# ?

Average Error: 0 → 0
Time: 3.6s
Precision: binary64
Cost: 6656

# ?

$\frac{-450}{{\left(\left({11}^{2} + {20}^{2}\right) + 1\right)}^{\left(\frac{3}{2}\right)}}$
$\frac{-450}{{522}^{1.5}}$
(FPCore ()
:precision binary64
(/ (- 450.0) (pow (+ (+ (pow 11.0 2.0) (pow 20.0 2.0)) 1.0) (/ 3.0 2.0))))
(FPCore () :precision binary64 (/ -450.0 (pow 522.0 1.5)))
double code() {
return -450.0 / pow(((pow(11.0, 2.0) + pow(20.0, 2.0)) + 1.0), (3.0 / 2.0));
}

double code() {
return -450.0 / pow(522.0, 1.5);
}

real(8) function code()
code = -450.0d0 / ((((11.0d0 ** 2.0d0) + (20.0d0 ** 2.0d0)) + 1.0d0) ** (3.0d0 / 2.0d0))
end function

real(8) function code()
code = (-450.0d0) / (522.0d0 ** 1.5d0)
end function

public static double code() {
return -450.0 / Math.pow(((Math.pow(11.0, 2.0) + Math.pow(20.0, 2.0)) + 1.0), (3.0 / 2.0));
}

public static double code() {
return -450.0 / Math.pow(522.0, 1.5);
}

def code():
return -450.0 / math.pow(((math.pow(11.0, 2.0) + math.pow(20.0, 2.0)) + 1.0), (3.0 / 2.0))

def code():
return -450.0 / math.pow(522.0, 1.5)

function code()
return Float64(Float64(-450.0) / (Float64(Float64((11.0 ^ 2.0) + (20.0 ^ 2.0)) + 1.0) ^ Float64(3.0 / 2.0)))
end

function code()
return Float64(-450.0 / (522.0 ^ 1.5))
end

function tmp = code()
tmp = -450.0 / ((((11.0 ^ 2.0) + (20.0 ^ 2.0)) + 1.0) ^ (3.0 / 2.0));
end

function tmp = code()
tmp = -450.0 / (522.0 ^ 1.5);
end

code[] := N[((-450.0) / N[Power[N[(N[(N[Power[11.0, 2.0], $MachinePrecision] + N[Power[20.0, 2.0],$MachinePrecision]), $MachinePrecision] + 1.0),$MachinePrecision], N[(3.0 / 2.0), $MachinePrecision]],$MachinePrecision]), $MachinePrecision]  code[] := N[(-450.0 / N[Power[522.0, 1.5],$MachinePrecision]), \$MachinePrecision]

\frac{-450}{{\left(\left({11}^{2} + {20}^{2}\right) + 1\right)}^{\left(\frac{3}{2}\right)}}

\frac{-450}{{522}^{1.5}}


# Try it out?

Results

 In Out
Enter valid numbers for all inputs

# Derivation?

1. Initial program 0

$\frac{-450}{{\left(\left({11}^{2} + {20}^{2}\right) + 1\right)}^{\left(\frac{3}{2}\right)}}$
2. Simplified0

$\leadsto \color{blue}{\frac{-450}{{522}^{1.5}}}$
Proof
[Start]0 $\frac{-450}{{\left(\left({11}^{2} + {20}^{2}\right) + 1\right)}^{\left(\frac{3}{2}\right)}}$ $\frac{\color{blue}{-450}}{{\left(\left({11}^{2} + {20}^{2}\right) + 1\right)}^{\left(\frac{3}{2}\right)}}$ $\frac{-450}{{\left(\left(\color{blue}{121} + {20}^{2}\right) + 1\right)}^{\left(\frac{3}{2}\right)}}$ $\frac{-450}{{\left(\left(121 + \color{blue}{400}\right) + 1\right)}^{\left(\frac{3}{2}\right)}}$ $\frac{-450}{{\left(\color{blue}{521} + 1\right)}^{\left(\frac{3}{2}\right)}}$ $\frac{-450}{{\color{blue}{522}}^{\left(\frac{3}{2}\right)}}$ $\frac{-450}{{522}^{\color{blue}{1.5}}}$
3. Final simplification0

$\leadsto \frac{-450}{{522}^{1.5}}$

# Reproduce?

herbie shell --seed 1
(FPCore ()
:name "-450/(11^2+20^2+1)^(3/2)"
:precision binary64
(/ (- 450.0) (pow (+ (+ (pow 11.0 2.0) (pow 20.0 2.0)) 1.0) (/ 3.0 2.0))))