Toniolo and Linder, Equation (10+)

Average Error: 32.8 → 6.1

Time: 27.6s

Precision: binary64

Cost: 39880

Math

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

↓

\[\begin{array}{l} t_1 := 2 + {\left(\frac{k}{t}\right)}^{2}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{-55}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\frac{\frac{\ell}{\tan k}}{t_1}}}{t} \cdot \sqrt[3]{\frac{\ell \cdot 2}{\sin k}}\right)}^{3}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-71}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \frac{t}{\frac{\ell}{k}}}{\ell} \cdot \left(\tan k \cdot \sin k\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{\frac{\ell}{\tan k \cdot t_1}} \cdot \frac{\sqrt[3]{\frac{2}{\frac{\sin k}{\ell}}}}{t}\right)}^{3}\\ \end{array} \]

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 (pow (/ k t) 2.0))))
   (if (<= t -7.8e-55)
     (pow
      (* (/ (cbrt (/ (/ l (tan k)) t_1)) t) (cbrt (/ (* l 2.0) (sin k))))
      3.0)
     (if (<= t 4e-71)
       (/ 2.0 (* (/ (* k (/ t (/ l k))) l) (* (tan k) (sin k))))
       (pow
        (* (cbrt (/ l (* (tan k) t_1))) (/ (cbrt (/ 2.0 (/ (sin k) l))) t))
        3.0)))))

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 t_1 = 2.0 + pow((k / t), 2.0);
	double tmp;
	if (t <= -7.8e-55) {
		tmp = pow(((cbrt(((l / tan(k)) / t_1)) / t) * cbrt(((l * 2.0) / sin(k)))), 3.0);
	} else if (t <= 4e-71) {
		tmp = 2.0 / (((k * (t / (l / k))) / l) * (tan(k) * sin(k)));
	} else {
		tmp = pow((cbrt((l / (tan(k) * t_1))) * (cbrt((2.0 / (sin(k) / l))) / t)), 3.0);
	}
	return tmp;
}

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 + Math.pow((k / t), 2.0);
	double tmp;
	if (t <= -7.8e-55) {
		tmp = Math.pow(((Math.cbrt(((l / Math.tan(k)) / t_1)) / t) * Math.cbrt(((l * 2.0) / Math.sin(k)))), 3.0);
	} else if (t <= 4e-71) {
		tmp = 2.0 / (((k * (t / (l / k))) / l) * (Math.tan(k) * Math.sin(k)));
	} else {
		tmp = Math.pow((Math.cbrt((l / (Math.tan(k) * t_1))) * (Math.cbrt((2.0 / (Math.sin(k) / l))) / t)), 3.0);
	}
	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)
	t_1 = Float64(2.0 + (Float64(k / t) ^ 2.0))
	tmp = 0.0
	if (t <= -7.8e-55)
		tmp = Float64(Float64(cbrt(Float64(Float64(l / tan(k)) / t_1)) / t) * cbrt(Float64(Float64(l * 2.0) / sin(k)))) ^ 3.0;
	elseif (t <= 4e-71)
		tmp = Float64(2.0 / Float64(Float64(Float64(k * Float64(t / Float64(l / k))) / l) * Float64(tan(k) * sin(k))));
	else
		tmp = Float64(cbrt(Float64(l / Float64(tan(k) * t_1))) * Float64(cbrt(Float64(2.0 / Float64(sin(k) / l))) / t)) ^ 3.0;
	end
	return 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[(2.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e-55], N[Power[N[(N[(N[Power[N[(N[(l / N[Tan[k], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 1/3], $MachinePrecision] / t), $MachinePrecision] * N[Power[N[(N[(l * 2.0), $MachinePrecision] / N[Sin[k], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], If[LessEqual[t, 4e-71], N[(2.0 / N[(N[(N[(k * N[(t / N[(l / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision] * N[(N[Tan[k], $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[Power[N[(l / N[(N[Tan[k], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] * N[(N[Power[N[(2.0 / N[(N[Sin[k], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.8e-55

   1. Initial program 22.8

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

   2. Simplified 19.4

      \[\leadsto \color{blue}{\frac{2}{{t}^{3} \cdot \sin k} \cdot \frac{\ell}{\frac{2 + {\left(\frac{k}{t}\right)}^{2}}{\frac{\ell}{\tan k}}}} \]
      Proof
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (+.f64 (Rewrite<= metadata-eval (+.f64 1 1)) (pow.f64 (/.f64 k t) 2)) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 1 (pow.f64 (/.f64 k t) 2)))) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (tan.f64 k)) l)))): 3 points increase in error, 2 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) l))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 l l) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))))): 20 points increase in error, 4 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 2 (/.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (/.f64 (*.f64 l l) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))))): 6 points increase in error, 7 points decrease in error
      (/.f64 2 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) (*.f64 l l)))): 15 points increase in error, 15 points decrease in error
      (/.f64 2 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 l l)) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))))): 3 points increase in error, 14 points decrease in error
      (/.f64 2 (*.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))): 3 points increase in error, 6 points decrease in error
      (/.f64 2 (Rewrite<= associate-*l*_binary64 (*.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, 2 points decrease in error

   3. Applied egg-rr 15.6

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

   4. Applied egg-rr 6.8

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

   5. Simplified 6.8

      \[\leadsto {\left(\frac{\color{blue}{\sqrt[3]{\frac{\ell}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \cdot \sqrt[3]{\ell \cdot 2}}}{t \cdot \sqrt[3]{\sin k}}\right)}^{3} \]
      Proof
      (*.f64 (cbrt.f64 (/.f64 l (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (cbrt.f64 (*.f64 l 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (cbrt.f64 (*.f64 l 2))): 5 points increase in error, 7 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (cbrt.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 l)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (Rewrite<= unpow1/3_binary64 (pow.f64 (*.f64 2 l) 1/3))): 175 points increase in error, 30 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 (*.f64 2 l) 1/3) (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite=> unpow1/3_binary64 (cbrt.f64 (*.f64 2 l))) (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))): 30 points increase in error, 175 points decrease in error

   6. Applied egg-rr 6.7

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

   if -7.8e-55 < t < 3.9999999999999997e-71

   1. Initial program 57.0

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

   2. Simplified 56.9

      \[\leadsto \color{blue}{\frac{2}{\left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \frac{{t}^{3}}{\ell \cdot \ell}\right) \cdot \left(\sin k \cdot \tan k\right)}} \]
      Proof
      (/.f64 2 (*.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (*.f64 (+.f64 (Rewrite<= metadata-eval (+.f64 1 1)) (pow.f64 (/.f64 k t) 2)) (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (*.f64 (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 1 (pow.f64 (/.f64 k t) 2)))) (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (*.f64 (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)) (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k)))): 0 points increase in error, 0 points decrease in error
      (/.f64 2 (Rewrite<= associate-*r*_binary64 (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (*.f64 (sin.f64 k) (tan.f64 k)))))): 3 points increase in error, 3 points decrease in error
      (/.f64 2 (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))))): 1 points increase in error, 33 points decrease in error
      (/.f64 2 (Rewrite<= *-commutative_binary64 (*.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)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in k around inf 25.4

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

   4. Simplified 27.5

      \[\leadsto \frac{2}{\color{blue}{\left(\frac{k \cdot k}{\ell \cdot \ell} \cdot t\right)} \cdot \left(\sin k \cdot \tan k\right)} \]
      Proof
      (*.f64 (/.f64 (*.f64 k k) (*.f64 l l)) t): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 k 2)) (*.f64 l l)) t): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (pow.f64 k 2) (Rewrite<= unpow2_binary64 (pow.f64 l 2))) t): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 (pow.f64 k 2) (/.f64 (pow.f64 l 2) t))): 15 points increase in error, 23 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (pow.f64 k 2) t) (pow.f64 l 2))): 22 points increase in error, 14 points decrease in error

   5. Applied egg-rr 12.9

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

   6. Taylor expanded in k around 0 21.4

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

   7. Simplified 4.4

      \[\leadsto \frac{2}{\frac{\color{blue}{k \cdot \frac{t}{\frac{\ell}{k}}}}{\ell} \cdot \left(\sin k \cdot \tan k\right)} \]
      Proof
      (*.f64 k (/.f64 t (/.f64 l k))): 0 points increase in error, 0 points decrease in error
      (*.f64 k (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 t k) l))): 32 points increase in error, 24 points decrease in error
      (*.f64 k (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 k t)) l)): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 k (*.f64 k t)) l)): 37 points increase in error, 29 points decrease in error
      (/.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 k k) t)) l): 26 points increase in error, 31 points decrease in error
      (/.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 k 2)) t) l): 0 points increase in error, 0 points decrease in error

   if 3.9999999999999997e-71 < t

   1. Initial program 23.2

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

   2. Simplified 19.7

      \[\leadsto \color{blue}{\frac{2}{{t}^{3} \cdot \sin k} \cdot \frac{\ell}{\frac{2 + {\left(\frac{k}{t}\right)}^{2}}{\frac{\ell}{\tan k}}}} \]
      Proof
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (+.f64 (Rewrite<= metadata-eval (+.f64 1 1)) (pow.f64 (/.f64 k t) 2)) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 1 (pow.f64 (/.f64 k t) 2)))) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)) (/.f64 l (tan.f64 k))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (tan.f64 k)) l)))): 3 points increase in error, 2 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (/.f64 l (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) l))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 l l) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))))): 20 points increase in error, 4 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 2 (/.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (/.f64 (*.f64 l l) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))))): 6 points increase in error, 7 points decrease in error
      (/.f64 2 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) (*.f64 l l)))): 15 points increase in error, 15 points decrease in error
      (/.f64 2 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 l l)) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))))): 3 points increase in error, 14 points decrease in error
      (/.f64 2 (*.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))): 3 points increase in error, 6 points decrease in error
      (/.f64 2 (Rewrite<= associate-*l*_binary64 (*.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, 2 points decrease in error

   3. Applied egg-rr 15.6

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

   4. Applied egg-rr 6.9

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

   5. Simplified 6.9

      \[\leadsto {\left(\frac{\color{blue}{\sqrt[3]{\frac{\ell}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \cdot \sqrt[3]{\ell \cdot 2}}}{t \cdot \sqrt[3]{\sin k}}\right)}^{3} \]
      Proof
      (*.f64 (cbrt.f64 (/.f64 l (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (cbrt.f64 (*.f64 l 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (cbrt.f64 (*.f64 l 2))): 5 points increase in error, 7 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (cbrt.f64 (Rewrite<= *-commutative_binary64 (*.f64 2 l)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (Rewrite<= unpow1/3_binary64 (pow.f64 (*.f64 2 l) 1/3))): 175 points increase in error, 30 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 (*.f64 2 l) 1/3) (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite=> unpow1/3_binary64 (cbrt.f64 (*.f64 2 l))) (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))): 30 points increase in error, 175 points decrease in error

   6. Applied egg-rr 20.2

      \[\leadsto {\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\sqrt[3]{\frac{\frac{\ell}{\tan k}}{2 + {\left(\frac{k}{t}\right)}^{2}}}}{t} \cdot \sqrt[3]{\frac{\ell \cdot 2}{\sin k}}\right)} - 1\right)}}^{3} \]

   7. Simplified 6.9

      \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\ell}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \cdot \frac{\sqrt[3]{\frac{2}{\frac{\sin k}{\ell}}}}{t}\right)}}^{3} \]
      Proof
      (*.f64 (cbrt.f64 (/.f64 l (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (/.f64 (cbrt.f64 (/.f64 2 (/.f64 (sin.f64 k) l))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (/.f64 (cbrt.f64 (/.f64 2 (/.f64 (sin.f64 k) l))) t)): 2 points increase in error, 9 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (/.f64 (cbrt.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 2 l) (sin.f64 k)))) t)): 10 points increase in error, 3 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (/.f64 (cbrt.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 l 2)) (sin.f64 k))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k))) 1)) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 1 (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k))))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 t) (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k)))))): 20 points increase in error, 10 points decrease in error
      (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (Rewrite<= associate-/r/_binary64 (/.f64 1 (/.f64 t (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k))))))): 12 points increase in error, 21 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) 1) (/.f64 t (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k)))))): 19 points increase in error, 17 points decrease in error
      (/.f64 (Rewrite=> *-rgt-identity_binary64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (/.f64 t (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k))))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) t) (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k))))): 28 points increase in error, 23 points decrease in error
      (Rewrite<= expm1-log1p_binary64 (expm1.f64 (log1p.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) t) (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k))))))): 24 points increase in error, 10 points decrease in error
      (Rewrite<= expm1-def_binary64 (-.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 (/.f64 l (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) t) (cbrt.f64 (/.f64 (*.f64 l 2) (sin.f64 k)))))) 1)): 18 points increase in error, 95 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 6.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-55}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\frac{\frac{\ell}{\tan k}}{2 + {\left(\frac{k}{t}\right)}^{2}}}}{t} \cdot \sqrt[3]{\frac{\ell \cdot 2}{\sin k}}\right)}^{3}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-71}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \frac{t}{\frac{\ell}{k}}}{\ell} \cdot \left(\tan k \cdot \sin k\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{\frac{\ell}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \cdot \frac{\sqrt[3]{\frac{2}{\frac{\sin k}{\ell}}}}{t}\right)}^{3}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.1
Cost	39880

\[\begin{array}{l} t_1 := {\left(\sqrt[3]{\frac{\ell}{\tan k \cdot \left(2 + {\left(\frac{k}{t}\right)}^{2}\right)}} \cdot \frac{\sqrt[3]{\frac{2}{\frac{\sin k}{\ell}}}}{t}\right)}^{3}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{2}{\frac{k \cdot \frac{t}{\frac{\ell}{k}}}{\ell} \cdot \left(\tan k \cdot \sin k\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	9.9
Cost	39556

\[\begin{array}{l} t_1 := \frac{\sin k}{\ell}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+102}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\frac{2}{t_1}}}{t} \cdot \sqrt[3]{\frac{0.5}{\frac{t_1}{\cos k}}}\right)}^{3}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-54}:\\ \;\;\;\;\frac{\ell}{\sin k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\tan k \cdot \left(0.5 \cdot \frac{{t}^{3}}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 16500000:\\ \;\;\;\;\frac{2}{\frac{k \cdot \frac{t}{\frac{\ell}{k}}}{\ell} \cdot \left(\tan k \cdot \sin k\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{{\left(\frac{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}{\sqrt[3]{\ell}}\right)}^{3}}\\ \end{array} \]

Alternative 3
Error	10.6
Cost	27080

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+102}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\frac{2}{\frac{\sin k}{\ell}}}}{t} \cdot \sqrt[3]{\frac{\ell}{k} \cdot 0.5}\right)}^{3}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{\ell}{\sin k \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \left(\tan k \cdot \left(0.5 \cdot \frac{{t}^{3}}{\ell}\right)\right)\right)}\\ \mathbf{elif}\;t \leq 30500:\\ \;\;\;\;\frac{2}{\frac{k \cdot \frac{t}{\frac{\ell}{k}}}{\ell} \cdot \left(\tan k \cdot \sin k\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{{\left(\frac{t \cdot {\left(\sqrt[3]{k}\right)}^{2}}{\sqrt[3]{\ell}}\right)}^{3}}\\ \end{array} \]

Alternative 4
Error	10.9
Cost	26760

\[\begin{array}{l} t_1 := \frac{2}{\left(\tan k \cdot \sin k\right) \cdot \left(\frac{k}{\ell} \cdot \frac{t \cdot k}{\ell}\right)}\\ \mathbf{if}\;k \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-15}:\\ \;\;\;\;{\left(\frac{\sqrt[3]{\frac{2}{\frac{\sin k}{\ell}}}}{t} \cdot \sqrt[3]{\frac{\ell}{k} \cdot 0.5}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	10.9
Cost	19912

\[\begin{array}{l} t_1 := \frac{2}{\left(\tan k \cdot \sin k\right) \cdot \left(\frac{k}{\ell} \cdot \frac{t \cdot k}{\ell}\right)}\\ \mathbf{if}\;k \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-15}:\\ \;\;\;\;{\left(\frac{t}{{\left(\sqrt[3]{\frac{\ell}{k}}\right)}^{2}}\right)}^{-3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	13.3
Cost	14288

\[\begin{array}{l} t_1 := \tan k \cdot \sin k\\ t_2 := \ell \cdot \frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot k\right)\right)}\\ \mathbf{if}\;k \leq -0.000175:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 10^{+276}:\\ \;\;\;\;\frac{2}{t_1 \cdot \left(t \cdot \left(\frac{k}{\ell} \cdot \frac{k}{\ell}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	18.3
Cost	14024

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+55}:\\ \;\;\;\;\frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \mathbf{elif}\;t \leq 30000:\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{\ell}{k \cdot k}\right) \cdot \frac{2}{\tan k \cdot \sin k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 8
Error	13.3
Cost	14024

\[\begin{array}{l} t_1 := \ell \cdot \frac{2}{\left(\tan k \cdot \sin k\right) \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot k\right)\right)}\\ \mathbf{if}\;k \leq -0.17:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	13.2
Cost	14024

\[\begin{array}{l} t_1 := \tan k \cdot \sin k\\ \mathbf{if}\;k \leq -0.0038:\\ \;\;\;\;\ell \cdot \frac{2}{t_1 \cdot \left(\frac{k}{\ell} \cdot \left(t \cdot k\right)\right)}\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\ell \cdot \frac{\frac{\ell}{k}}{t \cdot k}}{t_1}\\ \end{array} \]

Alternative 10
Error	12.6
Cost	14024

\[\begin{array}{l} t_1 := \frac{2}{\left(\tan k \cdot \sin k\right) \cdot \left(\frac{k}{\ell} \cdot \frac{t \cdot k}{\ell}\right)}\\ \mathbf{if}\;k \leq -9.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	22.7
Cost	13512

\[\begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{2}{\frac{t}{\ell} \cdot \frac{{k}^{4}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]

Alternative 12
Error	23.0
Cost	7692

\[\begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{2}{\frac{t}{\ell} \cdot \frac{{k}^{4}}{\ell}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{2}{2 \cdot \left(t \cdot \frac{t \cdot t}{{\left(\frac{\ell}{k}\right)}^{2}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \end{array} \]

Alternative 13
Error	23.0
Cost	7564

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-144}:\\ \;\;\;\;\frac{2}{\frac{t}{\ell} \cdot \frac{{k}^{4}}{\ell}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{1}{t} \cdot \frac{{\left(\frac{\ell}{k}\right)}^{2}}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \end{array} \]

Alternative 14
Error	24.9
Cost	7304

\[\begin{array}{l} t_1 := 2 \cdot \left(\ell \cdot \left(\ell \cdot \frac{{k}^{-4}}{t}\right)\right)\\ \mathbf{if}\;k \leq -13500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	24.1
Cost	7304

\[\begin{array}{l} t_1 := \frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-76}:\\ \;\;\;\;2 \cdot \left(\ell \cdot \left(\frac{\ell}{t} \cdot {k}^{-4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	24.0
Cost	7304

\[\begin{array}{l} t_1 := \frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-71}:\\ \;\;\;\;2 \cdot \left({k}^{-4} \cdot \frac{\ell}{\frac{t}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	23.5
Cost	7304

\[\begin{array}{l} t_1 := \frac{\frac{\ell}{k}}{t \cdot t} \cdot \frac{\frac{\ell}{k}}{t}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{2}{\frac{t}{\ell} \cdot \frac{{k}^{4}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	29.0
Cost	832

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

Reproduce

herbie shell --seed 2022329 
(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))))