Average Error: 32.4 → 4.7
Time: 33.2s
Precision: binary64
Cost: 21000
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
↓
\[\begin{array}{l} t_1 := \frac{2}{\frac{\frac{t}{\frac{\ell}{t \cdot \sin k}}}{\frac{\frac{\ell}{t}}{\tan k}} \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-100}:\\ \;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(FPCore (t l k)
 :precision binary64
 (/
  2.0
  (*
   (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
   (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))
↓
(FPCore (t l k)
 :precision binary64
 (let* ((t_1
         (/
          2.0
          (*
           (/ (/ t (/ l (* t (sin k)))) (/ (/ l t) (tan k)))
           (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
   (if (<= t -1e-20)
     t_1
     (if (<= t 1e-100)
       (/ (* l (/ (/ l k) (* k (* t 0.5)))) (* (sin k) (tan k)))
       t_1))))
double code(double t, double l, double k) {
	return 2.0 / ((((pow(t, 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + pow((k / t), 2.0)) + 1.0));
}
↓
double code(double t, double l, double k) {
	double t_1 = 2.0 / (((t / (l / (t * sin(k)))) / ((l / t) / tan(k))) * (1.0 + (1.0 + pow((k / t), 2.0))));
	double tmp;
	if (t <= -1e-20) {
		tmp = t_1;
	} else if (t <= 1e-100) {
		tmp = (l * ((l / k) / (k * (t * 0.5)))) / (sin(k) * tan(k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

real(8) function code(t, l, k)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = 2.0d0 / (((((t ** 3.0d0) / (l * l)) * sin(k)) * tan(k)) * ((1.0d0 + ((k / t) ** 2.0d0)) + 1.0d0))
end function
↓
real(8) function code(t, l, k)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (((t / (l / (t * sin(k)))) / ((l / t) / tan(k))) * (1.0d0 + (1.0d0 + ((k / t) ** 2.0d0))))
    if (t <= (-1d-20)) then
        tmp = t_1
    else if (t <= 1d-100) then
        tmp = (l * ((l / k) / (k * (t * 0.5d0)))) / (sin(k) * tan(k))
    else
        tmp = t_1
    end if
    code = tmp
end function

public static double code(double t, double l, double k) {
	return 2.0 / ((((Math.pow(t, 3.0) / (l * l)) * Math.sin(k)) * Math.tan(k)) * ((1.0 + Math.pow((k / t), 2.0)) + 1.0));
}
↓
public static double code(double t, double l, double k) {
	double t_1 = 2.0 / (((t / (l / (t * Math.sin(k)))) / ((l / t) / Math.tan(k))) * (1.0 + (1.0 + Math.pow((k / t), 2.0))));
	double tmp;
	if (t <= -1e-20) {
		tmp = t_1;
	} else if (t <= 1e-100) {
		tmp = (l * ((l / k) / (k * (t * 0.5)))) / (Math.sin(k) * Math.tan(k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

def code(t, l, k):
	return 2.0 / ((((math.pow(t, 3.0) / (l * l)) * math.sin(k)) * math.tan(k)) * ((1.0 + math.pow((k / t), 2.0)) + 1.0))
↓
def code(t, l, k):
	t_1 = 2.0 / (((t / (l / (t * math.sin(k)))) / ((l / t) / math.tan(k))) * (1.0 + (1.0 + math.pow((k / t), 2.0))))
	tmp = 0
	if t <= -1e-20:
		tmp = t_1
	elif t <= 1e-100:
		tmp = (l * ((l / k) / (k * (t * 0.5)))) / (math.sin(k) * math.tan(k))
	else:
		tmp = t_1
	return tmp

function code(t, l, k)
	return Float64(2.0 / Float64(Float64(Float64(Float64((t ^ 3.0) / Float64(l * l)) * sin(k)) * tan(k)) * Float64(Float64(1.0 + (Float64(k / t) ^ 2.0)) + 1.0)))
end
↓
function code(t, l, k)
	t_1 = Float64(2.0 / Float64(Float64(Float64(t / Float64(l / Float64(t * sin(k)))) / Float64(Float64(l / t) / tan(k))) * Float64(1.0 + Float64(1.0 + (Float64(k / t) ^ 2.0)))))
	tmp = 0.0
	if (t <= -1e-20)
		tmp = t_1;
	elseif (t <= 1e-100)
		tmp = Float64(Float64(l * Float64(Float64(l / k) / Float64(k * Float64(t * 0.5)))) / Float64(sin(k) * tan(k)));
	else
		tmp = t_1;
	end
	return tmp
end

function tmp = code(t, l, k)
	tmp = 2.0 / (((((t ^ 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + ((k / t) ^ 2.0)) + 1.0));
end
↓
function tmp_2 = code(t, l, k)
	t_1 = 2.0 / (((t / (l / (t * sin(k)))) / ((l / t) / tan(k))) * (1.0 + (1.0 + ((k / t) ^ 2.0))));
	tmp = 0.0;
	if (t <= -1e-20)
		tmp = t_1;
	elseif (t <= 1e-100)
		tmp = (l * ((l / k) / (k * (t * 0.5)))) / (sin(k) * tan(k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

code[t_, l_, k_] := N[(2.0 / N[(N[(N[(N[(N[Power[t, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[t_, l_, k_] := Block[{t$95$1 = N[(2.0 / N[(N[(N[(t / N[(l / N[(t * N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(l / t), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(1.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e-20], t$95$1, If[LessEqual[t, 1e-100], N[(N[(l * N[(N[(l / k), $MachinePrecision] / N[(k * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Sin[k], $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}
↓
\begin{array}{l}
t_1 := \frac{2}{\frac{\frac{t}{\frac{\ell}{t \cdot \sin k}}}{\frac{\frac{\ell}{t}}{\tan k}} \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\\
\mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t \leq 10^{-100}:\\
\;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if t < -9.99999999999999945e-21 or 1e-100 < t

    1. Initial program 22.7

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

    2. Applied egg-rr16.4

      \[\leadsto \frac{2}{\left(\left(\color{blue}{\left(\frac{t \cdot t}{\ell} \cdot \frac{t}{\ell}\right)} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

    3. Applied egg-rr7.4

      \[\leadsto \frac{2}{\left(\color{blue}{\frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}}} \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

    4. Applied egg-rr4.3

      \[\leadsto \frac{2}{\color{blue}{\frac{\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)}{\frac{\frac{\ell}{t}}{\tan k}}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

    5. Applied egg-rr4.2

      \[\leadsto \frac{2}{\frac{\color{blue}{\frac{t}{\frac{\ell}{t \cdot \sin k}}}}{\frac{\frac{\ell}{t}}{\tan k}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

    if -9.99999999999999945e-21 < t < 1e-100

    1. Initial program 56.5

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]

    2. Simplified54.1

      \[\leadsto \color{blue}{\frac{\frac{2}{\frac{{t}^{3}}{\ell}}}{2 + {\left(\frac{k}{t}\right)}^{2}} \cdot \frac{\frac{\ell}{\sin k}}{\tan k}} \]
      Proof
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (Rewrite<= metadata-eval (+.f64 1 1)) (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 1 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 1 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)) (Rewrite<= associate-/r*_binary64 (/.f64 l (*.f64 (sin.f64 k) (tan.f64 k))))): 21 points increase in error, 2 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) l) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k))))): 9 points increase in error, 21 points decrease in error
      (/.f64 (Rewrite<= associate-/r/_binary64 (/.f64 2 (/.f64 (/.f64 (pow.f64 t 3) l) l))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 3 points increase in error, 2 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-/r*_binary64 (/.f64 (pow.f64 t 3) (*.f64 l l)))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 35 points increase in error, 4 points decrease in error
      (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))): 0 points increase in error, 7 points decrease in error
      (/.f64 (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (*.f64 (sin.f64 k) (tan.f64 k))))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)): 4 points increase in error, 2 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)): 2 points increase in error, 25 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))): 3 points increase in error, 1 points decrease in error

    3. Taylor expanded in t around 0 20.4

      \[\leadsto \color{blue}{\left(2 \cdot \frac{\ell}{{k}^{2} \cdot t}\right)} \cdot \frac{\frac{\ell}{\sin k}}{\tan k} \]

    4. Applied egg-rr18.0

      \[\leadsto \color{blue}{\frac{\left(\frac{2}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \ell}{\sin k \cdot \tan k}} \]

    5. Applied egg-rr5.9

      \[\leadsto \frac{\color{blue}{\frac{\frac{\ell}{k}}{\left(t \cdot 0.5\right) \cdot k}} \cdot \ell}{\sin k \cdot \tan k} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\ \;\;\;\;\frac{2}{\frac{\frac{t}{\frac{\ell}{t \cdot \sin k}}}{\frac{\frac{\ell}{t}}{\tan k}} \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\\ \mathbf{elif}\;t \leq 10^{-100}:\\ \;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{\frac{t}{\frac{\ell}{t \cdot \sin k}}}{\frac{\frac{\ell}{t}}{\tan k}} \cdot \left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error4.9
Cost21000
\[\begin{array}{l} t_1 := {\left(\frac{k}{t}\right)}^{2}\\ t_2 := t \cdot \sin k\\ \mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\ \;\;\;\;\frac{2}{\frac{\left(t_2 \cdot \frac{t}{\ell}\right) \cdot \left(\tan k \cdot \left(2 + t_1\right)\right)}{\frac{\ell}{t}}}\\ \mathbf{elif}\;t \leq 10^{-100}:\\ \;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(1 + \left(1 + t_1\right)\right) \cdot \frac{\frac{t_2}{\frac{\ell}{t}}}{\frac{\frac{\ell}{t}}{\tan k}}}\\ \end{array} \]
Alternative 2
Error4.8
Cost20872
\[\begin{array}{l} t_1 := \frac{2}{\frac{\frac{t}{\ell} \cdot \left(\left(t \cdot \sin k\right) \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}{\frac{\frac{\ell}{t}}{\tan k}}}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-111}:\\ \;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 3
Error4.7
Cost20872
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t}}{\tan k} \cdot \frac{2}{\frac{t}{\ell} \cdot \left(\left(t \cdot \sin k\right) \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-111}:\\ \;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Error4.7
Cost20872
\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ t_2 := t \cdot \sin k\\ \mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\ \;\;\;\;\frac{2}{\frac{\left(t_2 \cdot \frac{t}{\ell}\right) \cdot \left(\tan k \cdot t_1\right)}{\frac{\ell}{t}}}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-111}:\\ \;\;\;\;\frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\tan k} \cdot \frac{2}{\frac{t}{\ell} \cdot \left(t_2 \cdot t_1\right)}\\ \end{array} \]
Alternative 5
Error8.3
Cost14600
\[\begin{array}{l} t_1 := \frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{if}\;k \leq -1 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 10^{-12}:\\ \;\;\;\;\frac{2}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot \frac{\left(t \cdot \sin k\right) \cdot \frac{t}{\ell}}{\frac{\frac{\ell}{t}}{k}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error15.6
Cost14288
\[\begin{array}{l} t_1 := \sin k \cdot \tan k\\ t_2 := \frac{\frac{\frac{\ell}{k} \cdot \left(2 \cdot \ell\right)}{t \cdot k}}{t_1}\\ \mathbf{if}\;t \leq -15500000000:\\ \;\;\;\;\frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{elif}\;t \leq 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-125}:\\ \;\;\;\;\frac{\frac{\frac{\ell}{k} \cdot \left(2 \cdot \frac{\ell}{t}\right)}{k}}{t_1}\\ \mathbf{elif}\;t \leq 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{\frac{k}{\ell} \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]
Alternative 7
Error16.2
Cost14156
\[\begin{array}{l} t_1 := \frac{\frac{\frac{\ell}{k} \cdot \left(2 \cdot \ell\right)}{t \cdot k}}{\sin k \cdot \tan k}\\ \mathbf{if}\;k \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1 \cdot 10^{-160}:\\ \;\;\;\;{\left(\left(\frac{t}{\ell} \cdot \left(k \cdot k\right)\right) \cdot \frac{t}{\frac{\ell}{t}}\right)}^{-1}\\ \mathbf{elif}\;k \leq 10^{-15}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell \cdot {t}^{-3}}{k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error15.1
Cost14156
\[\begin{array}{l} t_1 := \frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot \left(t \cdot 0.5\right)}}{\sin k \cdot \tan k}\\ \mathbf{if}\;k \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1 \cdot 10^{-160}:\\ \;\;\;\;{\left(\left(\frac{t}{\ell} \cdot \left(k \cdot k\right)\right) \cdot \frac{t}{\frac{\ell}{t}}\right)}^{-1}\\ \mathbf{elif}\;k \leq 10^{-15}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell \cdot {t}^{-3}}{k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error21.1
Cost13640
\[\begin{array}{l} \mathbf{if}\;t \leq -1.76 \cdot 10^{-44}:\\ \;\;\;\;\frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;\left(2 \cdot \left(\frac{\ell}{t} \cdot \frac{1}{k \cdot k}\right)\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{\frac{k}{\ell} \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]
Alternative 10
Error21.1
Cost13512
\[\begin{array}{l} \mathbf{if}\;t \leq -1.76 \cdot 10^{-44}:\\ \;\;\;\;\frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;\left(2 \cdot \left(\frac{\ell}{t} \cdot \frac{1}{k \cdot k}\right)\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{k}{\ell} \cdot {t}^{1.5}\right)}^{-2}\\ \end{array} \]
Alternative 11
Error23.0
Cost7432
\[\begin{array}{l} \mathbf{if}\;t \leq -1.76 \cdot 10^{-44}:\\ \;\;\;\;\frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;\left(2 \cdot \left(\frac{\ell}{t} \cdot \frac{1}{k \cdot k}\right)\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{k}{\ell \cdot {t}^{-3}}} \cdot \frac{1}{k}\\ \end{array} \]
Alternative 12
Error22.9
Cost7304
\[\begin{array}{l} \mathbf{if}\;t \leq -1.76 \cdot 10^{-44}:\\ \;\;\;\;\frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;\left(2 \cdot \left(\frac{\ell}{t} \cdot \frac{1}{k \cdot k}\right)\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell \cdot {t}^{-3}}{k}\\ \end{array} \]
Alternative 13
Error21.7
Cost1352
\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{if}\;t \leq -1.76 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;\left(2 \cdot \left(\frac{\ell}{t} \cdot \frac{1}{k \cdot k}\right)\right) \cdot \frac{\ell}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error23.0
Cost1224
\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;\frac{2 \cdot \ell}{\frac{k}{\frac{\ell}{k}} \cdot \left(k \cdot \left(t \cdot k\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Error21.8
Cost1224
\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-100}:\\ \;\;\;\;\frac{\left(2 \cdot \frac{\ell}{t}\right) \cdot \frac{\ell}{k \cdot k}}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 16
Error28.1
Cost964
\[\begin{array}{l} \mathbf{if}\;k \leq -1.5 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \frac{\frac{\ell}{t}}{t}}{k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k}\\ \end{array} \]
Alternative 17
Error28.7
Cost832
\[\frac{\ell}{k \cdot \left(t \cdot t\right)} \cdot \frac{\ell}{t \cdot k} \]

Error

Reproduce

herbie shell --seed 2022295 
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10+)"
  :precision binary64
  (/ 2.0 (* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))