?

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}}

Error?

Try it out?

Your Program's Arguments

    Results

    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

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

      metadata-eval [=>]0

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

      metadata-eval [=>]0

      \[ \frac{-450}{{\left(\left(\color{blue}{121} + {20}^{2}\right) + 1\right)}^{\left(\frac{3}{2}\right)}} \]

      metadata-eval [=>]0

      \[ \frac{-450}{{\left(\left(121 + \color{blue}{400}\right) + 1\right)}^{\left(\frac{3}{2}\right)}} \]

      metadata-eval [=>]0

      \[ \frac{-450}{{\left(\color{blue}{521} + 1\right)}^{\left(\frac{3}{2}\right)}} \]

      metadata-eval [=>]0

      \[ \frac{-450}{{\color{blue}{522}}^{\left(\frac{3}{2}\right)}} \]

      metadata-eval [=>]0

      \[ \frac{-450}{{522}^{\color{blue}{1.5}}} \]

    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))))