Average Error: 0.0 → 0.0
Time: 10.0s
Precision: binary64
Cost: 14784
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \]
↓
\[\begin{array}{l} t_1 := -2 - {\left(2 + \frac{\frac{2}{t}}{\frac{-1}{t} + -1}\right)}^{2}\\ \frac{t_1 + 1}{t_1} \end{array} \]
(FPCore (t)
 :precision binary64
 (-
  1.0
  (/
   1.0
   (+
    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 (pow (+ 2.0 (/ (/ 2.0 t) (+ (/ -1.0 t) -1.0))) 2.0))))
   (/ (+ t_1 1.0) t_1)))
double code(double t) {
	return 1.0 - (1.0 / (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 - pow((2.0 + ((2.0 / t) / ((-1.0 / t) + -1.0))), 2.0);
	return (t_1 + 1.0) / t_1;
}

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

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

def code(t):
	return 1.0 - (1.0 / (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 - math.pow((2.0 + ((2.0 / t) / ((-1.0 / t) + -1.0))), 2.0)
	return (t_1 + 1.0) / t_1

function code(t)
	return Float64(1.0 - Float64(1.0 / 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(2.0 + Float64(Float64(2.0 / t) / Float64(Float64(-1.0 / t) + -1.0))) ^ 2.0))
	return Float64(Float64(t_1 + 1.0) / t_1)
end

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

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

1 - \frac{1}{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 - {\left(2 + \frac{\frac{2}{t}}{\frac{-1}{t} + -1}\right)}^{2}\\
\frac{t_1 + 1}{t_1}
\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

Alternatives

Alternative 1
Error0.0
Cost2880
\[\begin{array}{l} t_1 := \frac{2}{t + 1} + -2\\ t_2 := \frac{\frac{2}{t}}{\frac{t + 1}{t}} + -2\\ \frac{\left(-2 - t_1 \cdot t_1\right) + 1}{-2 - t_2 \cdot t_2} \end{array} \]
Alternative 2
Error0.0
Cost1856
\[\begin{array}{l} t_1 := 2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\\ 1 - \frac{1}{2 + t_1 \cdot t_1} \end{array} \]
Alternative 3
Error0.5
Cost1608
\[\begin{array}{l} \mathbf{if}\;t \leq -9.434969598260269:\\ \;\;\;\;\left(-0.16666666666666666 + \frac{-0.2222222222222222}{t}\right) + \left(1 + \frac{0.037037037037037035}{t \cdot t}\right)\\ \mathbf{elif}\;t \leq 0.12462912159661302:\\ \;\;\;\;1 - \frac{1}{2 + \left(t \cdot 2\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334 + \frac{-0.2222222222222222}{t}\\ \end{array} \]
Alternative 4
Error0.5
Cost964
\[\begin{array}{l} \mathbf{if}\;t \leq -9.434969598260269:\\ \;\;\;\;\left(-0.16666666666666666 + \frac{-0.2222222222222222}{t}\right) + \left(1 + \frac{0.037037037037037035}{t \cdot t}\right)\\ \mathbf{elif}\;t \leq 0.12462912159661302:\\ \;\;\;\;0.5 + t \cdot t\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334 + \frac{-0.2222222222222222}{t}\\ \end{array} \]
Alternative 5
Error0.5
Cost708
\[\begin{array}{l} \mathbf{if}\;t \leq -9.434969598260269:\\ \;\;\;\;0.8333333333333334 + \frac{\frac{0.037037037037037035}{t} - 0.2222222222222222}{t}\\ \mathbf{elif}\;t \leq 0.12462912159661302:\\ \;\;\;\;0.5 + t \cdot t\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334 + \frac{-0.2222222222222222}{t}\\ \end{array} \]
Alternative 6
Error0.8
Cost584
\[\begin{array}{l} \mathbf{if}\;t \leq -9.434969598260269:\\ \;\;\;\;0.8333333333333334\\ \mathbf{elif}\;t \leq 0.12462912159661302:\\ \;\;\;\;0.5 + t \cdot t\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334\\ \end{array} \]
Alternative 7
Error0.5
Cost584
\[\begin{array}{l} t_1 := 0.8333333333333334 + \frac{-0.2222222222222222}{t}\\ \mathbf{if}\;t \leq -9.434969598260269:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.12462912159661302:\\ \;\;\;\;0.5 + t \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error0.9
Cost328
\[\begin{array}{l} \mathbf{if}\;t \leq -9.434969598260269:\\ \;\;\;\;0.8333333333333334\\ \mathbf{elif}\;t \leq 0.12462912159661302:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334\\ \end{array} \]
Alternative 9
Error26.4
Cost64
\[0.8333333333333334 \]

Error

Reproduce

herbie shell --seed 2022325 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))