Average Error: 47.2 → 1.1
Time: 31.0s
Precision: binary64
Cost: 20489
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)} \]
↓
\[\begin{array}{l} t_1 := \frac{\cos k}{k} \cdot \ell\\ \mathbf{if}\;k \leq -1.1 \cdot 10^{-80} \lor \neg \left(k \leq 8.5 \cdot 10^{-49}\right):\\ \;\;\;\;2 \cdot \frac{t_1}{\frac{{\sin k}^{2} \cdot t}{\frac{\ell}{k}}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{t_1}{k \cdot \left(t \cdot \frac{k}{\frac{\ell}{k}}\right)}\\ \end{array} \]
(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 (* (/ (cos k) k) l)))
   (if (or (<= k -1.1e-80) (not (<= k 8.5e-49)))
     (* 2.0 (/ t_1 (/ (* (pow (sin k) 2.0) t) (/ l k))))
     (* 2.0 (/ t_1 (* k (* t (/ k (/ l k)))))))))
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 = (cos(k) / k) * l;
	double tmp;
	if ((k <= -1.1e-80) || !(k <= 8.5e-49)) {
		tmp = 2.0 * (t_1 / ((pow(sin(k), 2.0) * t) / (l / k)));
	} else {
		tmp = 2.0 * (t_1 / (k * (t * (k / (l / k)))));
	}
	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 = (cos(k) / k) * l
    if ((k <= (-1.1d-80)) .or. (.not. (k <= 8.5d-49))) then
        tmp = 2.0d0 * (t_1 / (((sin(k) ** 2.0d0) * t) / (l / k)))
    else
        tmp = 2.0d0 * (t_1 / (k * (t * (k / (l / k)))))
    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 = (Math.cos(k) / k) * l;
	double tmp;
	if ((k <= -1.1e-80) || !(k <= 8.5e-49)) {
		tmp = 2.0 * (t_1 / ((Math.pow(Math.sin(k), 2.0) * t) / (l / k)));
	} else {
		tmp = 2.0 * (t_1 / (k * (t * (k / (l / k)))));
	}
	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 = (math.cos(k) / k) * l
	tmp = 0
	if (k <= -1.1e-80) or not (k <= 8.5e-49):
		tmp = 2.0 * (t_1 / ((math.pow(math.sin(k), 2.0) * t) / (l / k)))
	else:
		tmp = 2.0 * (t_1 / (k * (t * (k / (l / k)))))
	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(Float64(cos(k) / k) * l)
	tmp = 0.0
	if ((k <= -1.1e-80) || !(k <= 8.5e-49))
		tmp = Float64(2.0 * Float64(t_1 / Float64(Float64((sin(k) ^ 2.0) * t) / Float64(l / k))));
	else
		tmp = Float64(2.0 * Float64(t_1 / Float64(k * Float64(t * Float64(k / Float64(l / k))))));
	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 = (cos(k) / k) * l;
	tmp = 0.0;
	if ((k <= -1.1e-80) || ~((k <= 8.5e-49)))
		tmp = 2.0 * (t_1 / (((sin(k) ^ 2.0) * t) / (l / k)));
	else
		tmp = 2.0 * (t_1 / (k * (t * (k / (l / k)))));
	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[(N[(N[Cos[k], $MachinePrecision] / k), $MachinePrecision] * l), $MachinePrecision]}, If[Or[LessEqual[k, -1.1e-80], N[Not[LessEqual[k, 8.5e-49]], $MachinePrecision]], N[(2.0 * N[(t$95$1 / N[(N[(N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision] * t), $MachinePrecision] / N[(l / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 / N[(k * N[(t * N[(k / N[(l / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

\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{\cos k}{k} \cdot \ell\\
\mathbf{if}\;k \leq -1.1 \cdot 10^{-80} \lor \neg \left(k \leq 8.5 \cdot 10^{-49}\right):\\
\;\;\;\;2 \cdot \frac{t_1}{\frac{{\sin k}^{2} \cdot t}{\frac{\ell}{k}}}\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \frac{t_1}{k \cdot \left(t \cdot \frac{k}{\frac{\ell}{k}}\right)}\\


\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 k < -1.10000000000000005e-80 or 8.50000000000000069e-49 < k

    1. Initial program 44.9

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

    2. Simplified36.7

      \[\leadsto \color{blue}{\frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left({\left(\frac{k}{t}\right)}^{2} + 0\right)\right)}} \]
      Proof
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (+.f64 (pow.f64 (/.f64 k t) 2) (Rewrite<= metadata-eval (-.f64 1 1)))))): 2 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (pow.f64 (/.f64 k t) 2) 1) 1))))): 0 points increase in error, 2 points decrease in error
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (pow.f64 (/.f64 k t) 2))) 1)))): 2 points increase in error, 0 points decrease in error
      (/.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (tan.f64 k) (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (Rewrite<= *-commutative_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))): 0 points increase in error, 6 points decrease in error

    3. Taylor expanded in k around inf 19.3

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

    4. Simplified15.2

      \[\leadsto \color{blue}{2 \cdot \left(\frac{\cos k}{k \cdot k} \cdot \frac{\ell}{\frac{t \cdot {\sin k}^{2}}{\ell}}\right)} \]
      Proof
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (*.f64 k k)) (/.f64 l (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) l)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (Rewrite<= unpow2_binary64 (pow.f64 k 2))) (/.f64 l (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) l)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (pow.f64 k 2)) (/.f64 l (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 (sin.f64 k) 2) t)) l)))): 3 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (pow.f64 k 2)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 l l) (*.f64 (pow.f64 (sin.f64 k) 2) t))))): 3 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (pow.f64 k 2)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 l 2)) (*.f64 (pow.f64 (sin.f64 k) 2) t)))): 0 points increase in error, 3 points decrease in error
      (*.f64 2 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (cos.f64 k) (pow.f64 l 2)) (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (sin.f64 k) 2) t))))): 0 points increase in error, 3 points decrease in error

    5. Applied egg-rr4.0

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

    6. Applied egg-rr0.6

      \[\leadsto 2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{\color{blue}{\frac{{\sin k}^{2} \cdot t}{\frac{\ell}{k}}}} \]

    if -1.10000000000000005e-80 < k < 8.50000000000000069e-49

    1. Initial program 63.7

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

    2. Simplified60.3

      \[\leadsto \color{blue}{\frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left({\left(\frac{k}{t}\right)}^{2} + 0\right)\right)}} \]
      Proof
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (+.f64 (pow.f64 (/.f64 k t) 2) (Rewrite<= metadata-eval (-.f64 1 1)))))): 2 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (pow.f64 (/.f64 k t) 2) 1) 1))))): 0 points increase in error, 2 points decrease in error
      (/.f64 2 (*.f64 (tan.f64 k) (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (pow.f64 (/.f64 k t) 2))) 1)))): 2 points increase in error, 0 points decrease in error
      (/.f64 2 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (tan.f64 k) (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (Rewrite<= *-commutative_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))): 0 points increase in error, 6 points decrease in error

    3. Taylor expanded in k around inf 47.2

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

    4. Simplified33.3

      \[\leadsto \color{blue}{2 \cdot \left(\frac{\cos k}{k \cdot k} \cdot \frac{\ell}{\frac{t \cdot {\sin k}^{2}}{\ell}}\right)} \]
      Proof
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (*.f64 k k)) (/.f64 l (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) l)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (Rewrite<= unpow2_binary64 (pow.f64 k 2))) (/.f64 l (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) l)))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (pow.f64 k 2)) (/.f64 l (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 (sin.f64 k) 2) t)) l)))): 3 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (pow.f64 k 2)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 l l) (*.f64 (pow.f64 (sin.f64 k) 2) t))))): 3 points increase in error, 0 points decrease in error
      (*.f64 2 (*.f64 (/.f64 (cos.f64 k) (pow.f64 k 2)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 l 2)) (*.f64 (pow.f64 (sin.f64 k) 2) t)))): 0 points increase in error, 3 points decrease in error
      (*.f64 2 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (cos.f64 k) (pow.f64 l 2)) (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (sin.f64 k) 2) t))))): 0 points increase in error, 3 points decrease in error

    5. Applied egg-rr30.3

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

    6. Taylor expanded in k around 0 23.5

      \[\leadsto 2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{\color{blue}{\frac{{k}^{2} \cdot t}{\ell}} \cdot k} \]

    7. Simplified4.7

      \[\leadsto 2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{\color{blue}{\left(\frac{k}{\frac{\ell}{k}} \cdot t\right)} \cdot k} \]
      Proof
      (*.f64 2 (/.f64 (*.f64 (/.f64 (cos.f64 k) k) l) (*.f64 (*.f64 (/.f64 k (/.f64 l k)) t) k))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (/.f64 (*.f64 (/.f64 (cos.f64 k) k) l) (*.f64 (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 k k) l)) t) k))): 0 points increase in error, 0 points decrease in error
      (*.f64 2 (/.f64 (*.f64 (/.f64 (cos.f64 k) k) l) (*.f64 (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 k 2)) l) t) k))): 5 points increase in error, 0 points decrease in error
      (*.f64 2 (/.f64 (*.f64 (/.f64 (cos.f64 k) k) l) (*.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (pow.f64 k 2) (/.f64 l t))) k))): 0 points increase in error, 5 points decrease in error
      (*.f64 2 (/.f64 (*.f64 (/.f64 (cos.f64 k) k) l) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (pow.f64 k 2) t) l)) k))): 3 points increase in error, 0 points decrease in error
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.1 \cdot 10^{-80} \lor \neg \left(k \leq 8.5 \cdot 10^{-49}\right):\\ \;\;\;\;2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{\frac{{\sin k}^{2} \cdot t}{\frac{\ell}{k}}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{k \cdot \left(t \cdot \frac{k}{\frac{\ell}{k}}\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error3.0
Cost20488
\[\begin{array}{l} t_1 := \sin k \cdot t\\ t_2 := \frac{2}{\tan k}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_2 \cdot \frac{\ell}{t_1}}{k}\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+154}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_2}{\frac{k \cdot t_1}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{{\sin k}^{2} \cdot t} \cdot \left(\frac{\cos k}{k} \cdot \frac{\ell}{k}\right)\right)\\ \end{array} \]
Alternative 2
Error5.2
Cost14156
\[\begin{array}{l} t_1 := \frac{\ell}{k} \cdot \left(\ell \cdot \frac{\frac{\frac{2}{\tan k}}{k}}{\sin k \cdot t}\right)\\ \mathbf{if}\;\ell \leq -2.9 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 3 \cdot 10^{-183}:\\ \;\;\;\;2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{k \cdot \left(t \cdot \frac{k}{\frac{\ell}{k}}\right)}\\ \mathbf{elif}\;\ell \leq 4.3 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k} \cdot \left(\frac{2}{\sin k \cdot \left(k \cdot \tan k\right)} \cdot \frac{\ell}{t}\right)\\ \end{array} \]
Alternative 3
Error2.5
Cost14152
\[\begin{array}{l} t_1 := \sin k \cdot t\\ t_2 := \frac{2}{\tan k}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_2 \cdot \frac{\ell}{t_1}}{k}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+77}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_2}{\frac{k \cdot t_1}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_2}{k \cdot \left(\frac{\sin k}{-\ell} \cdot \left(-t\right)\right)}\\ \end{array} \]
Alternative 4
Error4.2
Cost14025
\[\begin{array}{l} \mathbf{if}\;k \leq -4.2 \cdot 10^{-15} \lor \neg \left(k \leq 7 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\ell}{k} \cdot \left(\frac{2}{\sin k \cdot \left(k \cdot \tan k\right)} \cdot \frac{\ell}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{k \cdot \left(t \cdot \frac{k}{\frac{\ell}{k}}\right)}\\ \end{array} \]
Alternative 5
Error3.0
Cost14025
\[\begin{array}{l} t_1 := \frac{2}{\tan k}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-14} \lor \neg \left(t \leq 1.12 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_1 \cdot \frac{\ell}{\sin k \cdot t}}{k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k} \cdot \left(\ell \cdot \frac{\frac{t_1}{\sin k}}{k \cdot t}\right)\\ \end{array} \]
Alternative 6
Error2.9
Cost14025
\[\begin{array}{l} t_1 := \frac{2}{\tan k}\\ t_2 := \sin k \cdot t\\ \mathbf{if}\;t \leq -5 \cdot 10^{-10} \lor \neg \left(t \leq 5.5 \cdot 10^{+153}\right):\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_1 \cdot \frac{\ell}{t_2}}{k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{t_1}{\frac{k \cdot t_2}{\ell}}\\ \end{array} \]
Alternative 7
Error22.7
Cost7488
\[2 \cdot \frac{\frac{\cos k}{k} \cdot \ell}{k \cdot \left(t \cdot \frac{k}{\frac{\ell}{k}}\right)} \]
Alternative 8
Error22.9
Cost7360
\[\frac{\ell}{k} \cdot \frac{\frac{2}{\tan k}}{t \cdot \left(k \cdot \frac{k}{\ell}\right)} \]
Alternative 9
Error24.5
Cost1220
\[\begin{array}{l} t_1 := k \cdot \frac{k}{\ell}\\ \mathbf{if}\;\ell \leq -7 \cdot 10^{-197}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{t \cdot \left(k \cdot k\right)}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{1}{\left(k \cdot t_1\right) \cdot \left(t \cdot \frac{k}{\ell}\right)}\\ \end{array} \]
Alternative 10
Error23.6
Cost1088
\[2 \cdot \frac{1}{\frac{\frac{k}{\frac{\ell}{k}}}{\frac{\frac{\ell}{k \cdot t}}{k}}} \]
Alternative 11
Error25.7
Cost960
\[2 \cdot \left(\frac{\ell}{k \cdot k} \cdot \frac{\frac{\ell}{t}}{k \cdot k}\right) \]
Alternative 12
Error25.7
Cost960
\[2 \cdot \frac{\ell}{\left(k \cdot t\right) \cdot \left(k \cdot \left(k \cdot \frac{k}{\ell}\right)\right)} \]
Alternative 13
Error25.6
Cost960
\[2 \cdot \frac{\ell}{k \cdot \left(k \cdot \frac{k}{\frac{\ell}{k \cdot t}}\right)} \]

Error

Reproduce

herbie shell --seed 2022349 
(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))))