ENA, Section 1.4, Exercise 4d

Time bar (total: 8.9s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze16.0ms (0.2%)

Memory
-16.7MiB live, 22.1MiB allocated
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 (17.8%)

Memory
68.6MiB live, 1 471.1MiB allocated
Samples
495.0ms4 901×0valid
434.0ms2 764×1valid
108.0ms591×2valid
92.0ms176×0invalid
Precisions
Click to see histograms. Total time spent on operations: 740.0ms
ival-sqrt: 209.0ms (28.2% of total)
ival-mult: 175.0ms (23.6% of total)
ival-sub: 150.0ms (20.3% of total)
adjust: 82.0ms (11.1% of total)
ival-<=: 80.0ms (10.8% of total)
ival-and: 23.0ms (3.1% of total)
exact: 18.0ms (2.4% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

explain208.0ms (2.3%)

Memory
-29.3MiB live, 106.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1120-0-(-.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)))cancellation1120
Confusion
Predicted +Predicted -
+1120
-0144
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+11200
-00144
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0144
1112
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
38.0ms292×0valid
18.0ms174×1valid
7.0ms46×2valid
Compiler

Compiled 84 to 28 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-sub: 7.0ms (29.2% of total)
ival-sqrt: 6.0ms (25% of total)
ival-mult: 5.0ms (20.9% of total)
adjust: 4.0ms (16.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess29.0ms (0.3%)

Memory
7.0MiB live, 43.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01846
14344
211841
327841
448841
555741
656841
068
0108
1148
2228
3348
4528
5948
61618
72068
82898
93198
103358
03358
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
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶59.4%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.1%)

Memory
8.0MiB live, 8.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff0
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0624
01024
11424
22224
33424
45224
59424
616124
720624
828924
931924
1033524
033524
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

localize29.0ms (0.3%)

Memory
-6.4MiB live, 31.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.0078125
(-.f64 (*.f64 x x) eps)
accuracy0.01171875
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy25.97181987112223
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Samples
10.0ms146×0valid
9.0ms87×1valid
3.0ms23×2valid
Compiler

Compiled 50 to 14 computations (72% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-sub: 4.0ms (34.1% of total)
ival-sqrt: 3.0ms (25.6% of total)
ival-mult: 3.0ms (25.6% of total)
adjust: 2.0ms (17.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated
Counts
4 → 49
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
Calls

6 calls:

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

simplify190.0ms (2.1%)

Memory
2.0MiB live, 123.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02571067
17841053
225921015
369531012
08103948
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 #s(literal -1 binary64))) (sqrt.f64 eps))
(- 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 (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 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (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)
(fma.f64 x x (neg.f64 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)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (*.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))
(/ (- (* 1/2 (/ (+ (* 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 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 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 #s(literal -1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 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 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 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 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (*.f64 #s(literal 1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #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) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 #s(literal 1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #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 (fma.f64 (*.f64 #s(literal 1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (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))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(*.f64 (neg.f64 x) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 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 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #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))
(fma.f64 x x (neg.f64 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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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 (pow.f64 x #s(literal 4 binary64)) (/.f64 (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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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 (pow.f64 x #s(literal 4 binary64)) (/.f64 (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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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 (pow.f64 x #s(literal 4 binary64)) (/.f64 (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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.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)) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) 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 (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 (*.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)))) (neg.f64 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 (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))))) (neg.f64 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 (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))))) (neg.f64 eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)

rewrite205.0ms (2.3%)

Memory
-4.6MiB live, 187.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0622
01022
14222
231022
3360222
0854922
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 224
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))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64)))) (-.f64 (-.f64 (fma.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)) (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)) (-.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (fma.f64 x x eps) (*.f64 x x)) (-.f64 (fma.f64 x x eps) (*.f64 x x))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (/.f64 (-.f64 (fma.f64 x x eps) (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (fma.f64 x x (-.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 -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
(*.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))
(*.f64 (neg.f64 (-.f64 (fma.f64 x x eps) (*.f64 x x))) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (/.f64 (-.f64 x (sqrt.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 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(*.f64 (-.f64 (fma.f64 x x eps) (*.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64)))
(*.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 (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))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))))
(*.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 -1 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(/.f64 (fma.f64 (neg.f64 eps) eps (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x eps) #s(literal 1 binary64)))
(/.f64 (fma.f64 (neg.f64 eps) eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (neg.f64 eps) (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))
(neg.f64 (neg.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (*.f64 (fma.f64 x x eps) eps) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 x x eps) eps)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 (fma.f64 x x eps) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (*.f64 (fma.f64 x x eps) eps) (-.f64 (*.f64 (fma.f64 x x eps) eps) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 eps) eps (pow.f64 x #s(literal 4 binary64)))) (-.f64 (*.f64 x x) eps) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (*.f64 x x) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x))
(fma.f64 (*.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (*.f64 x x) (/.f64 (*.f64 x x) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x x (neg.f64 eps))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (fma.f64 x x #s(literal 0 binary64)) eps)
(-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (*.f64 (neg.f64 (log.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (*.f64 x x) (neg.f64 eps))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.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)))

eval54.0ms (0.6%)

Memory
8.8MiB live, 93.5MiB allocated
Compiler

Compiled 7 015 to 1 083 computations (84.6% saved)

prune14.0ms (0.2%)

Memory
-1.1MiB live, 36.0MiB allocated
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New25613269
Fresh000
Picked101
Done000
Total25713270
Accuracy
100.0%
Counts
270 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶58.7%
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
59.1%
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
59.1%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶59.4%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
59.0%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
54.6%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶6.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
59.3%
(*.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)))))
31.0%
#s(approx (- x (sqrt (- (* x x) eps))) (/.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 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
35.6%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶42.6%
#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))
46.7%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
Compiler

Compiled 506 to 298 computations (41.1% saved)

simplify391.0ms (4.4%)

Memory
-31.3MiB live, 280.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 19 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
(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff0
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff0
(sqrt.f64 x)
cost-diff1600
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x 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 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
(neg.f64 eps)
cost-diff0
(fma.f64 x x (neg.f64 eps))
cost-diff0
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
cost-diff0
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033182
057178
186178
2160178
3342178
4761178
51137178
61831178
73780178
85902178
96337178
106366178
116380178
126380178
136716178
146794178
156794178
166844178
176850178
187844178
08316178
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
x
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
(-.f64 x #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)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(sqrt.f64 x)
x
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
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)))
#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 (fma.f64 x x (neg.f64 eps))))
x
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
(-.f64 x #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)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(sqrt.f64 x)
x
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(*.f64 x x)
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)))
#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)

localize123.0ms (1.4%)

Memory
-16.2MiB live, 218.3MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.10546875
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy7.353462419343242
(*.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)
accuracy7.577322208860415
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy35.50474769552434
#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))
accuracy0.0
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy0.0078125
(-.f64 (*.f64 x x) eps)
accuracy0.01171875
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy26.42413334530846
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy0.0
(/.f64 eps x)
accuracy0.00390625
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy25.97181987112223
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy33.76154094669933
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy0.0
(neg.f64 x)
accuracy25.97181987112223
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy62.432843249294045
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy0.0
(fma.f64 x x (neg.f64 eps))
accuracy0.0
(neg.f64 eps)
accuracy0.01171875
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
accuracy25.97181987112223
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
Samples
39.0ms87×1valid
37.0ms146×0valid
12.0ms23×2valid
Compiler

Compiled 340 to 63 computations (81.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 66.0ms
ival-add: 15.0ms (22.6% of total)
ival-mult: 13.0ms (19.6% of total)
ival-sqrt: 8.0ms (12.1% of total)
ival-div: 7.0ms (10.5% of total)
adjust: 7.0ms (10.5% of total)
ival-neg: 6.0ms (9% of total)
ival-sub: 5.0ms (7.5% of total)
ival-pow: 3.0ms (4.5% of total)
exact: 1.0ms (1.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory
13.1MiB live, 13.1MiB allocated
Counts
20 → 92
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
(-.f64 x #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)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(sqrt.f64 x)
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) 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 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)
(* -1 x)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(sqrt x)
(- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (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) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(* 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 (/ 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)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* x (- (* 1/2 (/ eps (pow x 2))) 1))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 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 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -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 eps) (pow x 2))
(- (* 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)))) x)
(+ (* 1/8 (/ eps (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))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* 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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* (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)))))
(* -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)))))
(* -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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
Calls

6 calls:

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

simplify520.0ms (5.9%)

Memory
-22.5MiB live, 192.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03571877
110621853
235401792
084151692
Stop Event
1×iter limit
1×node limit
Counts
92 → 91
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)
(* -1 x)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(sqrt x)
(- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (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) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(* 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 (/ 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)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* x (- (* 1/2 (/ eps (pow x 2))) 1))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 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 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -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 eps) (pow x 2))
(- (* 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)))) x)
(+ (* 1/8 (/ eps (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))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* 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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* (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)))))
(* -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)))))
(* -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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
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 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 #s(literal 1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #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 #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))))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(* -1 x)
(neg.f64 x)
(* -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)
(sqrt x)
(sqrt.f64 x)
(- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.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))))
(- (* (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)))
(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) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (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)))))) (*.f64 x x) (*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (*.f64 x x) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 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 (*.f64 eps (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 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)))
(* 1/2 (/ 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)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (*.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))
(/ (- (* 1/2 (/ (+ (* 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)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* x (- (* 1/2 (/ eps (pow x 2))) 1))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64) #s(literal -1 binary64)) x)
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.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 (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(*.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)
(/ (+ (* 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)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(*.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 #s(literal 1/2 binary64) x) (/.f64 eps x) #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) (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 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64)))))
(* -1 (* 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)
(* -1 (* 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)
(* -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)))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(*.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 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(*.f64 (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 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(*.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))) (neg.f64 x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(*.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)))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) 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 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #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))
(fma.f64 x x (neg.f64 eps))
(- (* 1/2 (/ eps x)) x)
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (neg.f64 x))
(- (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) x)
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps (neg.f64 x))
(- (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) x)
(-.f64 (*.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)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(* 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 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(*.f64 (-.f64 (/.f64 x eps) (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (- (* -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 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))
(*.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 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) eps)
(* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(*.f64 (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 (*.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 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* -1 (* eps (- (* -1 (/ 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)
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (+.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (+.f64 (/.f64 (-.f64 x (/.f64 (*.f64 (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) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (*.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)))) (neg.f64 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 (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))))) (neg.f64 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 (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))))) (neg.f64 eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 (/.f64 x eps) (/.f64 #s(literal 1/2 binary64) x)) eps)
(* -1 (* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (neg.f64 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 (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)))))) (neg.f64 eps))
(* -1 (* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (neg.f64 eps))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)

rewrite179.0ms (2%)

Memory
0.3MiB live, 226.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033160
057156
1216156
21535156
08290156
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 785
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
(-.f64 x #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)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(sqrt.f64 x)
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) 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 x x) eps)
Outputs
(*.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (pow.f64 (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (*.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (*.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x))) (neg.f64 (-.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (*.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps)))) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (+.f64 (sqrt.f64 (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 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))))
(/.f64 (-.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps)))) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (fma.f64 x x (neg.f64 eps)) (-.f64 (*.f64 x x) (*.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (*.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))))
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))))))
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(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(*.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(pow.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 (neg.f64 eps) (*.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 (fma.f64 x x eps) (*.f64 eps eps))) (*.f64 (fma.f64 x x eps) (fma.f64 x x eps)))
(/.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 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (neg.f64 eps) (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (neg.f64 (fma.f64 x x eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) (neg.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (fma.f64 x x eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) (neg.f64 eps)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(neg.f64 (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)) (neg.f64 eps))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x) (neg.f64 eps))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 eps))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 eps))
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x))
(fma.f64 x x (neg.f64 eps))
(sqrt.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 (neg.f64 eps) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (neg.f64 eps) (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) (neg.f64 eps))))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) (neg.f64 eps))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (fma.f64 x x #s(literal 0 binary64)) eps)
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x x)))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (fma.f64 x x (neg.f64 eps)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (fma.f64 x x (neg.f64 eps))))
(+.f64 (*.f64 x x) (neg.f64 eps))
(+.f64 (neg.f64 eps) (*.f64 x x))

eval141.0ms (1.6%)

Memory
45.3MiB live, 235.9MiB allocated
Compiler

Compiled 20 667 to 3 017 computations (85.4% saved)

prune30.0ms (0.3%)

Memory
-14.2MiB live, 72.5MiB allocated
Pruning

18 alts after pruning (15 fresh and 3 done)

PrunedKeptTotal
New7269735
Fresh268
Picked235
Done000
Total73018748
Accuracy
100.0%
Counts
748 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶59.1%
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
59.1%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓59.4%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
▶59.0%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
▶54.6%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓6.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
5.4%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
31.0%
#s(approx (- x (sqrt (- (* x x) eps))) (/.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 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
41.7%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))) eps) (-.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) (/.f64 #s(literal 1/2 binary64) x))))
▶42.6%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
43.9%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) (sqrt.f64 x) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (pow.f64 x #s(literal 5/2 binary64))) eps))
43.2%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) (neg.f64 (neg.f64 x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (neg.f64 (neg.f64 x)))) eps))
44.1%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (*.f64 (sqrt.f64 x) (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x)))) (pow.f64 x #s(literal 3/2 binary64))) eps))
44.3%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
46.7%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
44.4%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
▶28.8%
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))))
Compiler

Compiled 816 to 520 computations (36.3% saved)

simplify145.0ms (1.6%)

Memory
-14.9MiB live, 154.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))
cost-diff0
(/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))
cost-diff0
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64))))
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))))
cost-diff0
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
cost-diff0
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff0
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff5760
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) 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-diff896
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
cost-diff0
(neg.f64 eps)
cost-diff0
#s(approx (- (* x x) eps) (neg.f64 eps))
cost-diff0
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff0
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) eps)
cost-diff256
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
cost-diff896
(-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
046340
076334
1129334
2242334
3468311
4949302
52775302
66163302
08368302
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
eps
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(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 (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 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))
eps
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))
#s(literal 1/2 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 1/8 binary64) eps)
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
Outputs
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))
(neg.f64 eps)
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
eps
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(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 (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 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (/.f64 eps x)))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (/.f64 eps x))
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))))
(/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) eps)
eps
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))
#s(literal 1/2 binary64)
(*.f64 x x)
x
(*.f64 #s(literal 1/8 binary64) eps)
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)

localize129.0ms (1.4%)

Memory
15.8MiB live, 245.1MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.014003759768442016
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))
accuracy0.0546875
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))
accuracy26.13817472519261
(/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))
accuracy35.50474769552434
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))))
accuracy0.21484375
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy7.353462419343242
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy7.577322208860415
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy35.50474769552434
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy0.01171875
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))
accuracy0.1171875
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
accuracy0.6049916235644613
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
accuracy25.97181987112223
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
accuracy0.0
(neg.f64 eps)
accuracy0.01171875
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy25.97181987112223
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy28.180461155720444
#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy0.01171875
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.03515625
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
accuracy0.25390625
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
accuracy25.77833412237445
(-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))
Samples
44.0ms89×1valid
42.0ms146×0valid
13.0ms21×2valid
Compiler

Compiled 594 to 86 computations (85.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 69.0ms
ival-mult: 23.0ms (33.2% of total)
ival-div: 15.0ms (21.7% of total)
adjust: 8.0ms (11.6% of total)
ival-sub: 7.0ms (10.1% of total)
ival-add: 6.0ms (8.7% of total)
ival-sqrt: 3.0ms (4.3% of total)
ival-pow: 3.0ms (4.3% of total)
ival-neg: 3.0ms (4.3% of total)
exact: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series32.0ms (0.4%)

Memory
-29.6MiB live, 91.2MiB allocated
Counts
24 → 113
Calls
Call 1
Inputs
(-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(-.f64 (*.f64 x x) eps)
(*.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 (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))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))
Outputs
(* -1 eps)
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (pow x 2) eps)
(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))
(* 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 2))
(* 1/8 (pow eps 2))
(+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2))))
(- (* -1 x) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) 1)) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) 1)) (* (sqrt eps) (sqrt -1)))
-1
(- (/ (pow x 2) eps) 1)
(* 1/8 eps)
(+ (* 1/8 eps) (* 1/2 (pow x 2)))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(* -2 x)
(* x (- (* 1/2 (/ eps (pow x 2))) 2))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/8 (/ 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))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/8 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (+ (* 1/2 (/ eps (pow x 2))) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) 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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1/2 (/ eps x))
(* -1 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x))
(* -1 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x))
(* -1 (/ (- (* 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))
(* 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)))
(* eps (+ (* 1/8 eps) (* 1/2 (pow x 2))))
(- (* 1/2 (/ eps 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)))) (* 2 x))
(/ (+ (* -1 eps) (pow x 2)) 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)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* (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 eps 2) (+ 1/8 (* 1/2 (/ (pow x 2) eps))))
(* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (+ 1/8 (* 1/2 (/ (pow x 2) eps))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* -1 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1/2 (/ (pow x 2) eps)) 1/8)))
Calls

6 calls:

TimeVariablePointExpression
10.0ms
x
@0
((- (- (* x x) eps) (* x x)) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (- x (sqrt (- (* x x) eps))) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ 1/8 (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (pow x 3)) (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (- (neg (sqrt (- (* x x) eps))) x) (sqrt (- (* x x) eps)) (+ (* x (/ x eps)) -1) (+ (* 1/2 (* x x)) (* 1/8 eps)))
4.0ms
eps
@inf
((- (- (* x x) eps) (* x x)) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (- x (sqrt (- (* x x) eps))) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ 1/8 (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (pow x 3)) (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (- (neg (sqrt (- (* x x) eps))) x) (sqrt (- (* x x) eps)) (+ (* x (/ x eps)) -1) (+ (* 1/2 (* x x)) (* 1/8 eps)))
4.0ms
eps
@-inf
((- (- (* x x) eps) (* x x)) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (- x (sqrt (- (* x x) eps))) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ 1/8 (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (pow x 3)) (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (- (neg (sqrt (- (* x x) eps))) x) (sqrt (- (* x x) eps)) (+ (* x (/ x eps)) -1) (+ (* 1/2 (* x x)) (* 1/8 eps)))
3.0ms
eps
@0
((- (- (* x x) eps) (* x x)) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (- x (sqrt (- (* x x) eps))) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ 1/8 (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (pow x 3)) (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (- (neg (sqrt (- (* x x) eps))) x) (sqrt (- (* x x) eps)) (+ (* x (/ x eps)) -1) (+ (* 1/2 (* x x)) (* 1/8 eps)))
3.0ms
x
@-inf
((- (- (* x x) eps) (* x x)) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (* (+ (* x (/ x eps)) -1) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (- x (sqrt (- (* x x) eps))) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ 1/8 (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (pow x 3)) (* eps (+ (* 1/2 (* x x)) (* 1/8 eps))) (- (neg (sqrt (- (* x x) eps))) x) (sqrt (- (* x x) eps)) (+ (* x (/ x eps)) -1) (+ (* 1/2 (* x x)) (* 1/8 eps)))

simplify179.0ms (2%)

Memory
10.0MiB live, 162.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04562343
114252221
248552180
083652050
Stop Event
1×iter limit
1×node limit
Counts
113 → 112
Calls
Call 1
Inputs
(* -1 eps)
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (pow x 2) eps)
(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))
(* 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 2))
(* 1/8 (pow eps 2))
(+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2))))
(- (* -1 x) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) 1)) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) 1)) (* (sqrt eps) (sqrt -1)))
-1
(- (/ (pow x 2) eps) 1)
(* 1/8 eps)
(+ (* 1/8 eps) (* 1/2 (pow x 2)))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(* -2 x)
(* x (- (* 1/2 (/ eps (pow x 2))) 2))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/8 (/ 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))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/8 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (+ (* 1/2 (/ eps (pow x 2))) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) 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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1/2 (/ eps x))
(* -1 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x))
(* -1 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x))
(* -1 (/ (- (* 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))
(* 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)))
(* eps (+ (* 1/8 eps) (* 1/2 (pow x 2))))
(- (* 1/2 (/ eps 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)))) (* 2 x))
(/ (+ (* -1 eps) (pow x 2)) 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)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* (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 eps 2) (+ 1/8 (* 1/2 (/ (pow x 2) eps))))
(* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (+ 1/8 (* 1/2 (/ (pow x 2) eps))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* -1 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1/2 (/ (pow x 2) eps)) 1/8)))
Outputs
(* -1 eps)
(neg.f64 eps)
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(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)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(* eps (+ (* 1/8 eps) (* 1/2 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) eps)) eps)
(- (* 1/2 (/ eps x)) (* 2 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x))
(- (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (* 2 x))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps (*.f64 #s(literal -2 binary64) x))
(- (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (* 2 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 (*.f64 #s(literal -2 binary64) x))
(/ (+ (* -1 eps) (pow x 2)) eps)
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) x)
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) x)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) #s(literal -1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 eps))) (pow.f64 eps #s(literal 3 binary64))))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+.f64 x (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/8 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* (pow eps 2) (+ 1/8 (* 1/2 (/ (pow x 2) eps))))
(*.f64 (*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) #s(literal 1/8 binary64)) eps) eps)
(* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (neg.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 (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))) eps)
(* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps))))) eps)
(* eps (+ 1/8 (* 1/2 (/ (pow x 2) eps))))
(*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) #s(literal 1/8 binary64)) 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)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) eps) x))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (-.f64 (/.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) eps (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))))) (neg.f64 eps)) eps) x)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.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 (+.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps)) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 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 (fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 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 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64)) (fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 eps))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* -1 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (+.f64 x (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 eps))))
(* -1 (* eps (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (+.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) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps) x) eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1/2 (/ (pow x 2) eps)) 1/8)))
(*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) #s(literal -1/8 binary64)) (neg.f64 eps))

rewrite274.0ms (3.1%)

Memory
19.9MiB live, 185.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046292
076284
1295273
22211273
08631272
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
24 → 701
Calls
Call 1
Inputs
(-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(-.f64 (*.f64 x x) eps)
(*.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 (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))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 binary64)))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)))
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))
Outputs
(*.f64 (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64)))
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(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 #s(literal -1/8 binary64) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/512 binary64) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 #s(literal 1/8 binary64) eps) (-.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 #s(literal -1/8 binary64) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 #s(literal -1/8 binary64) eps)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 #s(literal 1/8 binary64) eps) (-.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))) (fma.f64 #s(literal 1/512 binary64) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))))
(/.f64 (fma.f64 #s(literal 1/512 binary64) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/64 binary64) (*.f64 eps eps) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) eps))))
(/.f64 (fma.f64 #s(literal 1/512 binary64) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 #s(literal 1/8 binary64) eps) (-.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 #s(literal 1/8 binary64) eps))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))
(fma.f64 #s(literal 1/8 binary64) eps (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 eps #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) eps))
(fma.f64 x (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/8 binary64) eps))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 #s(literal -1/8 binary64) eps))) (/.f64 (pow.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x (*.f64 #s(literal -1/8 binary64) eps))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) eps))
(+.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))

eval212.0ms (2.4%)

Memory
-21.0MiB live, 221.3MiB allocated
Compiler

Compiled 29 331 to 3 842 computations (86.9% saved)

prune34.0ms (0.4%)

Memory
11.3MiB live, 49.8MiB allocated
Pruning

12 alts after pruning (7 fresh and 5 done)

PrunedKeptTotal
New8895894
Fresh8210
Picked325
Done033
Total90012912
Accuracy
100.0%
Counts
912 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
59.1%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶99.6%
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
▶59.1%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓59.4%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓59.0%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
✓54.6%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓6.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶5.4%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
▶46.7%
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
▶44.4%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
29.2%
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) eps) (*.f64 x x)) x)))
Compiler

Compiled 412 to 249 computations (39.6% saved)

simplify176.0ms (2%)

Memory
7.5MiB live, 128.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 19 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
045327
068327
1115321
2196321
3365298
4778298
52568298
67159298
08492292
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
#s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
x
#s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
x
(/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 (/.f64 eps x) x)
(/.f64 eps x)
eps
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
Outputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
#s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(-.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(*.f64 x x)
x
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
x
#s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 x (/.f64 (fma.f64 x x (neg.f64 eps)) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
x
(/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (fma.f64 x x (neg.f64 eps)) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(fma.f64 x x (neg.f64 eps))
(*.f64 x x)
eps
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 (/.f64 eps x) x)
(/.f64 eps x)
eps
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)

localize198.0ms (2.2%)

Memory
-16.1MiB live, 155.0MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.05859375
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
accuracy0.21484375
(/.f64 (/.f64 eps x) x)
accuracy7.353462419343242
(*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
accuracy35.50474769552434
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
accuracy0.0078125
(-.f64 (*.f64 x x) eps)
accuracy0.01171875
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.3203125
(/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy25.97181987112223
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy0.0
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
accuracy25.97181987112223
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
accuracy28.295506701937665
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
accuracy33.76154094669933
#s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))))
accuracy0.0
(/.f64 #s(literal 1/2 binary64) x)
accuracy0.21875
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy34.002226493466324
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy0.0078125
(-.f64 (*.f64 x x) eps)
accuracy0.01171875
(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy0.03515625
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
accuracy0.25390625
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
Samples
94.0ms87×1valid
64.0ms146×0valid
16.0ms23×2valid
Compiler

Compiled 563 to 80 computations (85.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 96.0ms
adjust: 31.0ms (32.3% of total)
ival-add: 23.0ms (24% of total)
ival-div: 15.0ms (15.6% of total)
ival-mult: 11.0ms (11.5% of total)
ival-sub: 9.0ms (9.4% of total)
ival-sqrt: 3.0ms (3.1% of total)
ival-neg: 3.0ms (3.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series21.0ms (0.2%)

Memory
0.7MiB live, 38.8MiB allocated
Counts
21 → 100
Calls
Call 1
Inputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
#s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))
(neg.f64 eps)
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
#s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (/.f64 eps x) x)
Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* -1 eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- (* -1 x) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) 1)) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) 1)) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ 1/2 x)
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (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)))))))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(- (pow x 2) 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))
(/ 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 (/ (+ (* -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 (- (* 1/2 (/ eps (pow x 2))) 2))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(/ (- (* 1/8 (/ (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)))))
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/8 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (+ (* 1/2 (/ eps (pow x 2))) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) 2)))
(* -1 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x))
(* -1 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x))
(* -1 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* -1 (* 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))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(- (* 1/2 (/ eps x)) (* 2 x))
(- (* 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)))) (* 2 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 (/ (+ (* -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 (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ (pow x 2) eps) 1))
(* (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)))))
(+ 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 (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
eps
@0
((/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (- (* x x) eps) (* x x)) (neg eps) (- (neg (sqrt (- (* x x) eps))) x) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (* (/ eps x) -1/2) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (sqrt (- (* x x) eps)) (/ (/ eps x) x))
3.0ms
eps
@inf
((/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (- (* x x) eps) (* x x)) (neg eps) (- (neg (sqrt (- (* x x) eps))) x) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (* (/ eps x) -1/2) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (sqrt (- (* x x) eps)) (/ (/ eps x) x))
3.0ms
eps
@-inf
((/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (- (* x x) eps) (* x x)) (neg eps) (- (neg (sqrt (- (* x x) eps))) x) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (* (/ eps x) -1/2) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (sqrt (- (* x x) eps)) (/ (/ eps x) x))
3.0ms
x
@0
((/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (- (* x x) eps) (* x x)) (neg eps) (- (neg (sqrt (- (* x x) eps))) x) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (* (/ eps x) -1/2) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (sqrt (- (* x x) eps)) (/ (/ eps x) x))
2.0ms
x
@-inf
((/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (- (- (* x x) eps) (* x x)) (neg eps) (- (neg (sqrt (- (* x x) eps))) x) (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (* (/ eps x) -1/2) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (sqrt (- (* x x) eps)) (/ (/ eps x) x))

simplify154.0ms (1.7%)

Memory
19.5MiB live, 212.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04502223
113912107
247822066
082261942
Stop Event
1×iter limit
1×node limit
Counts
100 → 99
Calls
Call 1
Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* -1 eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- (* -1 x) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) 1)) (* (sqrt eps) (sqrt -1)))
(- (* x (- (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) 1)) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ 1/2 x)
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (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)))))))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(- (pow x 2) 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))
(/ 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 (/ (+ (* -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 (- (* 1/2 (/ eps (pow x 2))) 2))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(/ (- (* 1/8 (/ (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)))))
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/8 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (+ (* 1/2 (/ eps (pow x 2))) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) 2)))
(* -1 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x))
(* -1 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x))
(* -1 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* -1 (* 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))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(- (* 1/2 (/ eps x)) (* 2 x))
(- (* 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)))) (* 2 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 (/ (+ (* -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 (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ (pow x 2) eps) 1))
(* (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)))))
(+ 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 (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* -1 eps)
(neg.f64 eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- (* -1 x) (* (sqrt eps) (sqrt -1)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x))
(- (* x (- (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) 1)) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (*.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))
(- (* x (- (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) 1)) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) x #s(literal -1 binary64)) x))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(- 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 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))) (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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (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 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x)) (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) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (*.f64 x x) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1/2 (/ eps x))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 x x)) x)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(pow x 2)
(*.f64 x x)
(* 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 (*.f64 x x) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(/ eps (pow x 2))
(/.f64 (/.f64 eps x) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) 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 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (neg.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 eps (/.f64 (/.f64 eps x) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))))) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* x (- (* 1/2 (/ eps (pow x 2))) 2))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64)) x)
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64))) x)
(* 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 (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 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64)))) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) 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))
(/ (- (* 1/2 (/ (+ (* 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 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (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 eps (/.f64 (/.f64 eps x) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(*.f64 (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
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(*.f64 (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 eps) #s(literal -1/2 binary64)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps)) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 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 (fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 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 (fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64)) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)

rewrite498.0ms (5.6%)

Memory
-0.3MiB live, 161.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045278
068272
1268255
22172247
09266239
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
21 → 631
Calls
Call 1
Inputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
#s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))
(neg.f64 eps)
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
#s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
#s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (/.f64 eps x) x)
Outputs
(*.f64 (/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (*.f64 x x) (fma.f64 x x eps))) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(*.f64 (/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))))
(*.f64 (pow.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))
(*.f64 (neg.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))) (/.f64 #s(literal -1 binary64) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))
(*.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (pow.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(literal 1 binary64))) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))))) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 (*.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))
(/.f64 (neg.f64 (neg.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)))) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))))
(/.f64 (neg.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))
(neg.f64 (/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)))) #s(literal -1 binary64)))
#s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 eps #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (+.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 eps eps (*.f64 #s(literal 0 binary64) eps)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (+.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 eps eps (*.f64 #s(literal 0 binary64) eps))))
(neg.f64 eps)
(-.f64 #s(literal 0 binary64) eps)
(+.f64 #s(literal 0 binary64) (neg.f64 eps))
(*.f64 (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))) #s(literal -1 binary64)))
(*.f64 (-.f64 (*.f64 x x) (fma.f64 x x eps)) (/.f64 #s(literal -1 binary64) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))
(pow.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (-.f64 (*.f64 x x) (fma.f64 x x eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))) (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))))))
(/.f64 (-.f64 (*.f64 (fma.f64 x x (neg.f64 eps)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) (*.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (*.f64 x x))) (fma.f64 x x (fma.f64 x x (neg.f64 eps))))
(/.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps)))) (*.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))) (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 x x (neg.f64 eps)) (-.f64 (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x eps)))) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (-.f64 (*.f64 x x) (fma.f64 x x eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))) (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (-.f64 (*.f64 x x) (fma.f64 x x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))) (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (fma.f64 x x (neg.f64 eps)) (-.f64 (*.f64 x x) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x eps))) (neg.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x eps))) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x eps)) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x)))
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x eps)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(neg.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x))
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (neg.f64 x))
(fma.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) (neg.f64 x))
(fma.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 x))
(fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x))
(fma.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 1/4 binary64)) (neg.f64 x))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64))) (neg.f64 x))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (pow.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (neg.f64 x))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 x))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(fma.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)) (fma.f64 x x (neg.f64 eps)) (neg.f64 x))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) #s(literal -1 binary64) (neg.f64 x))
(fma.f64 (fma.f64 x x (neg.f64 eps)) (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64))) (neg.f64 x))
(fma.f64 (fma.f64 x x (neg.f64 eps)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)) (neg.f64 x))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps)))))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 x)))
(-.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(-.f64 (/.f64 (fma.f64 x x (neg.f64 eps)) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)
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(/.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -3/2 binary64))) (pow.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 x x eps) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps))) (fma.f64 x x (neg.f64 eps)))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (sqrt.f64 (fma.f64 x x eps))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)) (*.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 x x)) #s(literal 1 binary64))) (*.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 x x)) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 x x)) (neg.f64 eps))) (*.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 x x)) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 x x)) eps)) (*.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (*.f64 x x)) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) x) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 eps))) (fma.f64 x x (neg.f64 eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)) (fma.f64 x x (neg.f64 eps)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 eps))) (fma.f64 x x (neg.f64 eps)))
(/.f64 (-.f64 (*.f64 (neg.f64 x) x) (neg.f64 eps)) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.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 (/.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64))) (fma.f64 x x eps))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64)) (pow.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -3/2 binary64))) (pow.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (neg.f64 (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (fma.f64 x x eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 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)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x eps) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) eps)) (fma.f64 x x (neg.f64 eps)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (-.f64 (*.f64 x x) (neg.f64 eps))))
(/.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 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (neg.f64 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)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (fma.f64 x x eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 x x (neg.f64 eps)) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(fma.f64 (*.f64 x x) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64)) (neg.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(fma.f64 x (/.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (neg.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(-.f64 (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(fabs.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(+.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(+.f64 (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (neg.f64 (/.f64 eps (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))
(*.f64 (pow.f64 (/.f64 x (neg.f64 eps)) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 eps x))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x))
(*.f64 (/.f64 (neg.f64 eps) x) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 eps x) (pow.f64 x #s(literal -1 binary64)))
(*.f64 eps (pow.f64 x #s(literal -2 binary64)))
(pow.f64 (/.f64 (/.f64 x (/.f64 eps x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 eps x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (/.f64 eps x) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (*.f64 (neg.f64 eps) #s(literal 1 binary64))) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 (neg.f64 (*.f64 eps #s(literal 1 binary64))) (*.f64 (neg.f64 x) x))
(/.f64 (*.f64 (/.f64 eps x) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 x eps)))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 (*.f64 (neg.f64 eps) #s(literal 1 binary64)) (*.f64 (neg.f64 x) x))
(/.f64 (*.f64 eps #s(literal 1 binary64)) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (/.f64 eps x)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 eps x))))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 x eps))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (/.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (/.f64 eps x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))
(/.f64 (/.f64 (neg.f64 eps) x) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x))
(/.f64 (/.f64 eps x) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 eps x) x)
(/.f64 (neg.f64 eps) (*.f64 (neg.f64 x) x))
(/.f64 eps (*.f64 x x))
(neg.f64 (/.f64 (/.f64 (neg.f64 eps) x) x))
(exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 eps x))) #s(literal -1 binary64)))

eval1.8s (20.1%)

Memory
3.0MiB live, 163.2MiB allocated
Compiler

Compiled 25 117 to 2 888 computations (88.5% saved)

prune180.0ms (2%)

Memory
-26.0MiB live, 59.0MiB allocated
Pruning

12 alts after pruning (5 fresh and 7 done)

PrunedKeptTotal
New8324836
Fresh112
Picked325
Done055
Total83612848
Accuracy
100.0%
Counts
848 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x))
47.2%
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(approx (- (neg (sqrt (- (* x x) eps))) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x))))
✓59.1%
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓59.4%
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓59.0%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
✓54.6%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓6.7%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓3.5%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓5.4%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
46.9%
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
44.3%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
29.2%
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) eps) (*.f64 x x)) x)))
Compiler

Compiled 1 038 to 345 computations (66.8% saved)

regimes28.0ms (0.3%)

Memory
20.9MiB live, 20.9MiB allocated
Counts
32 → 1
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(approx (- (neg (sqrt (- (* x x) eps))) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) eps) (*.f64 x x)) x)))
(/.f64 (-.f64 (*.f64 x x) (-.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 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps 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 (*.f64 #s(literal 1/8 binary64) eps) x) (neg.f64 (neg.f64 x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 (*.f64 x x) (neg.f64 (neg.f64 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)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps))) (pow.f64 x #s(literal 3 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))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) (sqrt.f64 x) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (pow.f64 x #s(literal 5/2 binary64))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (*.f64 (sqrt.f64 x) (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x)))) (pow.f64 x #s(literal 3/2 binary64))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))) eps) (-.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.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 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
Outputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x))
Calls

3 calls:

9.0ms
eps
9.0ms
x
9.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
99.6%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes47.0ms (0.5%)

Memory
-26.8MiB live, 11.4MiB allocated
Counts
12 → 1
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(approx (- (neg (sqrt (- (* x x) eps))) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
Outputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
Calls

3 calls:

38.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
4.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
99.6%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes12.0ms (0.1%)

Memory
10.4MiB live, 10.4MiB allocated
Counts
11 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(approx (- (neg (sqrt (- (* x x) eps))) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x))))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(approx (- (neg (sqrt (- (* x x) eps))) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x))))
Calls

3 calls:

4.0ms
eps
4.0ms
x
4.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
91.7%2x
83.9%2eps
99.5%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0%)

Memory
3.9MiB live, 3.9MiB allocated
Counts
10 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 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) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps))))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.4%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes4.0ms (0%)

Memory
3.6MiB live, 3.6MiB allocated
Counts
9 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
Outputs
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.4%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory
3.3MiB live, 3.3MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.3%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory
3.1MiB live, 3.1MiB allocated
Counts
7 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) #s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
(-.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 x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
97.0%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory
2.5MiB live, 2.5MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (sqrt (- (* x x) eps))) x)) (*.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
96.9%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 6 computations (25% saved)

regimes52.0ms (0.6%)

Memory
-29.9MiB live, 8.0MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
Calls

3 calls:

49.0ms
x
1.0ms
eps
1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
54.6%1eps
54.6%1x
54.6%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0%)

Memory
7.8MiB live, 7.8MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

3 calls:

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

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-2.5648315412148016e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-2.5648315412148016e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-2.5648315412148016e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-2.5648315412148016e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-2.5648315412148016e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-2.5648315412148016e-154
0.0
Compiler

Compiled 11 to 11 computations (0% saved)

simplify29.0ms (0.3%)

Memory
3.8MiB live, 42.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058349
182349
2108349
3132349
4146349
5154349
6158349
7159349
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))) (/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(approx (- (neg (sqrt (- (* x x) eps))) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x)))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 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) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
Outputs
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)))) (/.f64 #s(approx (- (- (* x x) eps) (* x x)) (neg.f64 eps)) #s(approx (- (neg (sqrt (- (* x x) eps))) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 #s(literal -2 binary64) x)))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 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) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (/ (- (- (* x x) eps) (* x x)) (- (neg (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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

soundness865.0ms (9.7%)

Memory
10.1MiB live, 762.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045278
068272
1268255
22172247
09266239
04502223
113912107
247822066
082261942
0622
01022
14222
231022
3360222
0854922
04562343
114252221
248552180
083652050
02571067
17841053
225921015
369531012
08103948
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 821 to 306 computations (62.7% saved)

preprocess57.0ms (0.6%)

Memory
21.8MiB live, 99.0MiB allocated
Compiler

Compiled 734 to 138 computations (81.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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