Toniolo and Linder, Equation (10+)

Average Accuracy: 49.5% → 86.3%

Time: 34.5s

Precision: binary64

Cost: 20873

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-80} \lor \neg \left(t \leq 2.8 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{2}{\frac{\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)}{\frac{\frac{\ell}{t}}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \ell}{\frac{k \cdot k}{\cos k} \cdot \frac{t}{\frac{\ell}{{\sin k}^{2}}}}\\ \end{array} \]

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
 (if (or (<= t -2.6e-80) (not (<= t 2.8e-60)))
   (/
    2.0
    (/
     (* (/ t l) (* t (sin k)))
     (/ (/ l t) (* (tan k) (+ 2.0 (pow (/ k t) 2.0))))))
   (/ (* 2.0 l) (* (/ (* k k) (cos k)) (/ t (/ l (pow (sin k) 2.0)))))))

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 tmp;
	if ((t <= -2.6e-80) || !(t <= 2.8e-60)) {
		tmp = 2.0 / (((t / l) * (t * sin(k))) / ((l / t) / (tan(k) * (2.0 + pow((k / t), 2.0)))));
	} else {
		tmp = (2.0 * l) / (((k * k) / cos(k)) * (t / (l / pow(sin(k), 2.0))));
	}
	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) :: tmp
    if ((t <= (-2.6d-80)) .or. (.not. (t <= 2.8d-60))) then
        tmp = 2.0d0 / (((t / l) * (t * sin(k))) / ((l / t) / (tan(k) * (2.0d0 + ((k / t) ** 2.0d0)))))
    else
        tmp = (2.0d0 * l) / (((k * k) / cos(k)) * (t / (l / (sin(k) ** 2.0d0))))
    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 tmp;
	if ((t <= -2.6e-80) || !(t <= 2.8e-60)) {
		tmp = 2.0 / (((t / l) * (t * Math.sin(k))) / ((l / t) / (Math.tan(k) * (2.0 + Math.pow((k / t), 2.0)))));
	} else {
		tmp = (2.0 * l) / (((k * k) / Math.cos(k)) * (t / (l / Math.pow(Math.sin(k), 2.0))));
	}
	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):
	tmp = 0
	if (t <= -2.6e-80) or not (t <= 2.8e-60):
		tmp = 2.0 / (((t / l) * (t * math.sin(k))) / ((l / t) / (math.tan(k) * (2.0 + math.pow((k / t), 2.0)))))
	else:
		tmp = (2.0 * l) / (((k * k) / math.cos(k)) * (t / (l / math.pow(math.sin(k), 2.0))))
	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)
	tmp = 0.0
	if ((t <= -2.6e-80) || !(t <= 2.8e-60))
		tmp = Float64(2.0 / Float64(Float64(Float64(t / l) * Float64(t * sin(k))) / Float64(Float64(l / t) / Float64(tan(k) * Float64(2.0 + (Float64(k / t) ^ 2.0))))));
	else
		tmp = Float64(Float64(2.0 * l) / Float64(Float64(Float64(k * k) / cos(k)) * Float64(t / Float64(l / (sin(k) ^ 2.0)))));
	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)
	tmp = 0.0;
	if ((t <= -2.6e-80) || ~((t <= 2.8e-60)))
		tmp = 2.0 / (((t / l) * (t * sin(k))) / ((l / t) / (tan(k) * (2.0 + ((k / t) ^ 2.0)))));
	else
		tmp = (2.0 * l) / (((k * k) / cos(k)) * (t / (l / (sin(k) ^ 2.0))));
	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_] := If[Or[LessEqual[t, -2.6e-80], N[Not[LessEqual[t, 2.8e-60]], $MachinePrecision]], N[(2.0 / N[(N[(N[(t / l), $MachinePrecision] * N[(t * N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(l / t), $MachinePrecision] / N[(N[Tan[k], $MachinePrecision] * N[(2.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * l), $MachinePrecision] / N[(N[(N[(k * k), $MachinePrecision] / N[Cos[k], $MachinePrecision]), $MachinePrecision] * N[(t / N[(l / N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6000000000000001e-80 or 2.8000000000000002e-60 < t

   1. Initial program 65.4%

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

   2. Simplified 65.4%

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

      [Start] 65.4	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 65.4	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      +-commutative [=>] 65.4	\[ \frac{2}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \color{blue}{\left(1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)\right)}\right)} \]

   3. Applied egg-rr 74.5%

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

   4. Applied egg-rr 88.4%

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

   5. Applied egg-rr 94.0%

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

   if -2.6000000000000001e-80 < t < 2.8000000000000002e-60

   1. Initial program 8.7%

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

   2. Simplified 7.5%

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

      [Start] 8.7	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-*l* [=>] 8.7	\[ \frac{2}{\color{blue}{\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)\right)}} \]
      associate-/r* [=>] 8.6	\[ \color{blue}{\frac{\frac{2}{\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k}}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}} \]
      associate-/r/ [<=] 8.6	\[ \frac{\frac{2}{\color{blue}{\frac{{t}^{3}}{\frac{\ell \cdot \ell}{\sin k}}}}}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      associate-/r/ [=>] 8.1	\[ \frac{\color{blue}{\frac{2}{{t}^{3}} \cdot \frac{\ell \cdot \ell}{\sin k}}}{\tan k \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
      times-frac [=>] 7.5	\[ \color{blue}{\frac{\frac{2}{{t}^{3}}}{\tan k} \cdot \frac{\frac{\ell \cdot \ell}{\sin k}}{\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1}} \]
      associate-/l* [=>] 7.5	\[ \frac{\frac{2}{{t}^{3}}}{\tan k} \cdot \frac{\color{blue}{\frac{\ell}{\frac{\sin k}{\ell}}}}{\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1} \]
      +-commutative [=>] 7.5	\[ \frac{\frac{2}{{t}^{3}}}{\tan k} \cdot \frac{\frac{\ell}{\frac{\sin k}{\ell}}}{\color{blue}{1 + \left(1 + {\left(\frac{k}{t}\right)}^{2}\right)}} \]
      associate-+r+ [=>] 7.5	\[ \frac{\frac{2}{{t}^{3}}}{\tan k} \cdot \frac{\frac{\ell}{\frac{\sin k}{\ell}}}{\color{blue}{\left(1 + 1\right) + {\left(\frac{k}{t}\right)}^{2}}} \]
      metadata-eval [=>] 7.5	\[ \frac{\frac{2}{{t}^{3}}}{\tan k} \cdot \frac{\frac{\ell}{\frac{\sin k}{\ell}}}{\color{blue}{2} + {\left(\frac{k}{t}\right)}^{2}} \]

   3. Applied egg-rr 9.0%

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

   4. Taylor expanded in k around inf 63.2%

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

   5. Simplified 66.2%

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

      [Start] 63.2	\[ \frac{\ell \cdot 2}{\frac{{k}^{2} \cdot \left({\sin k}^{2} \cdot t\right)}{\cos k \cdot \ell}} \]
      times-frac [=>] 64.2	\[ \frac{\ell \cdot 2}{\color{blue}{\frac{{k}^{2}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{\ell}}} \]
      unpow2 [=>] 64.2	\[ \frac{\ell \cdot 2}{\frac{\color{blue}{k \cdot k}}{\cos k} \cdot \frac{{\sin k}^{2} \cdot t}{\ell}} \]
      *-commutative [=>] 64.2	\[ \frac{\ell \cdot 2}{\frac{k \cdot k}{\cos k} \cdot \frac{\color{blue}{t \cdot {\sin k}^{2}}}{\ell}} \]
      associate-/l* [=>] 66.2	\[ \frac{\ell \cdot 2}{\frac{k \cdot k}{\cos k} \cdot \color{blue}{\frac{t}{\frac{\ell}{{\sin k}^{2}}}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-80} \lor \neg \left(t \leq 2.8 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{2}{\frac{\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)}{\frac{\frac{\ell}{t}}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \ell}{\frac{k \cdot k}{\cos k} \cdot \frac{t}{\frac{\ell}{{\sin k}^{2}}}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	80.1%
Cost	20488

\[\begin{array}{l} t_1 := \frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;2 \cdot \frac{\cos k}{\frac{\left(k \cdot k\right) \cdot \left(t \cdot {\sin k}^{2}\right)}{\ell \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{1}{\frac{t}{k} \cdot \frac{t}{k}}\right)\right)\right)}\\ \end{array} \]

Alternative 2
Accuracy	82.4%
Cost	20488

\[\begin{array}{l} t_1 := \frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{\frac{k \cdot k}{\cos k} \cdot \left(\frac{t}{\ell} \cdot \frac{{\sin k}^{2}}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{1}{\frac{t}{k} \cdot \frac{t}{k}}\right)\right)\right)}\\ \end{array} \]

Alternative 3
Accuracy	82.2%
Cost	20488

\[\begin{array}{l} t_1 := \frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \ell}{\frac{k \cdot k}{\cos k} \cdot \frac{t}{\frac{\ell}{{\sin k}^{2}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{1}{\frac{t}{k} \cdot \frac{t}{k}}\right)\right)\right)}\\ \end{array} \]

Alternative 4
Accuracy	78.4%
Cost	14920

\[\begin{array}{l} t_1 := \frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-152}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-105}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{1}{\frac{t}{k} \cdot \frac{t}{k}}\right)\right)\right)}\\ \end{array} \]

Alternative 5
Accuracy	78.4%
Cost	14793

\[\begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-149} \lor \neg \left(t \leq 4 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{2}{\frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}} \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{k}{t \cdot \frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \end{array} \]

Alternative 6
Accuracy	78.4%
Cost	14793

\[\begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{-152} \lor \neg \left(t \leq 1.3 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{2}{\frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}} \cdot \left(\tan k \cdot \left(1 + \left(1 + \frac{\frac{k}{t}}{\frac{t}{k}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \end{array} \]

Alternative 7
Accuracy	69.0%
Cost	14468

\[\begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-139}:\\ \;\;\;\;\frac{2}{\frac{t \cdot \frac{t \cdot k}{\ell}}{\frac{\ell}{t}} \cdot \left(\tan k \cdot \left(1 + \left({\left(\frac{k}{t}\right)}^{2} + 1\right)\right)\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-59}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 8
Accuracy	67.4%
Cost	13512

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{2}{\frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}} \cdot \left(2 \cdot k\right)}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-63}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 9
Accuracy	65.0%
Cost	7620

\[\begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{2}{\frac{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)}{\frac{\ell}{t}} \cdot \left(2 \cdot k\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-57}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{{t}^{3}} \cdot \left(-\frac{\ell}{-k}\right)\\ \end{array} \]

Alternative 10
Accuracy	61.8%
Cost	7432

\[\begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot t}}{t \cdot \left(k \cdot \frac{k}{\ell}\right)}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{{t}^{3}} \cdot \left(-\frac{\ell}{-k}\right)\\ \end{array} \]

Alternative 11
Accuracy	61.7%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot t}}{t \cdot \left(k \cdot \frac{k}{\ell}\right)}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-54}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k} \cdot \frac{\ell}{k \cdot {t}^{3}}\\ \end{array} \]

Alternative 12
Accuracy	61.5%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot t}}{t \cdot \left(k \cdot \frac{k}{\ell}\right)}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-54}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{k}{\ell} \cdot \left(k \cdot {t}^{3}\right)}\\ \end{array} \]

Alternative 13
Accuracy	55.3%
Cost	1360

\[\begin{array}{l} t_1 := \frac{\ell}{t \cdot t} \cdot \frac{\frac{\ell}{k \cdot k}}{t}\\ \mathbf{if}\;k \leq -1.25 \cdot 10^{+52}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\ell}{\frac{t \cdot \left(k \cdot k\right)}{\ell}}\\ \mathbf{elif}\;k \leq -9 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{\left(\ell \cdot \ell\right) \cdot \frac{-0.3333333333333333}{t}}{k}}{k}\\ \mathbf{elif}\;k \leq 9 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \left(\ell \cdot \frac{-0.3333333333333333}{k}\right)}{t \cdot k}\\ \end{array} \]

Alternative 14
Accuracy	55.3%
Cost	1360

\[\begin{array}{l} t_1 := \frac{\ell}{t} \cdot \frac{\frac{\ell}{k \cdot k}}{t \cdot t}\\ \mathbf{if}\;k \leq -2.5 \cdot 10^{+52}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\ell}{\frac{t \cdot \left(k \cdot k\right)}{\ell}}\\ \mathbf{elif}\;k \leq -9 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{\left(\ell \cdot \ell\right) \cdot \frac{-0.3333333333333333}{t}}{k}}{k}\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell \cdot \left(\ell \cdot \frac{-0.3333333333333333}{k}\right)}{t \cdot k}\\ \end{array} \]

Alternative 15
Accuracy	60.4%
Cost	1352

\[\begin{array}{l} t_1 := k \cdot \frac{k}{\ell}\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot t}}{t \cdot t_1}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-57}:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \left(-0.3333333333333333 + \frac{\frac{2}{k}}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot t_1}\\ \end{array} \]

Alternative 16
Accuracy	46.9%
Cost	1224

\[\begin{array}{l} t_1 := \frac{t}{\ell} \cdot k\\ \mathbf{if}\;\ell \cdot \ell \leq 4 \cdot 10^{+61}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\frac{\ell}{k}}{t_1}\\ \mathbf{elif}\;\ell \cdot \ell \leq 10^{+302}:\\ \;\;\;\;\left(\ell \cdot \ell\right) \cdot \frac{-0.3333333333333333}{k \cdot \left(t \cdot k\right)}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\ell}{k \cdot t_1}\\ \end{array} \]

Alternative 17
Accuracy	46.8%
Cost	1224

\[\begin{array}{l} t_1 := \frac{t}{\ell} \cdot k\\ \mathbf{if}\;\ell \cdot \ell \leq 4 \cdot 10^{+61}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\frac{\ell}{k}}{t_1}\\ \mathbf{elif}\;\ell \cdot \ell \leq 10^{+302}:\\ \;\;\;\;\left(\ell \cdot \ell\right) \cdot \frac{\frac{-0.3333333333333333}{k}}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\ell}{k \cdot t_1}\\ \end{array} \]

Alternative 18
Accuracy	56.6%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;k \leq -3.4 \cdot 10^{+81} \lor \neg \left(k \leq 4 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{\ell \cdot \left(\ell \cdot \frac{-0.3333333333333333}{k}\right)}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot \left(k \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 19
Accuracy	57.2%
Cost	1096

\[\begin{array}{l} t_1 := k \cdot \frac{k}{\ell}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{\ell}{t \cdot t}}{t \cdot t_1}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{\ell \cdot \left(\ell \cdot \frac{-0.3333333333333333}{k}\right)}{t \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{t}}{\left(t \cdot t\right) \cdot t_1}\\ \end{array} \]

Alternative 20
Accuracy	46.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1.4 \cdot 10^{+39} \lor \neg \left(\ell \leq 1.25 \cdot 10^{+143}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\ell}{\frac{t \cdot \left(k \cdot k\right)}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\ell}{k} \cdot \left(\ell \cdot \frac{-0.3333333333333333}{t}\right)}{k}\\ \end{array} \]

Alternative 21
Accuracy	48.2%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1.6 \cdot 10^{+39} \lor \neg \left(\ell \leq 8.5 \cdot 10^{+118}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\ell}{\frac{t \cdot \left(k \cdot k\right)}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(\ell \cdot \ell\right) \cdot \frac{-0.3333333333333333}{t}}{k}}{k}\\ \end{array} \]

Alternative 22
Accuracy	45.3%
Cost	704

\[-0.3333333333333333 \cdot \left(\frac{\ell}{k} \cdot \frac{\frac{\ell}{t}}{k}\right) \]

Alternative 23
Accuracy	46.5%
Cost	704

\[-0.3333333333333333 \cdot \frac{\ell}{k \cdot \left(\frac{t}{\ell} \cdot k\right)} \]

Reproduce

herbie shell --seed 2023122 
(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))))