eps (neg.f64 (neg.f64 x)))
(/.f64 eps (neg.f64 x))
(/.f64 eps x)
(neg.f64 (/.f64 eps x))
(fma.f64 eps (/.f64 eps x) (/.f64 eps x))
(fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (/.f64 eps x))
(fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) (/.f64 eps x))
(-.f64 (/.f64 eps x) (/.f64 eps x))
(+.f64 (/.f64 eps x) (/.f64 eps x))
(*.f64 eps (/.f64 eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (fma.f64 eps (neg.f64 (neg.f64 x)) (*.f64 x eps)) (*.f64 x (neg.f64 (neg.f64 x))))
(/.f64 (fma.f64 eps (*.f64 eps x) (*.f64 x eps)) (*.f64 x (*.f64 eps x)))
(/.f64 (fma.f64 eps (neg.f64 x) (*.f64 x eps)) (*.f64 x x))
(/.f64 (fma.f64 eps x (*.f64 (neg.f64 (neg.f64 x)) eps)) (*.f64 (neg.f64 (neg.f64 x)) x))
(/.f64 (fma.f64 eps x (*.f64 (*.f64 eps x) eps)) (*.f64 (*.f64 eps x) x))
(/.f64 (fma.f64 eps x (*.f64 (neg.f64 x) eps)) (*.f64 (neg.f64 x) x))
(/.f64 (fma.f64 eps x (*.f64 x eps)) (*.f64 x x))
(/.f64 eps (neg.f64 (*.f64 eps x)))
(/.f64 eps (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 eps (*.f64 eps x))
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eval307.0ms (5.1%)

Memory
56.2MiB live, 607.9MiB allocated; 87ms collecting garbage
Compiler

Compiled 105 226 to 5 860 computations (94.4% saved)

prune33.0ms (0.6%)

Memory
11.9MiB live, 104.8MiB allocated; 9ms collecting garbage
Pruning

9 alts after pruning (3 fresh and 6 done)

PrunedKeptTotal
New1 71431 717
Fresh000
Picked123
Done044
Total1 71591 724
Accuracy
100.0%
Counts
1 724 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓52.5%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
▶64.4%
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
▶99.5%
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓64.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓61.4%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓6.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶11.0%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
✓41.5%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
Compiler

Compiled 141 to 79 computations (44% saved)

simplify152.0ms (2.5%)

Memory
-15.1MiB live, 169.5MiB allocated; 52ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff0
(+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
cost-diff0
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
cost-diff2
(+.f64 eps #s(literal 0 binary64))
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))
cost-diff0
(/.f64 eps x)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
020102
03298
14398
27398
311898
428198
5134498
6593598
0851998
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(/.f64 eps x)
eps
x
(/.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 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
(+.f64 (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)
x
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(/.f64 eps x)
eps
x
(/.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 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
(+.f64 (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)
x

localize104.0ms (1.7%)

Memory
-20.1MiB live, 115.2MiB allocated; 38ms collecting garbage
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy0.01953125
(+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
accuracy0.28515625
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
accuracy23.843731952616675
#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy0.00390625
(-.f64 (*.f64 x x) eps)
accuracy0.0078125
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.01953125
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.28515625
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy0.0
(/.f64 eps x)
accuracy56.95184656855603
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
Samples
60.0ms159×0valid
15.0ms71×1valid
8.0ms26×2valid
Compiler

Compiled 88 to 15 computations (83% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-sub: 31.0ms (59.1% of total)
ival-div: 6.0ms (11.4% of total)
adjust: 5.0ms (9.5% of total)
ival-sqrt: 3.0ms (5.7% of total)
ival-add: 3.0ms (5.7% of total)
ival-mult: 3.0ms (5.7% of total)
ival-neg: 1.0ms (1.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory
-31.6MiB live, 14.5MiB allocated; 3ms collecting garbage
Counts
11 → 83
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(/.f64 eps x)
(/.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 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(+.f64 (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))
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)))
(/ eps x)
(* (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)
(* 1/2 (/ 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)
(/ (+ (* 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 (* 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 (/ (+ (* -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))))))))
(* 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))
eps
(* 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)))))
(- (+ (* -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))
(* -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)))))
(+ 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)))))
Calls

6 calls:

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

simplify193.0ms (3.2%)

Memory
43.5MiB live, 178.9MiB allocated; 21ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04302002
114441905
264541887
088021776
Stop Event
1×iter limit
1×node limit
Counts
83 → 81
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)))
(/ eps x)
(* (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)
(* 1/2 (/ 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)
(/ (+ (* 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 (* 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 (/ (+ (* -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))))))))
(* 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))
eps
(* 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)))))
(- (+ (* -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))
(* -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)))))
(+ 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)))))
Outputs
(* -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 (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 (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))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(/ eps x)
(/.f64 eps x)
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 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 (fma.f64 (/.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 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))) x (*.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 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 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))) 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) (*.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 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 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)
(* 1/2 (/ 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 #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)
(fma.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 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64))))
(/ (- (* 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 #s(literal -1/8 binary64) x) (/.f64 (*.f64 eps eps) x) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(/ (+ (* 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)
(fma.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 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64))))
(/ (- (+ (* -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 (neg.f64 (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 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 (/.f64 eps 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 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))) 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 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 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 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 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 (/.f64 eps x) x)) x) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (neg.f64 x) (-.f64 (*.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)))))))
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(* -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 (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 (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 (*.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)))))
(fma.f64 (*.f64 x (/.f64 x eps)) eps (neg.f64 eps))

rewrite52.0ms (0.9%)

Memory
-14.4MiB live, 29.9MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02090
03286
110886
086686
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
11 → 97
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(/.f64 eps x)
(/.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 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(+.f64 (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))
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 x)))
(/.f64 (*.f64 eps eps) (*.f64 eps x))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (*.f64 eps eps) x))
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps x)
(neg.f64 (/.f64 (neg.f64 eps) x))
(neg.f64 (/.f64 eps (neg.f64 x)))
(+.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 eps x))
(+.f64 (/.f64 eps x) (/.f64 #s(literal 0 binary64) x))
(*.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 (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) (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(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)) (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(+.f64 (/.f64 #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 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (+.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 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (+.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)))
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) x)
(-.f64 (/.f64 (-.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 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) eps))) (/.f64 (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 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(+.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 (*.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)
eps
(*.f64 (/.f64 eps (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x x))) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(*.f64 (/.f64 eps (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))))
(/.f64 (-.f64 (*.f64 (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))) #s(literal 0 binary64)) (-.f64 (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 0 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))))
(/.f64 (fma.f64 (neg.f64 eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (*.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 0 binary64))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (fma.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (*.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal 0 binary64))) (*.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (*.f64 eps eps) (*.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (*.f64 eps eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (neg.f64 eps) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(neg.f64 (/.f64 (neg.f64 eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(neg.f64 (/.f64 eps (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))))
(fma.f64 (/.f64 eps (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x x))) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 0 binary64))
(+.f64 (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (neg.f64 (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x x)) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))))
(fma.f64 (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)) x)
(-.f64 (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (/.f64 (*.f64 x x) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(+.f64 (/.f64 (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)) (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps)))))
(+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
(+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(*.f64 (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)))
(pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
(exp.f64 (*.f64 (log.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(*.f64 (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(pow.f64 (*.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 2 binary64))
(pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1 binary64))
#s(approx (- (* x x) eps) (neg.f64 eps))
(sqrt.f64 (*.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(approx (- (* x x) eps) (neg.f64 eps))))

eval37.0ms (0.6%)

Memory
-0.6MiB live, 42.8MiB allocated; 8ms collecting garbage
Compiler

Compiled 4 741 to 791 computations (83.3% saved)

prune8.0ms (0.1%)

Memory
14.4MiB live, 14.5MiB allocated; 0ms collecting garbage
Pruning

10 alts after pruning (2 fresh and 8 done)

PrunedKeptTotal
New1732175
Fresh000
Picked123
Done066
Total17410184
Accuracy
100.0%
Counts
184 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓52.5%
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
✓99.5%
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
64.4%
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
41.9%
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps x)) x))
✓64.6%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓61.4%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓6.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓11.0%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
✓41.5%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
Compiler

Compiled 436 to 164 computations (62.4% saved)

regimes52.0ms (0.9%)

Memory
-34.6MiB live, 26.5MiB allocated; 10ms collecting garbage
Counts
16 → 1
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps x)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (*.f64 (+.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 (/.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 (-.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:

42.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
5.0ms
eps
5.0ms
x
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)

regimes10.0ms (0.2%)

Memory
16.9MiB live, 16.9MiB allocated; 0ms collecting garbage
Counts
10 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps x)) x))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps x)) x))
Calls

3 calls:

3.0ms
eps
3.0ms
x
3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.6%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
88.0%2x
83.0%2eps
Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory
6.9MiB live, 6.9MiB allocated; 0ms collecting garbage
Counts
9 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.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 #s(literal 1/2 binary64) (/.f64 eps x)))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.6%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory
8.0MiB live, 8.1MiB allocated; 0ms collecting garbage
Counts
6 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(-.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 #s(literal 1/2 binary64) (/.f64 eps x)))
Calls

1 calls:

2.0ms
(-.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)

regimes40.0ms (0.7%)

Memory
-35.1MiB live, 10.6MiB allocated; 7ms collecting garbage
Counts
3 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(-.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))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
Calls

3 calls:

36.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
64.8%2eps
64.5%2x
67.9%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

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

3 calls:

1.0ms
eps
1.0ms
x
1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
11.0%1x
11.0%1eps
11.0%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes3.0ms (0.1%)

Memory
6.1MiB live, 6.0MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

3 calls:

1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
3.2%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.2%1x
3.2%1eps
Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.935814195557444e-153
-1.7516903768102048e-155
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
-1.935814195557444e-153
-1.7516903768102048e-155
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
-1.935814195557444e-153
-1.7516903768102048e-155
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
-1.935814195557444e-153
-1.7516903768102048e-155
Compiler

Compiled 11 to 11 computations (0% saved)

simplify12.0ms (0.2%)

Memory
12.1MiB live, 12.1MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036172
154172
278172
3100172
4112172
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 -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(-.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 -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

derivations631.0ms (10.5%)

Memory
-0.6MiB live, 471.6MiB allocated; 75ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02571067
18071053
233631038
08415979
0622
01022
14222
032022
04302002
114441905
264541887
088021776
022174
035145
1141127
21321104
08873104
028160
047160
1155144
01182144
Stop Event
1×fuel
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 172 to 36 computations (79.1% saved)

preprocess92.0ms (1.5%)

Memory
-14.5MiB live, 121.2MiB allocated; 37ms collecting garbage
Compiler

Compiled 380 to 98 computations (74.2% saved)

end0.0ms (0%)

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

Profiling

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