?

Average Error: 0 → 0
Time: 3.7s
Precision: binary64
Cost: 13376

?

\[\left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \cdot 11 - \frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21 \]
↓
\[{522}^{-0.5} \cdot -4950 + \frac{-8820}{{122}^{1.5}} \]
(FPCore ()
 :precision binary64
 (-
  (* (* (- 450.0) (pow 522.0 (/ (- 1.0) 2.0))) 11.0)
  (* (/ 420.0 (pow 122.0 (/ 3.0 2.0))) 21.0)))
↓
(FPCore ()
 :precision binary64
 (+ (* (pow 522.0 -0.5) -4950.0) (/ -8820.0 (pow 122.0 1.5))))
double code() {
	return ((-450.0 * pow(522.0, (-1.0 / 2.0))) * 11.0) - ((420.0 / pow(122.0, (3.0 / 2.0))) * 21.0);
}
↓
double code() {
	return (pow(522.0, -0.5) * -4950.0) + (-8820.0 / pow(122.0, 1.5));
}

real(8) function code()
    code = ((-450.0d0 * (522.0d0 ** (-1.0d0 / 2.0d0))) * 11.0d0) - ((420.0d0 / (122.0d0 ** (3.0d0 / 2.0d0))) * 21.0d0)
end function
↓
real(8) function code()
    code = ((522.0d0 ** (-0.5d0)) * (-4950.0d0)) + ((-8820.0d0) / (122.0d0 ** 1.5d0))
end function

public static double code() {
	return ((-450.0 * Math.pow(522.0, (-1.0 / 2.0))) * 11.0) - ((420.0 / Math.pow(122.0, (3.0 / 2.0))) * 21.0);
}
↓
public static double code() {
	return (Math.pow(522.0, -0.5) * -4950.0) + (-8820.0 / Math.pow(122.0, 1.5));
}

def code():
	return ((-450.0 * math.pow(522.0, (-1.0 / 2.0))) * 11.0) - ((420.0 / math.pow(122.0, (3.0 / 2.0))) * 21.0)
↓
def code():
	return (math.pow(522.0, -0.5) * -4950.0) + (-8820.0 / math.pow(122.0, 1.5))

function code()
	return Float64(Float64(Float64(Float64(-450.0) * (522.0 ^ Float64(Float64(-1.0) / 2.0))) * 11.0) - Float64(Float64(420.0 / (122.0 ^ Float64(3.0 / 2.0))) * 21.0))
end
↓
function code()
	return Float64(Float64((522.0 ^ -0.5) * -4950.0) + Float64(-8820.0 / (122.0 ^ 1.5)))
end

function tmp = code()
	tmp = ((-450.0 * (522.0 ^ (-1.0 / 2.0))) * 11.0) - ((420.0 / (122.0 ^ (3.0 / 2.0))) * 21.0);
end
↓
function tmp = code()
	tmp = ((522.0 ^ -0.5) * -4950.0) + (-8820.0 / (122.0 ^ 1.5));
end

code[] := N[(N[(N[((-450.0) * N[Power[522.0, N[((-1.0) / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 11.0), $MachinePrecision] - N[(N[(420.0 / N[Power[122.0, N[(3.0 / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 21.0), $MachinePrecision]), $MachinePrecision]
↓
code[] := N[(N[(N[Power[522.0, -0.5], $MachinePrecision] * -4950.0), $MachinePrecision] + N[(-8820.0 / N[Power[122.0, 1.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \cdot 11 - \frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21
↓
{522}^{-0.5} \cdot -4950 + \frac{-8820}{{122}^{1.5}}

Error?

Try it out?

Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    Derivation?

    1. Initial program 0

      \[\left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \cdot 11 - \frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21 \]

    2. Simplified0

      \[\leadsto \color{blue}{{522}^{-0.5} \cdot -4950 + \frac{-8820}{{122}^{1.5}}} \]
      Proof

      [Start]0

      \[ \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \cdot 11 - \frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21 \]

      sub-neg [=>]0

      \[ \color{blue}{\left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \cdot 11 + \left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right)} \]

      +-commutative [=>]0

      \[ \color{blue}{\left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right) + \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \cdot 11} \]

      *-commutative [=>]0

      \[ \left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right) + \color{blue}{11 \cdot \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right)} \]

      metadata-eval [<=]0

      \[ \left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right) + \color{blue}{\left(--11\right)} \cdot \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \]

      metadata-eval [<=]0

      \[ \left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right) + \left(-\color{blue}{\left(-11\right)}\right) \cdot \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right) \]

      cancel-sign-sub-inv [<=]0

      \[ \color{blue}{\left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right) - \left(-11\right) \cdot \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right)} \]

      sub-neg [=>]0

      \[ \color{blue}{\left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right) + \left(-\left(-11\right) \cdot \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right)\right)} \]

      +-commutative [=>]0

      \[ \color{blue}{\left(-\left(-11\right) \cdot \left(\left(-450\right) \cdot {522}^{\left(\frac{-1}{2}\right)}\right)\right) + \left(-\frac{420}{{122}^{\left(\frac{3}{2}\right)}} \cdot 21\right)} \]

    3. Final simplification0

      \[\leadsto {522}^{-0.5} \cdot -4950 + \frac{-8820}{{122}^{1.5}} \]

    Reproduce?

    herbie shell --seed 1 
(FPCore ()
  :name "-450*522^(-1/2)*11 - (420/(122)^(3/2))*21"
  :precision binary64
  (- (* (* (- 450.0) (pow 522.0 (/ (- 1.0) 2.0))) 11.0) (* (/ 420.0 (pow 122.0 (/ 3.0 2.0))) 21.0)))