Average Error: 0.0 → 0.0
Time: 13.9s
Precision: binary64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \]
↓
\[\begin{array}{l} t_1 := 2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\\ \frac{1 + t_1 \cdot t_1}{2 + \log \left(e^{{t_1}^{2}}\right)} \end{array} \]
(FPCore (t)
 :precision binary64
 (/
  (+
   1.0
   (*
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))
  (+
   2.0
   (*
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))))
↓
(FPCore (t)
 :precision binary64
 (let* ((t_1 (+ 2.0 (/ (/ -2.0 t) (+ 1.0 (/ 1.0 t))))))
   (/ (+ 1.0 (* t_1 t_1)) (+ 2.0 (log (exp (pow t_1 2.0)))))))
double code(double t) {
	return (1.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))))) / (2.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t))))));
}
↓
double code(double t) {
	double t_1 = 2.0 + ((-2.0 / t) / (1.0 + (1.0 / t)));
	return (1.0 + (t_1 * t_1)) / (2.0 + log(exp(pow(t_1, 2.0))));
}

real(8) function code(t)
    real(8), intent (in) :: t
    code = (1.0d0 + ((2.0d0 - ((2.0d0 / t) / (1.0d0 + (1.0d0 / t)))) * (2.0d0 - ((2.0d0 / t) / (1.0d0 + (1.0d0 / t)))))) / (2.0d0 + ((2.0d0 - ((2.0d0 / t) / (1.0d0 + (1.0d0 / t)))) * (2.0d0 - ((2.0d0 / t) / (1.0d0 + (1.0d0 / t))))))
end function
↓
real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = 2.0d0 + (((-2.0d0) / t) / (1.0d0 + (1.0d0 / t)))
    code = (1.0d0 + (t_1 * t_1)) / (2.0d0 + log(exp((t_1 ** 2.0d0))))
end function

public static double code(double t) {
	return (1.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))))) / (2.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t))))));
}
↓
public static double code(double t) {
	double t_1 = 2.0 + ((-2.0 / t) / (1.0 + (1.0 / t)));
	return (1.0 + (t_1 * t_1)) / (2.0 + Math.log(Math.exp(Math.pow(t_1, 2.0))));
}

def code(t):
	return (1.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))))) / (2.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t))))))
↓
def code(t):
	t_1 = 2.0 + ((-2.0 / t) / (1.0 + (1.0 / t)))
	return (1.0 + (t_1 * t_1)) / (2.0 + math.log(math.exp(math.pow(t_1, 2.0))))

function code(t)
	return Float64(Float64(1.0 + Float64(Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))) * Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))))) / Float64(2.0 + Float64(Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))) * Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))))))
end
↓
function code(t)
	t_1 = Float64(2.0 + Float64(Float64(-2.0 / t) / Float64(1.0 + Float64(1.0 / t))))
	return Float64(Float64(1.0 + Float64(t_1 * t_1)) / Float64(2.0 + log(exp((t_1 ^ 2.0)))))
end

function tmp = code(t)
	tmp = (1.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))))) / (2.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t))))));
end
↓
function tmp = code(t)
	t_1 = 2.0 + ((-2.0 / t) / (1.0 + (1.0 / t)));
	tmp = (1.0 + (t_1 * t_1)) / (2.0 + log(exp((t_1 ^ 2.0))));
end

code[t_] := N[(N[(1.0 + N[(N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[(N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[t_] := Block[{t$95$1 = N[(2.0 + N[(N[(-2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 + N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[Log[N[Exp[N[Power[t$95$1, 2.0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
\begin{array}{l}
t_1 := 2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\\
\frac{1 + t_1 \cdot t_1}{2 + \log \left(e^{{t_1}^{2}}\right)}
\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \]

  2. Applied egg-rr0.0

    \[\leadsto \frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \color{blue}{\log \left(e^{{\left(2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\right)}^{2}}\right)}} \]

  3. Final simplification0.0

    \[\leadsto \frac{1 + \left(2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\right)}{2 + \log \left(e^{{\left(2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\right)}^{2}}\right)} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (t)
  :name "Kahan p13 Example 2"
  :precision binary64
  (/ (+ 1.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))) (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))))