# ?

Average Error: 0 → 0
Time: 3.4s
Precision: binary64
Cost: 13504

# ?

$\frac{-420}{{\left({21}^{2} + 1\right)}^{\left(\frac{3}{2}\right)}} \cdot 21 - \left(11 \cdot 450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}$
$21 \cdot \frac{-420}{{442}^{1.5}} + {522}^{-0.5} \cdot -4950$
(FPCore ()
:precision binary64
(-
(* (/ (- 420.0) (pow (+ (pow 21.0 2.0) 1.0) (/ 3.0 2.0))) 21.0)
(* (* 11.0 450.0) (pow 522.0 (/ (- 1.0) 2.0)))))
(FPCore ()
:precision binary64
(+ (* 21.0 (/ -420.0 (pow 442.0 1.5))) (* (pow 522.0 -0.5) -4950.0)))
double code() {
return ((-420.0 / pow((pow(21.0, 2.0) + 1.0), (3.0 / 2.0))) * 21.0) - ((11.0 * 450.0) * pow(522.0, (-1.0 / 2.0)));
}

double code() {
return (21.0 * (-420.0 / pow(442.0, 1.5))) + (pow(522.0, -0.5) * -4950.0);
}

real(8) function code()
code = ((-420.0d0 / (((21.0d0 ** 2.0d0) + 1.0d0) ** (3.0d0 / 2.0d0))) * 21.0d0) - ((11.0d0 * 450.0d0) * (522.0d0 ** (-1.0d0 / 2.0d0)))
end function

real(8) function code()
code = (21.0d0 * ((-420.0d0) / (442.0d0 ** 1.5d0))) + ((522.0d0 ** (-0.5d0)) * (-4950.0d0))
end function

public static double code() {
return ((-420.0 / Math.pow((Math.pow(21.0, 2.0) + 1.0), (3.0 / 2.0))) * 21.0) - ((11.0 * 450.0) * Math.pow(522.0, (-1.0 / 2.0)));
}

public static double code() {
return (21.0 * (-420.0 / Math.pow(442.0, 1.5))) + (Math.pow(522.0, -0.5) * -4950.0);
}

def code():
return ((-420.0 / math.pow((math.pow(21.0, 2.0) + 1.0), (3.0 / 2.0))) * 21.0) - ((11.0 * 450.0) * math.pow(522.0, (-1.0 / 2.0)))

def code():
return (21.0 * (-420.0 / math.pow(442.0, 1.5))) + (math.pow(522.0, -0.5) * -4950.0)

function code()
return Float64(Float64(Float64(Float64(-420.0) / (Float64((21.0 ^ 2.0) + 1.0) ^ Float64(3.0 / 2.0))) * 21.0) - Float64(Float64(11.0 * 450.0) * (522.0 ^ Float64(Float64(-1.0) / 2.0))))
end

function code()
return Float64(Float64(21.0 * Float64(-420.0 / (442.0 ^ 1.5))) + Float64((522.0 ^ -0.5) * -4950.0))
end

function tmp = code()
tmp = ((-420.0 / (((21.0 ^ 2.0) + 1.0) ^ (3.0 / 2.0))) * 21.0) - ((11.0 * 450.0) * (522.0 ^ (-1.0 / 2.0)));
end

function tmp = code()
tmp = (21.0 * (-420.0 / (442.0 ^ 1.5))) + ((522.0 ^ -0.5) * -4950.0);
end

code[] := N[(N[(N[((-420.0) / N[Power[N[(N[Power[21.0, 2.0], $MachinePrecision] + 1.0),$MachinePrecision], N[(3.0 / 2.0), $MachinePrecision]],$MachinePrecision]), $MachinePrecision] * 21.0),$MachinePrecision] - N[(N[(11.0 * 450.0), $MachinePrecision] * N[Power[522.0, N[((-1.0) / 2.0),$MachinePrecision]], $MachinePrecision]),$MachinePrecision]), $MachinePrecision]  code[] := N[(N[(21.0 * N[(-420.0 / N[Power[442.0, 1.5],$MachinePrecision]), $MachinePrecision]),$MachinePrecision] + N[(N[Power[522.0, -0.5], $MachinePrecision] * -4950.0),$MachinePrecision]), \$MachinePrecision]

\frac{-420}{{\left({21}^{2} + 1\right)}^{\left(\frac{3}{2}\right)}} \cdot 21 - \left(11 \cdot 450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}

21 \cdot \frac{-420}{{442}^{1.5}} + {522}^{-0.5} \cdot -4950


# Try it out?

Results

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# Derivation?

1. Initial program 0

$\frac{-420}{{\left({21}^{2} + 1\right)}^{\left(\frac{3}{2}\right)}} \cdot 21 - \left(11 \cdot 450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}$
2. Final simplification0

$\leadsto 21 \cdot \frac{-420}{{442}^{1.5}} + {522}^{-0.5} \cdot -4950$

# Reproduce?

herbie shell --seed 1
(FPCore ()
:name "(-420/(21^2+1)^(3/2))*21 - 11*450*522^(-1/2)"
:precision binary64
(- (* (/ (- 420.0) (pow (+ (pow 21.0 2.0) 1.0) (/ 3.0 2.0))) 21.0) (* (* 11.0 450.0) (pow 522.0 (/ (- 1.0) 2.0)))))