?

Average Error: 0 → 0
Time: 6.1s
Precision: binary64
Cost: 13120

?

\[\frac{\frac{1000000}{6344721}}{\sqrt{{\left(\left(-9000\right) \cdot {801}^{\left(\frac{-3}{2}\right)} - 12600 \cdot {901}^{\left(\frac{-3}{2}\right)}\right)}^{2} + {\left(\frac{1000000}{6344721}\right)}^{2}}} \]
↓
\[\frac{0.15761134335142554}{\sqrt{\sqrt{0.13684035092367203} + 0.3995061409426643}} \]
(FPCore ()
 :precision binary64
 (/
  (/ 1000000.0 6344721.0)
  (sqrt
   (+
    (pow
     (-
      (* (- 9000.0) (pow 801.0 (/ (- 3.0) 2.0)))
      (* 12600.0 (pow 901.0 (/ (- 3.0) 2.0))))
     2.0)
    (pow (/ 1000000.0 6344721.0) 2.0)))))
↓
(FPCore ()
 :precision binary64
 (/
  0.15761134335142554
  (sqrt (+ (sqrt 0.13684035092367203) 0.3995061409426643))))
double code() {
	return (1000000.0 / 6344721.0) / sqrt((pow(((-9000.0 * pow(801.0, (-3.0 / 2.0))) - (12600.0 * pow(901.0, (-3.0 / 2.0)))), 2.0) + pow((1000000.0 / 6344721.0), 2.0)));
}
↓
double code() {
	return 0.15761134335142554 / sqrt((sqrt(0.13684035092367203) + 0.3995061409426643));
}

real(8) function code()
    code = (1000000.0d0 / 6344721.0d0) / sqrt(((((-9000.0d0 * (801.0d0 ** (-3.0d0 / 2.0d0))) - (12600.0d0 * (901.0d0 ** (-3.0d0 / 2.0d0)))) ** 2.0d0) + ((1000000.0d0 / 6344721.0d0) ** 2.0d0)))
end function
↓
real(8) function code()
    code = 0.15761134335142554d0 / sqrt((sqrt(0.13684035092367203d0) + 0.3995061409426643d0))
end function

public static double code() {
	return (1000000.0 / 6344721.0) / Math.sqrt((Math.pow(((-9000.0 * Math.pow(801.0, (-3.0 / 2.0))) - (12600.0 * Math.pow(901.0, (-3.0 / 2.0)))), 2.0) + Math.pow((1000000.0 / 6344721.0), 2.0)));
}
↓
public static double code() {
	return 0.15761134335142554 / Math.sqrt((Math.sqrt(0.13684035092367203) + 0.3995061409426643));
}

def code():
	return (1000000.0 / 6344721.0) / math.sqrt((math.pow(((-9000.0 * math.pow(801.0, (-3.0 / 2.0))) - (12600.0 * math.pow(901.0, (-3.0 / 2.0)))), 2.0) + math.pow((1000000.0 / 6344721.0), 2.0)))
↓
def code():
	return 0.15761134335142554 / math.sqrt((math.sqrt(0.13684035092367203) + 0.3995061409426643))

function code()
	return Float64(Float64(1000000.0 / 6344721.0) / sqrt(Float64((Float64(Float64(Float64(-9000.0) * (801.0 ^ Float64(Float64(-3.0) / 2.0))) - Float64(12600.0 * (901.0 ^ Float64(Float64(-3.0) / 2.0)))) ^ 2.0) + (Float64(1000000.0 / 6344721.0) ^ 2.0))))
end
↓
function code()
	return Float64(0.15761134335142554 / sqrt(Float64(sqrt(0.13684035092367203) + 0.3995061409426643)))
end

function tmp = code()
	tmp = (1000000.0 / 6344721.0) / sqrt(((((-9000.0 * (801.0 ^ (-3.0 / 2.0))) - (12600.0 * (901.0 ^ (-3.0 / 2.0)))) ^ 2.0) + ((1000000.0 / 6344721.0) ^ 2.0)));
end
↓
function tmp = code()
	tmp = 0.15761134335142554 / sqrt((sqrt(0.13684035092367203) + 0.3995061409426643));
end

code[] := N[(N[(1000000.0 / 6344721.0), $MachinePrecision] / N[Sqrt[N[(N[Power[N[(N[((-9000.0) * N[Power[801.0, N[((-3.0) / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(12600.0 * N[Power[901.0, N[((-3.0) / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(1000000.0 / 6344721.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[] := N[(0.15761134335142554 / N[Sqrt[N[(N[Sqrt[0.13684035092367203], $MachinePrecision] + 0.3995061409426643), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

\frac{\frac{1000000}{6344721}}{\sqrt{{\left(\left(-9000\right) \cdot {801}^{\left(\frac{-3}{2}\right)} - 12600 \cdot {901}^{\left(\frac{-3}{2}\right)}\right)}^{2} + {\left(\frac{1000000}{6344721}\right)}^{2}}}
↓
\frac{0.15761134335142554}{\sqrt{\sqrt{0.13684035092367203} + 0.3995061409426643}}

Error?

Try it out?

Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    Derivation?

    1. Initial program 0

      \[\frac{\frac{1000000}{6344721}}{\sqrt{{\left(\left(-9000\right) \cdot {801}^{\left(\frac{-3}{2}\right)} - 12600 \cdot {901}^{\left(\frac{-3}{2}\right)}\right)}^{2} + {\left(\frac{1000000}{6344721}\right)}^{2}}} \]

    2. Simplified0

      \[\leadsto \color{blue}{\frac{0.15761134335142554}{\sqrt{\left({901}^{-1.5} \cdot \left(9000 \cdot {801}^{-1.5}\right)\right) \cdot 25200 + 0.3995061409426643}}} \]
      Proof

      [Start]0

      \[ \frac{\frac{1000000}{6344721}}{\sqrt{{\left(\left(-9000\right) \cdot {801}^{\left(\frac{-3}{2}\right)} - 12600 \cdot {901}^{\left(\frac{-3}{2}\right)}\right)}^{2} + {\left(\frac{1000000}{6344721}\right)}^{2}}} \]

      metadata-eval [=>]0

      \[ \frac{\color{blue}{0.15761134335142554}}{\sqrt{{\left(\left(-9000\right) \cdot {801}^{\left(\frac{-3}{2}\right)} - 12600 \cdot {901}^{\left(\frac{-3}{2}\right)}\right)}^{2} + {\left(\frac{1000000}{6344721}\right)}^{2}}} \]

    3. Applied egg-rr0

      \[\leadsto \frac{0.15761134335142554}{\sqrt{\color{blue}{e^{\mathsf{log1p}\left(\sqrt{0.13684035092367203}\right)} - 0.6004938590573357}}} \]

    4. Simplified0

      \[\leadsto \frac{0.15761134335142554}{\sqrt{\color{blue}{\sqrt{0.13684035092367203} + 0.3995061409426643}}} \]
      Proof

      [Start]0

      \[ \frac{0.15761134335142554}{\sqrt{e^{\mathsf{log1p}\left(\sqrt{0.13684035092367203}\right)} - 0.6004938590573357}} \]

      metadata-eval [<=]0

      \[ \frac{0.15761134335142554}{\sqrt{e^{\mathsf{log1p}\left(\sqrt{0.13684035092367203}\right)} - \color{blue}{\left(1 - 0.3995061409426643\right)}}} \]

      associate-+l- [<=]0

      \[ \frac{0.15761134335142554}{\sqrt{\color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt{0.13684035092367203}\right)} - 1\right) + 0.3995061409426643}}} \]

      expm1-def [=>]0

      \[ \frac{0.15761134335142554}{\sqrt{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{0.13684035092367203}\right)\right)} + 0.3995061409426643}} \]

      expm1-log1p [=>]0

      \[ \frac{0.15761134335142554}{\sqrt{\color{blue}{\sqrt{0.13684035092367203}} + 0.3995061409426643}} \]

    5. Final simplification0

      \[\leadsto \frac{0.15761134335142554}{\sqrt{\sqrt{0.13684035092367203} + 0.3995061409426643}} \]

    Reproduce?

    herbie shell --seed 1 
(FPCore ()
  :name "((1000000/6344721)/sqrt((-9000*801^(-3/2)-12600*901^(-3/2))^2+(1000000/6344721)^2))"
  :precision binary64
  (/ (/ 1000000.0 6344721.0) (sqrt (+ (pow (- (* (- 9000.0) (pow 801.0 (/ (- 3.0) 2.0))) (* 12600.0 (pow 901.0 (/ (- 3.0) 2.0)))) 2.0) (pow (/ 1000000.0 6344721.0) 2.0)))))