Toniolo and Linder, Equation (10+)

Average Error: 32.7 → 10.0

Time: 58.4s

Precision: binary64

Cost: 20872

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\frac{2}{\left(\frac{t}{\ell} \cdot \sin k\right) \cdot t}}{\frac{\left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right) \cdot t}{\ell}}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{2}{\frac{\frac{{\left(k \cdot \sin k\right)}^{2} \cdot \frac{t}{\cos k}}{\ell}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(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) (sin k)) t))
          (/ (* (* (tan k) (+ 2.0 (pow (/ k t) 2.0))) t) l))))
   (if (<= t -4.3e-23)
     t_1
     (if (<= t 9.6e-120)
       (/ 2.0 (/ (/ (* (pow (* k (sin k)) 2.0) (/ t (cos k))) l) l))
       t_1))))

C

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) * sin(k)) * t)) / (((tan(k) * (2.0 + pow((k / t), 2.0))) * t) / l);
	double tmp;
	if (t <= -4.3e-23) {
		tmp = t_1;
	} else if (t <= 9.6e-120) {
		tmp = 2.0 / (((pow((k * sin(k)), 2.0) * (t / cos(k))) / l) / l);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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) * sin(k)) * t)) / (((tan(k) * (2.0d0 + ((k / t) ** 2.0d0))) * t) / l)
    if (t <= (-4.3d-23)) then
        tmp = t_1
    else if (t <= 9.6d-120) then
        tmp = 2.0d0 / (((((k * sin(k)) ** 2.0d0) * (t / cos(k))) / l) / l)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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) * Math.sin(k)) * t)) / (((Math.tan(k) * (2.0 + Math.pow((k / t), 2.0))) * t) / l);
	double tmp;
	if (t <= -4.3e-23) {
		tmp = t_1;
	} else if (t <= 9.6e-120) {
		tmp = 2.0 / (((Math.pow((k * Math.sin(k)), 2.0) * (t / Math.cos(k))) / l) / l);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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) * math.sin(k)) * t)) / (((math.tan(k) * (2.0 + math.pow((k / t), 2.0))) * t) / l)
	tmp = 0
	if t <= -4.3e-23:
		tmp = t_1
	elif t <= 9.6e-120:
		tmp = 2.0 / (((math.pow((k * math.sin(k)), 2.0) * (t / math.cos(k))) / l) / l)
	else:
		tmp = t_1
	return tmp

Julia

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(2.0 / Float64(Float64(Float64(t / l) * sin(k)) * t)) / Float64(Float64(Float64(tan(k) * Float64(2.0 + (Float64(k / t) ^ 2.0))) * t) / l))
	tmp = 0.0
	if (t <= -4.3e-23)
		tmp = t_1;
	elseif (t <= 9.6e-120)
		tmp = Float64(2.0 / Float64(Float64(Float64((Float64(k * sin(k)) ^ 2.0) * Float64(t / cos(k))) / l) / l));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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) * sin(k)) * t)) / (((tan(k) * (2.0 + ((k / t) ^ 2.0))) * t) / l);
	tmp = 0.0;
	if (t <= -4.3e-23)
		tmp = t_1;
	elseif (t <= 9.6e-120)
		tmp = 2.0 / (((((k * sin(k)) ^ 2.0) * (t / cos(k))) / l) / l);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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[(2.0 / N[(N[(N[(t / l), $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[Tan[k], $MachinePrecision] * N[(2.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e-23], t$95$1, If[LessEqual[t, 9.6e-120], N[(2.0 / N[(N[(N[(N[Power[N[(k * N[Sin[k], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(t / N[Cos[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.30000000000000002e-23 or 9.5999999999999998e-120 < t

   1. Initial program 23.6

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

   2. Simplified 23.5

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

   3. Applied egg-rr 17.3

      \[\leadsto \color{blue}{\frac{\sqrt[3]{4}}{\frac{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}{\ell}} \cdot \frac{\sqrt[3]{2}}{\frac{{t}^{3} \cdot \sin k}{\ell}}} \]

   4. Applied egg-rr 16.5

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

   5. Applied egg-rr 12.6

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

   6. Simplified 12.6

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

   7. Applied egg-rr 13.5

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

   8. Simplified 4.6

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

   if -4.30000000000000002e-23 < t < 9.5999999999999998e-120

   1. Initial program 56.1

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

   2. Simplified 56.4

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

   3. Taylor expanded in t around 0 27.0

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

   4. Simplified 27.0

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

   5. Applied egg-rr 24.1

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

Alternatives

Alternative 1
Error	13.3
Cost	21136

\[\begin{array}{l} t_1 := \frac{2}{\frac{\sin k \cdot t}{\ell} \cdot \frac{\left(t \cdot t\right) \cdot \left(\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}{\ell}}\\ t_2 := \frac{1}{k \cdot t}\\ t_3 := {\left(k \cdot \sin k\right)}^{2} \cdot \frac{t}{\cos k}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+192}:\\ \;\;\;\;\frac{t_2}{\frac{t}{\ell}} \cdot \frac{t_2}{\frac{1}{\ell}}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-88}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;\ell \ne 0:\\ \;\;\;\;\frac{2 \cdot \ell}{\frac{t_3}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{t_3}{\ell \cdot \ell}}\\ \end{array}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\left(k \cdot t\right) \cdot k}}{\frac{t}{\ell}} \cdot \frac{1}{\frac{t}{\ell}}\\ \end{array} \]

Alternative 2
Error	16.0
Cost	20492

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ t_3 := {\left(k \cdot \sin k\right)}^{2} \cdot \frac{t}{\cos k}\\ \mathbf{if}\;t \leq -130000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 0.00026:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;\ell \ne 0:\\ \;\;\;\;\frac{2 \cdot \ell}{\frac{t_3}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{t_3}{\ell \cdot \ell}}\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	16.0
Cost	20360

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ \mathbf{if}\;t \leq -135000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8:\\ \;\;\;\;\frac{2}{\frac{\frac{{\left(k \cdot \sin k\right)}^{2} \cdot t}{\ell \cdot \cos k}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	16.0
Cost	20360

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ \mathbf{if}\;t \leq -125000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2:\\ \;\;\;\;\frac{2}{\frac{\frac{{\left(k \cdot \sin k\right)}^{2} \cdot \frac{t}{\cos k}}{\ell}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	20.6
Cost	14408

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ \mathbf{if}\;t \leq -0.075:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;2 \cdot \left(\frac{{k}^{-4} \cdot \left(\ell \cdot \ell\right)}{t} + \frac{\left({k}^{-2} \cdot \ell\right) \cdot \ell}{t \cdot -6}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	17.9
Cost	14408

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ \mathbf{if}\;t \leq -0.076:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-38}:\\ \;\;\;\;\frac{2}{\frac{\frac{\left(\left(k \cdot k\right) \cdot \frac{1 - \cos \left(k + k\right)}{2}\right) \cdot t}{\cos k}}{\ell \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	20.5
Cost	8072

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ \mathbf{if}\;t \leq -0.075:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(\frac{{k}^{-4} \cdot \left(\ell \cdot \ell\right)}{t} + -0.16666666666666666 \cdot \frac{\frac{\ell \cdot \ell}{k \cdot k}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	20.8
Cost	7304

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ \mathbf{if}\;t \leq -0.075:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-37}:\\ \;\;\;\;2 \cdot \frac{{k}^{-4} \cdot \left(\ell \cdot \ell\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	21.6
Cost	1480

\[\begin{array}{l} t_1 := \frac{1}{k \cdot t}\\ t_2 := \frac{t_1}{\frac{t}{\ell}} \cdot \frac{t_1}{\frac{1}{\ell}}\\ \mathbf{if}\;t \leq -0.13:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{\frac{\frac{1}{k \cdot k}}{\frac{t}{\ell \cdot \ell}}}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	25.9
Cost	1356

\[\begin{array}{l} t_1 := \frac{\frac{\frac{1}{\left(k \cdot t\right) \cdot k}}{\frac{t}{\ell}}}{\frac{t}{\ell}}\\ \mathbf{if}\;\ell \leq -2.4 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq -2.4 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{\frac{\frac{1}{k \cdot k}}{\frac{t}{\ell \cdot \ell}}}{t}}{t}\\ \mathbf{elif}\;\ell \leq 1.3 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{\ell \cdot \ell}{k \cdot t} \cdot \frac{1}{t}}{k \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	25.9
Cost	1356

\[\begin{array}{l} t_1 := \frac{\frac{1}{\left(k \cdot t\right) \cdot k}}{\frac{t}{\ell}}\\ \mathbf{if}\;\ell \leq -2 \cdot 10^{+111}:\\ \;\;\;\;t_1 \cdot \frac{1}{\frac{t}{\ell}}\\ \mathbf{elif}\;\ell \leq -2.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{\frac{\frac{1}{k \cdot k}}{\frac{t}{\ell \cdot \ell}}}{t}}{t}\\ \mathbf{elif}\;\ell \leq 6 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{\ell \cdot \ell}{k \cdot t} \cdot \frac{1}{t}}{k \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{\frac{t}{\ell}}\\ \end{array} \]

Alternative 12
Error	25.8
Cost	1356

\[\begin{array}{l} t_1 := \frac{\frac{1}{\left(k \cdot t\right) \cdot k}}{\frac{t}{\ell}}\\ \mathbf{if}\;\ell \leq -2.4 \cdot 10^{+109}:\\ \;\;\;\;t_1 \cdot \frac{1}{\frac{t}{\ell}}\\ \mathbf{elif}\;\ell \leq -1.9 \cdot 10^{-150}:\\ \;\;\;\;\frac{2}{2 \cdot \left(t \cdot \left(\frac{t}{\ell \cdot \ell} \cdot \left(\left(k \cdot k\right) \cdot t\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 2.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{\ell \cdot \ell}{k \cdot t} \cdot \frac{1}{t}}{k \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{\frac{t}{\ell}}\\ \end{array} \]

Alternative 13
Error	24.6
Cost	1224

\[\begin{array}{l} t_1 := \frac{\frac{\frac{1}{\left(k \cdot t\right) \cdot k}}{\frac{t}{\ell}}}{\frac{t}{\ell}}\\ \mathbf{if}\;\ell \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{\ell \cdot \ell}{k \cdot t} \cdot \frac{1}{t}}{k \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	27.0
Cost	1220

\[\begin{array}{l} \mathbf{if}\;\ell \cdot \ell \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{\frac{\ell \cdot \ell}{k \cdot t} \cdot \frac{1}{t}}{k \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\left(k \cdot k\right) \cdot \left(t \cdot t\right)}}{\frac{\frac{t}{\ell}}{\ell}}\\ \end{array} \]

Alternative 15
Error	26.8
Cost	1220

\[\begin{array}{l} \mathbf{if}\;\ell \cdot \ell \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{\frac{\ell \cdot \ell}{k \cdot t} \cdot \frac{1}{t}}{k \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{1}{k \cdot k}}{\frac{t}{\ell}}}{\frac{t \cdot t}{\ell}}\\ \end{array} \]

Alternative 16
Error	28.5
Cost	960

\[\frac{\frac{\ell \cdot \ell}{k \cdot t} \cdot \frac{1}{t}}{k \cdot t} \]

Alternative 17
Error	36.5
Cost	832

\[\frac{\ell \cdot \ell}{\left(\left(k \cdot k\right) \cdot t\right) \cdot \left(t \cdot t\right)} \]

Alternative 18
Error	29.8
Cost	832

\[\frac{\frac{\ell \cdot \ell}{t}}{\left(k \cdot t\right) \cdot \left(k \cdot t\right)} \]

Alternative 19
Error	29.6
Cost	832

\[\frac{\frac{\ell \cdot \ell}{k \cdot t}}{\left(k \cdot t\right) \cdot t} \]

Reproduce

herbie shell --seed 2023010 
(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))))