Toniolo and Linder, Equation (10-)

Average Error: 75.34% → 1.74%

Time: 27.8s

Precision: binary64

Cost: 14025

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1 \cdot 10^{-210} \lor \neg \left(\ell \leq 5 \cdot 10^{-207}\right):\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{k} \cdot \frac{\frac{\ell}{k \cdot \sin k}}{t}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{\frac{\ell}{k}}{k}}{t \cdot \left(\sin k \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

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 (<= l -1e-210) (not (<= l 5e-207)))
   (* 2.0 (/ (* (/ l k) (/ (/ l (* k (sin k))) t)) (tan k)))
   (/ (* 2.0 (/ (/ l k) k)) (* t (* (sin k) (/ k l))))))

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 ((l <= -1e-210) || !(l <= 5e-207)) {
		tmp = 2.0 * (((l / k) * ((l / (k * sin(k))) / t)) / tan(k));
	} else {
		tmp = (2.0 * ((l / k) / k)) / (t * (sin(k) * (k / l)));
	}
	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 ((l <= (-1d-210)) .or. (.not. (l <= 5d-207))) then
        tmp = 2.0d0 * (((l / k) * ((l / (k * sin(k))) / t)) / tan(k))
    else
        tmp = (2.0d0 * ((l / k) / k)) / (t * (sin(k) * (k / l)))
    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 ((l <= -1e-210) || !(l <= 5e-207)) {
		tmp = 2.0 * (((l / k) * ((l / (k * Math.sin(k))) / t)) / Math.tan(k));
	} else {
		tmp = (2.0 * ((l / k) / k)) / (t * (Math.sin(k) * (k / l)));
	}
	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 (l <= -1e-210) or not (l <= 5e-207):
		tmp = 2.0 * (((l / k) * ((l / (k * math.sin(k))) / t)) / math.tan(k))
	else:
		tmp = (2.0 * ((l / k) / k)) / (t * (math.sin(k) * (k / l)))
	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 ((l <= -1e-210) || !(l <= 5e-207))
		tmp = Float64(2.0 * Float64(Float64(Float64(l / k) * Float64(Float64(l / Float64(k * sin(k))) / t)) / tan(k)));
	else
		tmp = Float64(Float64(2.0 * Float64(Float64(l / k) / k)) / Float64(t * Float64(sin(k) * Float64(k / l))));
	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 ((l <= -1e-210) || ~((l <= 5e-207)))
		tmp = 2.0 * (((l / k) * ((l / (k * sin(k))) / t)) / tan(k));
	else
		tmp = (2.0 * ((l / k) / k)) / (t * (sin(k) * (k / l)));
	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[l, -1e-210], N[Not[LessEqual[l, 5e-207]], $MachinePrecision]], N[(2.0 * N[(N[(N[(l / k), $MachinePrecision] * N[(N[(l / N[(k * N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(N[(l / k), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision] / N[(t * N[(N[Sin[k], $MachinePrecision] * N[(k / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -1e-210 or 5.00000000000000014e-207 < l

   1. Initial program 77.16

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

   2. Simplified 64.77

      \[\leadsto \color{blue}{\frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left({\left(\frac{k}{t}\right)}^{2} + 0\right)\right)}} \]
      Proof

      [Start] 77.16	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)} \]
      *-commutative [=>] 77.16	\[ \frac{2}{\color{blue}{\left(\tan k \cdot \left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right)\right)} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)} \]
      associate-*l* [=>] 77.11	\[ \frac{2}{\color{blue}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)\right)}} \]
      +-commutative [=>] 77.11	\[ \frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\color{blue}{\left({\left(\frac{k}{t}\right)}^{2} + 1\right)} - 1\right)\right)} \]
      associate--l+ [=>] 64.77	\[ \frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \color{blue}{\left({\left(\frac{k}{t}\right)}^{2} + \left(1 - 1\right)\right)}\right)} \]
      metadata-eval [=>] 64.77	\[ \frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left({\left(\frac{k}{t}\right)}^{2} + \color{blue}{0}\right)\right)} \]

   3. Taylor expanded in t around 0 36.48

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

   4. Simplified 26.22

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

      [Start] 36.48	\[ \frac{2}{\tan k \cdot \frac{{k}^{2} \cdot \left(\sin k \cdot t\right)}{{\ell}^{2}}} \]
      associate-*r* [=>] 37.67	\[ \frac{2}{\tan k \cdot \frac{\color{blue}{\left({k}^{2} \cdot \sin k\right) \cdot t}}{{\ell}^{2}}} \]
      unpow2 [=>] 37.67	\[ \frac{2}{\tan k \cdot \frac{\left({k}^{2} \cdot \sin k\right) \cdot t}{\color{blue}{\ell \cdot \ell}}} \]
      times-frac [=>] 26.24	\[ \frac{2}{\tan k \cdot \color{blue}{\left(\frac{{k}^{2} \cdot \sin k}{\ell} \cdot \frac{t}{\ell}\right)}} \]
      unpow2 [=>] 26.24	\[ \frac{2}{\tan k \cdot \left(\frac{\color{blue}{\left(k \cdot k\right)} \cdot \sin k}{\ell} \cdot \frac{t}{\ell}\right)} \]
      associate-*l* [=>] 26.22	\[ \frac{2}{\tan k \cdot \left(\frac{\color{blue}{k \cdot \left(k \cdot \sin k\right)}}{\ell} \cdot \frac{t}{\ell}\right)} \]

   5. Applied egg-rr 16.41

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

   6. Applied egg-rr 1.85

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

   if -1e-210 < l < 5.00000000000000014e-207

   1. Initial program 68.95

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

   2. Simplified 55.11

      \[\leadsto \color{blue}{\frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left({\left(\frac{k}{t}\right)}^{2} + 0\right)\right)}} \]
      Proof

      [Start] 68.95	\[ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)} \]
      *-commutative [=>] 68.95	\[ \frac{2}{\color{blue}{\left(\tan k \cdot \left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right)\right)} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)} \]
      associate-*l* [=>] 68.95	\[ \frac{2}{\color{blue}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)\right)}} \]
      +-commutative [=>] 68.95	\[ \frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left(\color{blue}{\left({\left(\frac{k}{t}\right)}^{2} + 1\right)} - 1\right)\right)} \]
      associate--l+ [=>] 55.11	\[ \frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \color{blue}{\left({\left(\frac{k}{t}\right)}^{2} + \left(1 - 1\right)\right)}\right)} \]
      metadata-eval [=>] 55.11	\[ \frac{2}{\tan k \cdot \left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \left({\left(\frac{k}{t}\right)}^{2} + \color{blue}{0}\right)\right)} \]

   3. Taylor expanded in t around 0 26.84

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

   4. Simplified 19.25

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

      [Start] 26.84	\[ \frac{2}{\tan k \cdot \frac{{k}^{2} \cdot \left(\sin k \cdot t\right)}{{\ell}^{2}}} \]
      associate-*r* [=>] 27.36	\[ \frac{2}{\tan k \cdot \frac{\color{blue}{\left({k}^{2} \cdot \sin k\right) \cdot t}}{{\ell}^{2}}} \]
      unpow2 [=>] 27.36	\[ \frac{2}{\tan k \cdot \frac{\left({k}^{2} \cdot \sin k\right) \cdot t}{\color{blue}{\ell \cdot \ell}}} \]
      times-frac [=>] 19.25	\[ \frac{2}{\tan k \cdot \color{blue}{\left(\frac{{k}^{2} \cdot \sin k}{\ell} \cdot \frac{t}{\ell}\right)}} \]
      unpow2 [=>] 19.25	\[ \frac{2}{\tan k \cdot \left(\frac{\color{blue}{\left(k \cdot k\right)} \cdot \sin k}{\ell} \cdot \frac{t}{\ell}\right)} \]
      associate-*l* [=>] 19.25	\[ \frac{2}{\tan k \cdot \left(\frac{\color{blue}{k \cdot \left(k \cdot \sin k\right)}}{\ell} \cdot \frac{t}{\ell}\right)} \]

   5. Applied egg-rr 14.74

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

   6. Simplified 0.24

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

      [Start] 14.74	\[ \frac{\frac{2}{\tan k} \cdot \frac{\ell}{t}}{k \cdot \sin k} \cdot \frac{\ell}{k} \]
      *-commutative [=>] 14.74	\[ \color{blue}{\frac{\ell}{k} \cdot \frac{\frac{2}{\tan k} \cdot \frac{\ell}{t}}{k \cdot \sin k}} \]
      associate-/l* [=>] 14.75	\[ \frac{\ell}{k} \cdot \color{blue}{\frac{\frac{2}{\tan k}}{\frac{k \cdot \sin k}{\frac{\ell}{t}}}} \]
      associate-*r/ [=>] 13.05	\[ \color{blue}{\frac{\frac{\ell}{k} \cdot \frac{2}{\tan k}}{\frac{k \cdot \sin k}{\frac{\ell}{t}}}} \]
      associate-/r/ [=>] 9.51	\[ \frac{\frac{\ell}{k} \cdot \frac{2}{\tan k}}{\color{blue}{\frac{k \cdot \sin k}{\ell} \cdot t}} \]
      *-commutative [=>] 9.51	\[ \frac{\frac{\ell}{k} \cdot \frac{2}{\tan k}}{\frac{\color{blue}{\sin k \cdot k}}{\ell} \cdot t} \]
      *-rgt-identity [<=] 9.51	\[ \frac{\frac{\ell}{k} \cdot \frac{2}{\tan k}}{\frac{\sin k \cdot \color{blue}{\left(k \cdot 1\right)}}{\ell} \cdot t} \]
      associate-*r/ [<=] 0.24	\[ \frac{\frac{\ell}{k} \cdot \frac{2}{\tan k}}{\color{blue}{\left(\sin k \cdot \frac{k \cdot 1}{\ell}\right)} \cdot t} \]
      *-rgt-identity [=>] 0.24	\[ \frac{\frac{\ell}{k} \cdot \frac{2}{\tan k}}{\left(\sin k \cdot \frac{\color{blue}{k}}{\ell}\right) \cdot t} \]

   7. Taylor expanded in k around 0 10.59

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

   8. Simplified 1.32

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

      [Start] 10.59	\[ \frac{2 \cdot \frac{\ell}{{k}^{2}}}{\left(\sin k \cdot \frac{k}{\ell}\right) \cdot t} \]
      unpow2 [=>] 10.59	\[ \frac{2 \cdot \frac{\ell}{\color{blue}{k \cdot k}}}{\left(\sin k \cdot \frac{k}{\ell}\right) \cdot t} \]
      associate-/r* [=>] 1.32	\[ \frac{2 \cdot \color{blue}{\frac{\frac{\ell}{k}}{k}}}{\left(\sin k \cdot \frac{k}{\ell}\right) \cdot t} \]

3. Recombined 2 regimes into one program.

4. Final simplification 1.74

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1 \cdot 10^{-210} \lor \neg \left(\ell \leq 5 \cdot 10^{-207}\right):\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{k} \cdot \frac{\frac{\ell}{k \cdot \sin k}}{t}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{\frac{\ell}{k}}{k}}{t \cdot \left(\sin k \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	5.8%
Cost	14025

\[\begin{array}{l} \mathbf{if}\;k \leq -7.8 \cdot 10^{-31} \lor \neg \left(k \leq 3.45 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\ell}{k \cdot \sin k} \cdot \left(\frac{\ell}{t} \cdot \frac{2}{k \cdot \tan k}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \frac{\frac{\ell}{k}}{k}}{t \cdot \left(\sin k \cdot \frac{k}{\ell}\right)}\\ \end{array} \]

Alternative 2
Error	5.79%
Cost	14024

\[\begin{array}{l} \mathbf{if}\;k \leq -5 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{2}{\tan k} \cdot \frac{\ell}{t}}{k} \cdot \frac{\frac{\ell}{k}}{\sin k}\\ \mathbf{elif}\;k \leq 7.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{2 \cdot \frac{\frac{\ell}{k}}{k}}{t \cdot \left(\sin k \cdot \frac{k}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{k \cdot \sin k} \cdot \left(\frac{\ell}{t} \cdot \frac{2}{k \cdot \tan k}\right)\\ \end{array} \]

Alternative 3
Error	0.56%
Cost	13760

\[\frac{\frac{\ell}{k} \cdot \frac{2}{\tan k}}{\frac{k}{\frac{\ell}{\sin k}} \cdot t} \]

Alternative 4
Error	0.52%
Cost	13760

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

Alternative 5
Error	36.96%
Cost	7360

\[\frac{\ell}{k} \cdot \frac{\frac{\frac{\frac{\ell}{k} \cdot 2}{k}}{t}}{\sin k} \]

Alternative 6
Error	35.99%
Cost	7360

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

Alternative 7
Error	42.22%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{-195}:\\ \;\;\;\;2 \cdot \frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot t}}{k \cdot k}\\ \mathbf{elif}\;\ell \leq -1 \cdot 10^{-266}:\\ \;\;\;\;2 \cdot \left(\ell \cdot \frac{\ell}{\left(k \cdot k\right) \cdot \left(k \cdot \left(k \cdot t\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{\ell}{t} \cdot \frac{\frac{\ell}{k \cdot k}}{k \cdot k}\right)\\ \end{array} \]

Alternative 8
Error	41.71%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;\ell \leq -2.6 \cdot 10^{-196}:\\ \;\;\;\;2 \cdot \frac{\ell \cdot \frac{\frac{\ell}{k}}{k \cdot t}}{k \cdot k}\\ \mathbf{elif}\;\ell \leq -1.5 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \left(\ell \cdot \frac{\ell}{\left(k \cdot k\right) \cdot \left(k \cdot \left(k \cdot t\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{\ell}{k \cdot \frac{k}{\frac{\ell}{t}}}}{k \cdot k}\\ \end{array} \]

Alternative 9
Error	44.67%
Cost	960

\[2 \cdot \left(\ell \cdot \frac{\ell}{\left(k \cdot k\right) \cdot \left(k \cdot \left(k \cdot t\right)\right)}\right) \]

Alternative 10
Error	42.72%
Cost	960

\[2 \cdot \left(\frac{\ell}{t} \cdot \frac{\frac{\ell}{k \cdot k}}{k \cdot k}\right) \]

Alternative 11
Error	38.88%
Cost	960

\[\frac{2 \cdot \frac{\ell}{k \cdot k}}{t \cdot \frac{k}{\frac{\ell}{k}}} \]

Reproduce

herbie shell --seed 2023089 
(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))))