ENA, Section 1.4, Exercise 4d

Time bar (total: 7.3s)

start0.0ms (0%)

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

analyze32.0ms (0.4%)

Memory
-8.7MiB live, 36.4MiB allocated; 7ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%12.8%87.2%0%0%0%0
0%0%12.8%87.2%0%0%0%1
0%0%12.8%87.2%0%0%0%2
50%6.4%6.4%87.2%0%0%0%3
57.1%6.4%4.8%87.2%0%1.6%0%4
69.2%7.2%3.2%87.2%0%2.4%0%5
75%7.2%2.4%87.2%0%3.2%0%6
82.6%7.6%1.6%87.2%0%3.6%0%7
86.4%7.6%1.2%87.2%0%4%0%8
90.7%7.8%0.8%87.2%0%4.2%0%9
92.6%7.8%0.6%87.2%0%4.4%0%10
95%7.9%0.4%87.2%0%4.5%0%11
96.3%8%0.3%87.2%0%4.5%0%12
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.6s (21.9%)

Memory
15.2MiB live, 1 935.7MiB allocated; 419ms collecting garbage
Samples
604.0ms4 895×0valid
382.0ms2 705×1valid
137.0ms656×2valid
12.0ms185×0invalid
Precisions
Click to see histograms. Total time spent on operations: 723.0ms
ival-sub: 156.0ms (21.6% of total)
ival-mult: 149.0ms (20.6% of total)
ival-<=: 149.0ms (20.6% of total)
ival-sqrt: 117.0ms (16.2% of total)
adjust: 109.0ms (15.1% of total)
ival-and: 23.0ms (3.2% of total)
exact: 17.0ms (2.4% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

explain154.0ms (2.1%)

Memory
-0.2MiB live, 189.6MiB allocated; 28ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1020-0-(-.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)))cancellation1020
Confusion
Predicted +Predicted -
+1020
-0154
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+10200
-00154
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0154
1102
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
44.0ms310×0valid
18.0ms160×1valid
7.0ms42×2valid
Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-sqrt: 25.0ms (46.9% of total)
ival-sub: 15.0ms (28.1% of total)
adjust: 7.0ms (13.1% of total)
ival-mult: 5.0ms (9.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess34.0ms (0.5%)

Memory
-24.1MiB live, 30.5MiB allocated; 14ms collecting garbage
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
0.9MiB live, 0.9MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶63.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0%)

Memory
10.1MiB live, 10.1MiB allocated; 0ms collecting garbage
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

localize31.0ms (0.4%)

Memory
13.9MiB live, 58.6MiB allocated; 5ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.01171875
(-.f64 (*.f64 x x) eps)
accuracy0.015625
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy23.1251652837185
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Samples
13.0ms80×1valid
8.0ms155×0valid
4.0ms21×2valid
Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
ival-mult: 6.0ms (38.6% of total)
ival-sub: 4.0ms (25.8% of total)
adjust: 3.0ms (19.3% of total)
ival-sqrt: 3.0ms (19.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
-25.6MiB live, 19.2MiB allocated; 4ms 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
4.0ms
x
@inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
2.0ms
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
@-inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms
eps
@0
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))

simplify190.0ms (2.6%)

Memory
13.3MiB live, 155.1MiB allocated; 19ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02571069
18071054
231081019
08668960
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 eps)) (sqrt.f64 #s(literal -1 binary64)) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(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))) (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) 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 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.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) (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) 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 (*.f64 x x) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (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 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 (/.f64 #s(literal 1/8 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 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 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.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 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (*.f64 #s(literal 1/2 binary64) eps))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 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)))))))
(*.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 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)
(* (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) (-.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)))))))
(*.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 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -1 binary64)) x)
(* -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))))))))
(*.f64 (neg.f64 x) (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 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)))))
(* 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 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 x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)) 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)))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))) 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)))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)))) 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 #s(literal 1/16 binary64) (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 #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 (-.f64 (*.f64 x (/.f64 x eps)) #s(literal 1 binary64)) eps)
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (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)) (neg.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal -1/2 binary64) (neg.f64 x)) eps))) 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 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) x) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps)))) eps)
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.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)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal -1/8 binary64) (*.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)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)

rewrite255.0ms (3.5%)

Memory
-36.9MiB live, 168.2MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0622
01022
14222
232022
3365222
0887022
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 199
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 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 x x (-.f64 (*.f64 x x) eps)) (fma.f64 x x (-.f64 (*.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (fma.f64 x x (-.f64 (*.f64 x x) eps)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))))
(*.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps)))))
(*.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
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(*.f64 x x)
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(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
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eval42.0ms (0.6%)

Memory
16.8MiB live, 59.9MiB allocated; 7ms collecting garbage
Compiler

Compiled 6 064 to 978 computations (83.9% saved)

prune10.0ms (0.1%)

Memory
32.5MiB live, 32.5MiB allocated; 0ms collecting garbage
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New23411245
Fresh000
Picked011
Done000
Total23412246
Accuracy
99.7%
Counts
246 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
52.4%
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))))
32.7%
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps)))) (*.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)))
63.4%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓63.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶63.9%
(-.f64 x (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
▶63.7%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
59.2%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
7.1%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
33.3%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (*.f64 #s(literal 1/2 binary64) eps))) x))
▶37.0%
#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))
▶42.3%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Compiler

Compiled 498 to 264 computations (47% saved)

simplify118.0ms (1.6%)

Memory
-9.4MiB live, 176.0MiB allocated; 22ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
cost-diff0
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff0
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff0
#s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))
cost-diff0
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))
cost-diff0
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
cost-diff3
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
cost-diff0
(/.f64 #s(literal 1/2 binary64) x)
cost-diff0
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
cost-diff0
(neg.f64 x)
cost-diff0
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
cost-diff0
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
cost-diff0
(fma.f64 x x eps)
cost-diff0
(sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
cost-diff0
(-.f64 x (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
cost-diff10
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
034246
057233
181233
2173231
3596217
42044210
54267204
66430204
08007204
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
x
(sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(fma.f64 x x eps)
eps
(/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))
#s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
(/.f64 x eps)
eps
#s(literal -1 binary64)
#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))
(*.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)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
Outputs
(-.f64 x (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x eps)
eps
(/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))
(sqrt.f64 #s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps)))
#s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(-.f64 (*.f64 x x) eps)
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
(fma.f64 (/.f64 x eps) x #s(literal -1 binary64))
(/.f64 x eps)
eps
#s(literal -1 binary64)
#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))
(*.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)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

localize168.0ms (2.3%)

Memory
6.0MiB live, 150.4MiB allocated; 18ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.0859375
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy6.426716219584271
(*.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)
accuracy7.801840744218811
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy38.17263089605457
#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))
accuracy0.015625
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))
accuracy0.078125
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
accuracy0.5700015536425816
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
accuracy23.1251652837185
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
accuracy0.0
(/.f64 #s(literal 1/2 binary64) x)
accuracy0.23828125
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy36.82998704571763
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy0.0
(neg.f64 x)
accuracy23.1251652837185
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy62.40834247330037
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy0.015625
(sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
accuracy0.017910009768442016
(/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))
accuracy0.02734375
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
accuracy23.1251652837185
(-.f64 x (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
Samples
73.0ms155×0valid
44.0ms80×1valid
31.0ms21×2valid
Compiler

Compiled 208 to 29 computations (86.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 126.0ms
ival-mult: 48.0ms (38.2% of total)
adjust: 28.0ms (22.3% of total)
ival-add: 16.0ms (12.7% of total)
ival-pow: 13.0ms (10.3% of total)
ival-div: 9.0ms (7.2% of total)
ival-sub: 5.0ms (4% of total)
ival-sqrt: 5.0ms (4% of total)
ival-neg: 1.0ms (0.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series41.0ms (0.6%)

Memory
-2.3MiB live, 42.5MiB allocated; 8ms collecting garbage
Counts
20 → 89
Calls
Call 1
Inputs
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(-.f64 x (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
(fma.f64 x x eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))
#s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))
#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))
(*.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)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
Outputs
(* -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)))))))))
eps
(+ eps (pow x 2))
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(+ (* -1 eps) (pow x 2))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
-1
(- (* 2 (/ (pow x 2) eps)) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps)))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) 1)
(- (/ (pow x 2) eps) 1)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
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 (/ eps (pow x 2))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1
(- (+ 1 (* -1 (/ eps (pow x 2)))) (/ eps (pow x 2)))
(- (+ 1 (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (* eps (- (* -1 eps) eps)) (pow x 4))))) (/ eps (pow x 2)))
(- (+ 1 (+ (* -1 (/ eps (pow x 2))) (/ (* (pow eps 2) (- (* -1 eps) eps)) (pow x 6)))) (+ (/ eps (pow x 2)) (/ (* eps (- (* -1 eps) eps)) (pow x 4))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (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 (* -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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) 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))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ 1 (* -2 (/ eps (pow x 2))))
(+ 1 (* eps (- (* 2 (/ eps (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* eps (- (* eps (+ (* -2 (/ eps (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(/ (+ (* -1 eps) (pow x 2)) eps)
(* 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 (+ 1 (/ (pow x 2) eps)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(- (/ (pow x 2) eps) (+ 1 (* -1 (/ (pow x 2) eps))))
(- (+ (* -1 (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) (pow eps 2))) (/ (pow x 2) eps)) (+ 1 (* -1 (/ (pow x 2) eps))))
(- (+ (/ (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))) (pow eps 3)) (/ (pow x 2) eps)) (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) (pow eps 2)))))
(* -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 (/ (pow x 2) eps)) 1)))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(- (* -1 (/ (- (* -1 (pow x 2)) (pow x 2)) eps)) 1)
(- (* -1 (/ (- (+ (* -1 (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (pow x 2))) (pow x 2)) eps)) 1)
(- (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))))) eps)) (* -1 (pow x 2))) (pow x 2)) eps)) 1)
Calls

6 calls:

TimeVariablePointExpression
22.0ms
x
@inf
((* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))) (- x (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))))) (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps)))) (+ (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (/ (- (* x x) eps) (+ (* x x) eps)) (+ (* x (/ x eps)) -1))
5.0ms
eps
@inf
((* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))) (- x (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))))) (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps)))) (+ (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (/ (- (* x x) eps) (+ (* x x) eps)) (+ (* x (/ x eps)) -1))
4.0ms
x
@0
((* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))) (- x (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))))) (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps)))) (+ (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (/ (- (* x x) eps) (+ (* x x) eps)) (+ (* x (/ x eps)) -1))
3.0ms
eps
@-inf
((* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))) (- x (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))))) (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps)))) (+ (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (/ (- (* x x) eps) (+ (* x x) eps)) (+ (* x (/ x eps)) -1))
3.0ms
eps
@0
((* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))) (- x (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps))))) (sqrt (* (+ (* x x) eps) (/ (- (* x x) eps) (+ (* x x) eps)))) (+ (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (/ (- (* x x) eps) (+ (* x x) eps)) (+ (* x (/ x eps)) -1))

simplify204.0ms (2.8%)

Memory
2.1MiB live, 189.2MiB allocated; 24ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03891664
112101613
244331578
081531493
Stop Event
1×iter limit
1×node limit
Counts
89 → 87
Calls
Call 1
Inputs
(* -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)))))))))
eps
(+ eps (pow x 2))
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(+ (* -1 eps) (pow x 2))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
-1
(- (* 2 (/ (pow x 2) eps)) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps)))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) 1)
(- (/ (pow x 2) eps) 1)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
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 (/ eps (pow x 2))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1
(- (+ 1 (* -1 (/ eps (pow x 2)))) (/ eps (pow x 2)))
(- (+ 1 (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (* eps (- (* -1 eps) eps)) (pow x 4))))) (/ eps (pow x 2)))
(- (+ 1 (+ (* -1 (/ eps (pow x 2))) (/ (* (pow eps 2) (- (* -1 eps) eps)) (pow x 6)))) (+ (/ eps (pow x 2)) (/ (* eps (- (* -1 eps) eps)) (pow x 4))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (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 (* -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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) 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))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ 1 (* -2 (/ eps (pow x 2))))
(+ 1 (* eps (- (* 2 (/ eps (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* eps (- (* eps (+ (* -2 (/ eps (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(/ (+ (* -1 eps) (pow x 2)) eps)
(* 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 (+ 1 (/ (pow x 2) eps)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(- (/ (pow x 2) eps) (+ 1 (* -1 (/ (pow x 2) eps))))
(- (+ (* -1 (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) (pow eps 2))) (/ (pow x 2) eps)) (+ 1 (* -1 (/ (pow x 2) eps))))
(- (+ (/ (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))) (pow eps 3)) (/ (pow x 2) eps)) (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) (pow eps 2)))))
(* -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 (/ (pow x 2) eps)) 1)))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(- (* -1 (/ (- (* -1 (pow x 2)) (pow x 2)) eps)) 1)
(- (* -1 (/ (- (+ (* -1 (/ (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (pow x 2))) (pow x 2)) eps)) 1)
(- (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))))) eps)) (* -1 (pow x 2))) (pow x 2)) eps)) 1)
Outputs
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (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 #s(literal 1/8 binary64) (*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #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))) (*.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 #s(literal -1/8 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) (*.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)))
eps
(+ eps (pow x 2))
(fma.f64 x x eps)
(* -1 x)
(neg.f64 x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) eps)) 1)
(-.f64 (*.f64 (/.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #s(literal 1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps)))) 1)
(-.f64 (*.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 x x)) eps)) eps) (*.f64 x x)) #s(literal 1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) 1)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 2 binary64) eps) x) x #s(literal -2 binary64)) (*.f64 eps eps)) (-.f64 (*.f64 (/.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #s(literal 1 binary64)))
(- (/ (pow x 2) eps) 1)
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(-.f64 (/.f64 (fma.f64 (*.f64 #s(literal 2 binary64) x) x (/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) eps)) eps) #s(literal 1 binary64))
(- (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (* (pow x 4) (- (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 (* (pow x 2) (- (* -1 (pow x 2)) (pow x 2))))) eps)) (* -1 (pow x 2))) (pow x 2)) eps)) 1)
(-.f64 (/.f64 (fma.f64 (*.f64 #s(literal 2 binary64) x) x (neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 eps)))) eps) #s(literal 1 binary64))

rewrite238.0ms (3.3%)

Memory
-2.7MiB live, 108.5MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
034215
057215
1189185
21405185
08249185
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 703
Calls
Call 1
Inputs
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(-.f64 x (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
(fma.f64 x x eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))
#s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))
#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))
(*.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)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
Outputs
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (fma.f64 eps (-.f64 eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (fma.f64 x x eps))
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (sqrt.f64 (fma.f64 x x eps))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (sqrt.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (-.f64 (*.f64 x x) eps)))))
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (fma.f64 x x eps)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (fma.f64 x x eps) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (fma.f64 x x eps) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (fma.f64 eps (-.f64 eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (-.f64 (*.f64 x x) eps)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (sqrt.f64 (fma.f64 x x eps))) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (sqrt.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (-.f64 (*.f64 x x) eps)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (fma.f64 x x eps)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (/.f64 (fma.f64 x x eps) (fma.f64 x x eps)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))
(*.f64 (/.f64 (fma.f64 x x eps) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 eps (-.f64 eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) #s(literal 1 binary64)) (-.f64 (*.f64 x x) eps))
(*.f64 (pow.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x x eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 eps (-.f64 eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (-.f64 (*.f64 x x) eps))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (sqrt.f64 (fma.f64 x x eps)) (sqrt.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (-.f64 (*.f64 x x) eps))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (fma.f64 x x eps))
(*.f64 (-.f64 (*.f64 x x) eps) (/.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))
(*.f64 (-.f64 (*.f64 x x) eps) (/.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(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 (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps))) (*.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.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 (*.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 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))) (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))) (+.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 (*.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (*.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (*.f64 (*.f64 eps (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (*.f64 eps (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))) (-.f64 (*.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (*.f64 eps (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 eps (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (*.f64 eps (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (*.f64 (*.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (*.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))) (-.f64 (*.f64 eps (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (*.f64 (*.f64 x x) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 x x)) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 x x))) (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) eps) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) eps))) (-.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 x x)) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) eps) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) eps)) (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 x x)) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 x x)))) (-.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) eps) (*.f64 (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.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 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64))) (fma.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 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (*.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))))))))
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(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (neg.f64 x) (/.f64 x eps)) (*.f64 (neg.f64 x) (/.f64 x eps)))) (+.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) (/.f64 x eps))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))))) (-.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) (fma.f64 (pow.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) (pow.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (neg.f64 (/.f64 x eps)) x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (neg.f64 (/.f64 x eps)) x) (*.f64 (neg.f64 (/.f64 x eps)) x) (*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (/.f64 x eps)) x)))))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (neg.f64 x) (/.f64 x eps)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (neg.f64 x) (/.f64 x eps)) (*.f64 (neg.f64 x) (/.f64 x eps)) (*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) (/.f64 x eps))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (-.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))) (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal -1 binary64) (*.f64 (/.f64 x eps) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) (*.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))
(/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) (*.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) #s(literal -1 binary64))) (*.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (*.f64 (/.f64 x eps) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))
(fma.f64 (/.f64 x eps) x #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) eps) #s(literal -1 binary64))
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 (/.f64 x eps) x))) (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 (/.f64 x eps) x))))
(-.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))) (pow.f64 (-.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (/.f64 x eps)) x))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) (/.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))))
(+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))) (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))))))
(+.f64 (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))))
(+.f64 (/.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (/.f64 x eps) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64)))))
(+.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (*.f64 (/.f64 x eps) x))

eval296.0ms (4.1%)

Memory
1.8MiB live, 234.3MiB allocated; 34ms collecting garbage
Compiler

Compiled 36 906 to 4 323 computations (88.3% saved)

prune75.0ms (1%)

Memory
-30.6MiB live, 64.5MiB allocated; 4ms collecting garbage
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New9177924
Fresh336
Picked325
Done011
Total92313936
Accuracy
99.9%
Counts
936 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.5%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
63.5%
(-.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)))
63.4%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓63.8%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓63.7%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
▶59.2%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶7.1%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶63.8%
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
42.5%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶40.2%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
▶40.2%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
24.3%
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))))
Compiler

Compiled 480 to 267 computations (44.4% saved)

simplify151.0ms (2.1%)

Memory
27.8MiB live, 164.3MiB allocated; 18ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
cost-diff2
(/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
cost-diff4
(fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64)))
cost-diff0
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
cost-diff0
(*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps)
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
cost-diff0
(/.f64 eps x)
cost-diff0
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
cost-diff0
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
cost-diff0
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
cost-diff0
(neg.f64 eps)
cost-diff0
#s(approx (- (* x x) eps) (neg.f64 eps))
cost-diff0
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff0
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff8
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff16
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037345
065318
1111291
2306290
31314284
46135284
08126283
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (*.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 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
x
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 eps x)
eps
x
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
(*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
(/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
(fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x))
(/.f64 eps x)
eps
x
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 x x)
Outputs
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
x
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
eps
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(neg.f64 (-.f64 (*.f64 x x) eps))
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
x
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps)
(*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
(/.f64 eps x)
eps
x
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
(*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x))
(*.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps)
(/.f64 eps x)
eps
x
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(*.f64 x x)

localize220.0ms (3%)

Memory
25.4MiB live, 352.4MiB allocated; 97ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy1.050097485936003
(/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
accuracy6.426716219584271
(*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
accuracy12.977476114650093
(fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64)))
accuracy38.17263089605457
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
accuracy0.05859375
(/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
accuracy0.14291000976844204
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
accuracy6.426716219584271
(*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps)
accuracy38.17263089605457
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
accuracy0.0
(/.f64 eps x)
accuracy0.00390625
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy23.1251652837185
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy36.314536605446676
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy0.0
(neg.f64 eps)
accuracy0.015625
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy23.1251652837185
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy25.22440787033225
#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy0.33203125
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy0.34212875976844204
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy4.760858033708704
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy23.059150973782387
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
Samples
91.0ms79×1valid
58.0ms155×0valid
37.0ms22×2valid
Compiler

Compiled 299 to 31 computations (89.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 153.0ms
adjust: 50.0ms (32.6% of total)
ival-div: 36.0ms (23.5% of total)
ival-mult: 32.0ms (20.9% of total)
ival-sqrt: 22.0ms (14.4% of total)
ival-add: 7.0ms (4.6% of total)
ival-sub: 4.0ms (2.6% of total)
ival-neg: 3.0ms (2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series59.0ms (0.8%)

Memory
-15.0MiB live, 73.9MiB allocated; 15ms collecting garbage
Counts
21 → 146
Calls
Call 1
Inputs
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x 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)
(-.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)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
(*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
eps
(+ eps (* -1 (pow x 2)))
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(pow x 2)
(* -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)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(* 1/8 (/ eps x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(+ (* x (- (* -1 (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* x (+ (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x)
(* -1 (pow x 2))
(* (pow x 2) (- (/ eps (pow x 2)) 1))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(* 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)))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* -1/2 x)
(* x (- (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) 1/2))
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (* -1/32 (/ (pow eps 2) (pow x 4))))) 1/2))
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 4))) (+ (* -1/64 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6)))))))) 1/2))
(* 2 x)
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))))))))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* -1 (* 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))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* -2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (* 5/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))) (* 5/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 6)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 6))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) (* 5/2 (/ 1 (pow x 2))))))
(+ (* -1/2 x) (* 1/2 x))
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
(* 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))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1/2 x) (* 3/8 (/ eps x)))
(+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))
(+ (* -1/2 x) (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))))
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))))
(* eps (+ 1 (* -1 (/ (pow x 2) eps))))
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
(* eps (- (/ 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))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(* -1 (* eps (- (/ (pow x 2) eps) 1)))
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x)))))
(- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) (* -1 x))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps))) eps)))
Calls

6 calls:

TimeVariablePointExpression
16.0ms
eps
@inf
((+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) eps) (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) (+ (* (/ eps x) (/ 1/8 x)) 1/2) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x)))
13.0ms
x
@0
((+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) eps) (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) (+ (* (/ eps x) (/ 1/8 x)) 1/2) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x)))
11.0ms
eps
@-inf
((+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) eps) (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) (+ (* (/ eps x) (/ 1/8 x)) 1/2) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x)))
6.0ms
x
@-inf
((+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) eps) (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) (+ (* (/ eps x) (/ 1/8 x)) 1/2) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x)))
6.0ms
x
@inf
((+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) eps) (/ (+ (* (/ eps x) (/ 1/8 x)) 1/2) x) (+ (* (/ eps x) (/ 1/8 x)) 1/2) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x)))

simplify238.0ms (3.3%)

Memory
17.4MiB live, 298.3MiB allocated; 70ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08364510
128744136
087253901
Stop Event
1×iter limit
1×node limit
Counts
146 → 144
Calls
Call 1
Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
eps
(+ eps (* -1 (pow x 2)))
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(pow x 2)
(* -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)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(* 1/8 (/ eps x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(+ (* x (- (* -1 (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* x (+ (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x)
(* -1 (pow x 2))
(* (pow x 2) (- (/ eps (pow x 2)) 1))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(* 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)))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* -1/2 x)
(* x (- (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) 1/2))
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (* -1/32 (/ (pow eps 2) (pow x 4))))) 1/2))
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 4))) (+ (* -1/64 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6)))))))) 1/2))
(* 2 x)
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))))))))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* -1 (* 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))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* -2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (* 5/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))) (* 5/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 6)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 6))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) (* 5/2 (/ 1 (pow x 2))))))
(+ (* -1/2 x) (* 1/2 x))
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
(* 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))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1/2 x) (* 3/8 (/ eps x)))
(+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))
(+ (* -1/2 x) (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))))
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))))
(* eps (+ 1 (* -1 (/ (pow x 2) eps))))
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
(* eps (- (/ 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))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(* -1 (* eps (- (/ (pow x 2) eps) 1)))
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x)))))
(- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) (* -1 x))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps))) eps)))
Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 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))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 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))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) #s(literal -1 binary64) (fma.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)))) x (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
eps
(+ eps (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x eps)
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 eps))) x (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps) eps)) (*.f64 (/.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) x (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x) (/.f64 #s(literal 1 binary64) (neg.f64 eps))) x (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* (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) (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 #s(literal -1/8 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (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 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 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))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 x x)) x)
(/ eps x)
(/.f64 eps x)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x))
(* 1/8 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) x)
(+ (* x (- (* -1 (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (*.f64 (neg.f64 x) (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))))) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* x (+ (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))))))) (/ 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))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x (neg.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x)
(/.f64 (fma.f64 eps #s(literal 3/8 binary64) (*.f64 #s(literal 1/8 binary64) eps)) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x)
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(* -1 (* eps (- (/ (pow x 2) eps) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)))
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) x) (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (neg.f64 eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) x) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)) #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (neg.f64 eps))) (neg.f64 eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
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(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) x) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) x)) (sqrt.f64 #s(literal -1 binary64)))) eps)) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
(* -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)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) eps)) eps)
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x)))))
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x)))
(- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) (* -1 x))
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rewrite795.0ms (10.9%)

Memory
-119.3MiB live, 227.7MiB allocated; 1.1s collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
037279
065252
1233215
21910215
08161215
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
21 → 709
Calls
Call 1
Inputs
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x 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)
(-.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)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
(*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Outputs
(*.f64 (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (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 (neg.f64 (/.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 x) x (-.f64 (*.f64 x x) eps))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (/.f64 (-.f64 (*.f64 x x) (neg.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x))))) (neg.f64 (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))))
(/.f64 (neg.f64 (fma.f64 (-.f64 (*.f64 x x) eps) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (neg.f64 x) x)))) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (fma.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 x x)))) (neg.f64 (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (neg.f64 x) x)))) (neg.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (neg.f64 x) x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (-.f64 (*.f64 x x) eps)))) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (neg.f64 x) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (neg.f64 (-.f64 (*.f64 x x) eps))))) (neg.f64 (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (-.f64 (*.f64 x x) (neg.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (/.f64 (-.f64 (*.f64 x x) (neg.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (pow.f64 (/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 2 binary64)))) (*.f64 (/.f64 (-.f64 (*.f64 x x) (neg.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) (neg.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (-.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 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (-.f64 (*.f64 x x) eps))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x)) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (-.f64 (*.f64 x x) eps))) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64)) (+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))) (*.f64 (+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))) (pow.f64 (/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 3 binary64)))) (*.f64 (+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))) (+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))))
(/.f64 (fma.f64 (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)) (*.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)) (*.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))) (*.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))
(/.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (neg.f64 x) x))) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 x x))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 x x))) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (fma.f64 (-.f64 (*.f64 x x) eps) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 x x))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (fma.f64 (*.f64 (neg.f64 x) x) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (neg.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (fma.f64 (*.f64 x x) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (neg.f64 (-.f64 (*.f64 x x) eps)))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (neg.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (fma.f64 (*.f64 x x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (-.f64 (*.f64 x x) eps))) (*.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (fma.f64 (*.f64 x x) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (/.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (*.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (-.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (fma.f64 (neg.f64 x) x (-.f64 (*.f64 x x) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) (neg.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 2 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 3 binary64))))) (neg.f64 (+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))))
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(/.f64 (*.f64 (/.f64 (*.f64 x (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))) x) eps) x)
(/.f64 (*.f64 (neg.f64 (*.f64 x (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)))) eps) (*.f64 (neg.f64 x) x))
(/.f64 (*.f64 eps (neg.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)))) (neg.f64 x))
(/.f64 (*.f64 eps (/.f64 (*.f64 x (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))) x)) x)
(/.f64 (*.f64 eps (neg.f64 (*.f64 x (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))))) (*.f64 (neg.f64 x) x))
(/.f64 (neg.f64 (*.f64 (*.f64 x (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))) eps)) (*.f64 (neg.f64 x) x))
(/.f64 (neg.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps)) (neg.f64 x))
(/.f64 (*.f64 (*.f64 x (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))) eps) (*.f64 x x))
(/.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps) x)
(fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64))) eps (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(fma.f64 (*.f64 (/.f64 x x) (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64)))) eps (*.f64 (*.f64 (/.f64 x x) (/.f64 #s(literal 1/2 binary64) x)) eps))
(fma.f64 eps (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64))) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))
(fma.f64 eps (*.f64 (/.f64 x x) (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64)))) (*.f64 eps (*.f64 (/.f64 x x) (/.f64 #s(literal 1/2 binary64) x))))
(+.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64))) eps) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(+.f64 (*.f64 (*.f64 (/.f64 x x) (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64)))) eps) (*.f64 (*.f64 (/.f64 x x) (/.f64 #s(literal 1/2 binary64) x)) eps))
(+.f64 (*.f64 eps (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64)))) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))
(+.f64 (*.f64 eps (*.f64 (/.f64 x x) (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal 3 binary64))))) (*.f64 eps (*.f64 (/.f64 x x) (/.f64 #s(literal 1/2 binary64) x))))
(*.f64 (/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 (/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (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 (/.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (*.f64 x x) eps) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (-.f64 (*.f64 x x) eps) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(neg.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (/.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (/.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))) (/.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(-.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 eps (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))

eval198.0ms (2.7%)

Memory
-22.4MiB live, 163.1MiB allocated; 73ms collecting garbage
Compiler

Compiled 29 690 to 3 249 computations (89.1% saved)

prune77.0ms (1.1%)

Memory
-29.9MiB live, 62.9MiB allocated; 6ms collecting garbage
Pruning

16 alts after pruning (11 fresh and 5 done)

PrunedKeptTotal
New7467753
Fresh145
Picked235
Done123
Total75016766
Accuracy
99.9%
Counts
766 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.3%
(/.f64 (fma.f64 (neg.f64 x) x (-.f64 (*.f64 x x) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
38.6%
(/.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (-.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
▶63.5%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
63.5%
(-.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)))
63.4%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶63.9%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓63.7%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
✓59.2%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓7.1%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓63.8%
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
42.5%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶40.3%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x)))
▶40.2%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
40.2%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (/.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) x)) (*.f64 x x)) eps))
▶4.3%
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
Compiler

Compiled 624 to 316 computations (49.4% saved)

simplify198.0ms (2.7%)

Memory
39.5MiB live, 321.4MiB allocated; 29ms collecting garbage
Localize:

Found 17 expressions of interest:

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

Useful iterations: 2 (0.0ms)

IterNodesCost
037250
061233
1101212
2246208
3615208
42989208
08151208
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
eps
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x)))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
x
(/.f64 eps x)
eps
#s(literal 1/2 binary64)
(/.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))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
(*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64)) x)
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64))
eps
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64)) x) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x))
(*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64)) x) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
x
(/.f64 eps x)
eps
#s(literal 1/2 binary64)
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
eps
(*.f64 x x)
x
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))

localize124.0ms (1.7%)

Memory
9.1MiB live, 240.7MiB allocated; 30ms collecting garbage
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy0.015625
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.02734375
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy0.296875
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy22.73672106963399
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
accuracy0.0
(/.f64 #s(literal 1/8 binary64) x)
accuracy0.1171875
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x))
accuracy0.14291000976844204
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
accuracy38.17263089605457
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x)))
accuracy0.14453125
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy6.426716219584271
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
accuracy12.131408957479898
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
accuracy38.17263089605457
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
accuracy61.262842463417314
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
accuracy0.0
(neg.f64 eps)
accuracy0.0
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
accuracy0.015625
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
accuracy23.1251652837185
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
Samples
55.0ms79×1valid
33.0ms155×0valid
14.0ms22×2valid
Compiler

Compiled 212 to 31 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 79.0ms
ival-div: 26.0ms (33.1% of total)
ival-mult: 20.0ms (25.4% of total)
adjust: 12.0ms (15.3% of total)
ival-add: 8.0ms (10.2% of total)
ival-sub: 5.0ms (6.4% of total)
ival-neg: 3.0ms (3.8% of total)
ival-sqrt: 3.0ms (3.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series23.0ms (0.3%)

Memory
-15.4MiB live, 29.3MiB allocated; 7ms collecting garbage
Counts
21 → 119
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x)))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
(-.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)
(neg.f64 eps)
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.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)))
(* (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)
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ 1/8 x)
eps
(+ (* 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)
(/ 1/8 (pow x 2))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
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)))))
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(/ (- (+ (* 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)))))))
(* -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))))))))
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))))))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -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))) (* -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))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* -1/2 x) (* 1/2 x))
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -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)))))
(* 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 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))))
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(- (+ (* -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)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 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 (/ 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
7.0ms
x
@-inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) (+ (* eps (/ 1/8 (* x x))) 1/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ eps x)) (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ 1/8 x) (- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (neg eps) (/ 1/8 (* x x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
4.0ms
x
@inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) (+ (* eps (/ 1/8 (* x x))) 1/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ eps x)) (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ 1/8 x) (- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (neg eps) (/ 1/8 (* x x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms
eps
@inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) (+ (* eps (/ 1/8 (* x x))) 1/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ eps x)) (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ 1/8 x) (- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (neg eps) (/ 1/8 (* x x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms
eps
@-inf
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) (+ (* eps (/ 1/8 (* x x))) 1/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ eps x)) (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ 1/8 x) (- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (neg eps) (/ 1/8 (* x x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms
x
@0
((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) (+ (* eps (/ 1/8 (* x x))) 1/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ eps x)) (+ (* (/ 1/8 x) (/ eps x)) 1/2) (/ 1/8 x) (- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (neg eps) (/ 1/8 (* x x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))

simplify219.0ms (3%)

Memory
9.8MiB live, 294.4MiB allocated; 66ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07223661
125243423
082873223
Stop Event
1×iter limit
1×node limit
Counts
119 → 117
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)
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ 1/8 x)
eps
(+ (* 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)
(/ 1/8 (pow x 2))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
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)))))
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(/ (- (+ (* 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)))))))
(* -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))))))))
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))))))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))))))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -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))) (* -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))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* -1/2 x) (* 1/2 x))
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -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)))))
(* 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 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))))
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(- (+ (* -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)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 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 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* (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) (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 -1/8 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 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64))) (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 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))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 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))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (/.f64 #s(literal 1 binary64) (neg.f64 eps)))) x (fma.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) (*.f64 x x))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
eps
(+ (* 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 (neg.f64 x) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #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 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 #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 -1/8 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 (/.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 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) eps))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (-.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (/.f64 #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)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 (fma.f64 (/.f64 (*.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (*.f64 x x))
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x)
(/.f64 (fma.f64 eps #s(literal 3/8 binary64) (*.f64 #s(literal 1/8 binary64) eps)) x)
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (-.f64 (fma.f64 eps #s(literal 3/8 binary64) (/.f64 (fma.f64 #s(literal -1/32 binary64) (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps #s(literal -3/8 binary64)) eps) #s(literal -1/4 binary64))) (*.f64 x x))) (fma.f64 (/.f64 #s(literal -1/16 binary64) x) (/.f64 (*.f64 eps eps) x) (*.f64 #s(literal -1/8 binary64) eps))) x)
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(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
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(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (-.f64 (*.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) (/.f64 #s(literal 1/2 binary64) x)) eps (*.f64 #s(literal 2 binary64) x))
(* 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))))
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(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (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 #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)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (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 #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)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #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)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))))
(+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps (/.f64 x #s(literal -1 binary64)))) (neg.f64 eps)))
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))
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(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2))))))
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(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 eps eps))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) eps)) eps)
(- (+ (* -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)))
(fma.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) eps) (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
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(* 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 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (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 #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)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))) eps)
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) (neg.f64 eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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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))))))
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(* -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)))))))
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(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))
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(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 (sqrt.f64 eps) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x))))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (neg.f64 (*.f64 (sqrt.f64 eps) x)) (*.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x)) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x))) (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 (sqrt.f64 eps) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 eps x))))) eps)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) 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 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 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #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))) (*.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 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) eps)) (neg.f64 eps))))

rewrite195.0ms (2.7%)

Memory
10.8MiB live, 275.7MiB allocated; 58ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
037231
061222
1223187
21872187
08842187
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
21 → 664
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x)))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
(-.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)
(neg.f64 eps)
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
Outputs
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)) (*.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (*.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 3/2 binary64)))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)) (/.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (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) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (/.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)))
(*.f64 (neg.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (sqrt.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(*.f64 (sqrt.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (sqrt.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 1 binary64))
(pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
(fabs.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(exp.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (sinh.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (neg.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64))
(pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(sqrt.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 2 binary64)))
(fabs.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 1 binary64)))
(exp.f64 (log.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
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(/.f64 (fabs.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (sqrt.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 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))
(fabs.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sinh.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))

eval162.0ms (2.2%)

Memory
4.4MiB live, 256.3MiB allocated; 126ms collecting garbage
Compiler

Compiled 30 390 to 3 217 computations (89.4% saved)

prune31.0ms (0.4%)

Memory
14.4MiB live, 60.9MiB allocated; 20ms collecting garbage
Pruning

10 alts after pruning (4 fresh and 6 done)

PrunedKeptTotal
New7882790
Fresh426
Picked235
Done235
Total79610806
Accuracy
100.0%
Counts
806 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.5%
(/.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (*.f64 x 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))
63.4%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓63.9%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓59.2%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓7.1%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
42.5%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
✓40.2%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
✓4.3%
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
Compiler

Compiled 843 to 254 computations (69.9% saved)

regimes30.0ms (0.4%)

Memory
-5.4MiB live, 40.5MiB allocated; 12ms collecting garbage
Counts
28 → 1
Calls
Call 1
Inputs
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (/.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) x)) (*.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 (sqrt.f64 (*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))))
(/.f64 (fma.f64 (neg.f64 x) x (-.f64 (*.f64 x x) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (*.f64 x #s(literal 1/2 binary64))) (*.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 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (*.f64 x 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 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
#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))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (*.f64 #s(literal 1/2 binary64) eps))) x))
(/.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (-.f64 (neg.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps)))) (*.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)))
Outputs
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
Calls

3 calls:

14.0ms
eps
7.0ms
x
7.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.5%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
99.5%1x
99.5%1eps
Compiler

Compiled 10 to 10 computations (0% saved)

regimes10.0ms (0.1%)

Memory
-29.3MiB live, 18.5MiB allocated; 1ms collecting garbage
Counts
9 → 2
Calls
Call 1
Inputs
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

3 calls:

3.0ms
eps
3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms
x
Results
AccuracySegmentsBranch
98.9%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
90.7%2x
84.8%2eps
Compiler

Compiled 10 to 10 computations (0% saved)

regimes3.0ms (0%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
96.7%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory
4.6MiB live, 4.6MiB allocated; 0ms collecting garbage
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Calls

1 calls:

2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
96.5%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory
10.9MiB live, 10.9MiB allocated; 0ms collecting garbage
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 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 x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
Calls

3 calls:

2.0ms
eps
2.0ms
x
1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
59.2%1eps
59.2%1x
60.8%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory
9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

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

3 calls:

1.0ms
eps
1.0ms
x
1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
4.3%1eps
4.3%1x
4.3%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.021100371707457e-150
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.021100371707457e-150
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.021100371707457e-150
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.021100371707457e-150
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

simplify49.0ms (0.7%)

Memory
-24.2MiB live, 31.0MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
042201
169183
2121183
3250171
4480167
5786167
62366163
77562163
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64)))
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))
Outputs
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) #s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7371020360979573/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64)))
#s(approx (+ (/ (* x x) (+ (sqrt (- (* x x) eps)) x)) (/ (* (neg (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps))) (+ (sqrt (- (* x x) eps)) x))) #s(literal 0 binary64))

derivations893.0ms (12.3%)

Memory
6.9MiB live, 385.4MiB allocated; 44ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08364510
128744136
087253901
034215
057215
1189185
21405185
08249185
02571069
18071054
231081019
08668960
037231
061222
1223187
21872187
08842187
0622
01022
14222
232022
3365222
0887022
Stop Event
1×fuel
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×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 303 to 40 computations (86.8% saved)

preprocess80.0ms (1.1%)

Memory
-5.0MiB live, 40.5MiB allocated; 5ms collecting garbage
Compiler

Compiled 642 to 106 computations (83.5% saved)

end0.0ms (0%)

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

Profiling

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