Average Error: 31.9 → 3.6
Time: 31.0s
Precision: binary64
Cost: 20872
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \]
↓
\[\begin{array}{l} t_1 := \frac{2}{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)} \cdot \frac{\frac{\frac{\ell}{t}}{2 + {\left(\frac{k}{t}\right)}^{2}}}{\tan k}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-60}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{t \cdot k}}{k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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
         (*
          (/ 2.0 (* t (* (/ t l) (sin k))))
          (/ (/ (/ l t) (+ 2.0 (pow (/ k t) 2.0))) (tan k)))))
   (if (<= t -1e-52)
     t_1
     (if (<= t 1e-60)
       (* (* 2.0 (/ (/ l (* t k)) k)) (/ (/ l (sin k)) (tan k)))
       t_1))))
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 * ((t / l) * sin(k)))) * (((l / t) / (2.0 + pow((k / t), 2.0))) / tan(k));
	double tmp;
	if (t <= -1e-52) {
		tmp = t_1;
	} else if (t <= 1e-60) {
		tmp = (2.0 * ((l / (t * k)) / k)) * ((l / sin(k)) / tan(k));
	} else {
		tmp = t_1;
	}
	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 = (2.0d0 / (t * ((t / l) * sin(k)))) * (((l / t) / (2.0d0 + ((k / t) ** 2.0d0))) / tan(k))
    if (t <= (-1d-52)) then
        tmp = t_1
    else if (t <= 1d-60) then
        tmp = (2.0d0 * ((l / (t * k)) / k)) * ((l / sin(k)) / tan(k))
    else
        tmp = t_1
    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 = (2.0 / (t * ((t / l) * Math.sin(k)))) * (((l / t) / (2.0 + Math.pow((k / t), 2.0))) / Math.tan(k));
	double tmp;
	if (t <= -1e-52) {
		tmp = t_1;
	} else if (t <= 1e-60) {
		tmp = (2.0 * ((l / (t * k)) / k)) * ((l / Math.sin(k)) / Math.tan(k));
	} else {
		tmp = t_1;
	}
	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 = (2.0 / (t * ((t / l) * math.sin(k)))) * (((l / t) / (2.0 + math.pow((k / t), 2.0))) / math.tan(k))
	tmp = 0
	if t <= -1e-52:
		tmp = t_1
	elif t <= 1e-60:
		tmp = (2.0 * ((l / (t * k)) / k)) * ((l / math.sin(k)) / math.tan(k))
	else:
		tmp = t_1
	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(2.0 / Float64(t * Float64(Float64(t / l) * sin(k)))) * Float64(Float64(Float64(l / t) / Float64(2.0 + (Float64(k / t) ^ 2.0))) / tan(k)))
	tmp = 0.0
	if (t <= -1e-52)
		tmp = t_1;
	elseif (t <= 1e-60)
		tmp = Float64(Float64(2.0 * Float64(Float64(l / Float64(t * k)) / k)) * Float64(Float64(l / sin(k)) / tan(k)));
	else
		tmp = t_1;
	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 = (2.0 / (t * ((t / l) * sin(k)))) * (((l / t) / (2.0 + ((k / t) ^ 2.0))) / tan(k));
	tmp = 0.0;
	if (t <= -1e-52)
		tmp = t_1;
	elseif (t <= 1e-60)
		tmp = (2.0 * ((l / (t * k)) / k)) * ((l / sin(k)) / tan(k));
	else
		tmp = t_1;
	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[(2.0 / N[(t * N[(N[(t / l), $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(l / t), $MachinePrecision] / N[(2.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e-52], t$95$1, If[LessEqual[t, 1e-60], N[(N[(2.0 * N[(N[(l / N[(t * k), $MachinePrecision]), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision] * N[(N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$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)}
↓
\begin{array}{l}
t_1 := \frac{2}{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)} \cdot \frac{\frac{\frac{\ell}{t}}{2 + {\left(\frac{k}{t}\right)}^{2}}}{\tan k}\\
\mathbf{if}\;t \leq -1 \cdot 10^{-52}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t \leq 10^{-60}:\\
\;\;\;\;\left(2 \cdot \frac{\frac{\ell}{t \cdot k}}{k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\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 t < -1e-52 or 9.9999999999999997e-61 < t

    1. Initial program 22.0

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

    2. Applied egg-rr20.9

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

    3. Applied egg-rr11.6

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

    4. Applied egg-rr7.8

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

    5. Applied egg-rr2.8

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

    if -1e-52 < t < 9.9999999999999997e-61

    1. Initial program 56.4

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

    2. Simplified53.5

      \[\leadsto \color{blue}{\frac{\frac{2}{\frac{{t}^{3}}{\ell}}}{2 + {\left(\frac{k}{t}\right)}^{2}} \cdot \frac{\frac{\ell}{\sin k}}{\tan k}} \]
      Proof
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (Rewrite<= metadata-eval (+.f64 1 1)) (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 1 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))) (/.f64 (/.f64 l (sin.f64 k)) (tan.f64 k))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)) (Rewrite<= associate-/r*_binary64 (/.f64 l (*.f64 (sin.f64 k) (tan.f64 k))))): 15 points increase in error, 7 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (/.f64 2 (/.f64 (pow.f64 t 3) l)) l) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k))))): 11 points increase in error, 12 points decrease in error
      (/.f64 (Rewrite<= associate-/r/_binary64 (/.f64 2 (/.f64 (/.f64 (pow.f64 t 3) l) l))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 4 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-/r*_binary64 (/.f64 (pow.f64 t 3) (*.f64 l l)))) (*.f64 (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1) (*.f64 (sin.f64 k) (tan.f64 k)))): 35 points increase in error, 2 points decrease in error
      (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (/.f64 2 (/.f64 (pow.f64 t 3) (*.f64 l l))) (*.f64 (sin.f64 k) (tan.f64 k))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))): 2 points increase in error, 1 points decrease in error
      (/.f64 (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (*.f64 (sin.f64 k) (tan.f64 k))))) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)): 1 points increase in error, 3 points decrease in error
      (/.f64 (/.f64 2 (Rewrite<= associate-*l*_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)): 2 points increase in error, 35 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.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)))): 1 points increase in error, 1 points decrease in error

    3. Taylor expanded in t around 0 20.5

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

    4. Applied egg-rr12.6

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

    5. Applied egg-rr5.6

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

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-52}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)} \cdot \frac{\frac{\frac{\ell}{t}}{2 + {\left(\frac{k}{t}\right)}^{2}}}{\tan k}\\ \mathbf{elif}\;t \leq 10^{-60}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{t \cdot k}}{k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot \left(\frac{t}{\ell} \cdot \sin k\right)} \cdot \frac{\frac{\frac{\ell}{t}}{2 + {\left(\frac{k}{t}\right)}^{2}}}{\tan k}\\ \end{array} \]

Alternatives

Alternative 1
Error9.7
Cost20172
\[\begin{array}{l} t_1 := \frac{2}{\frac{\left(k \cdot \left(t \cdot \frac{t}{\ell}\right)\right) \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \tan k\right)}{\frac{\ell}{t}}}\\ t_2 := \left(2 \cdot \frac{\frac{\ell}{t \cdot k}}{k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{if}\;k \leq -1 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 10^{-80}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\ell \cdot \frac{1}{k}}\right)}^{2}}{t}\right)}^{3}\\ \mathbf{elif}\;k \leq 1150000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error10.2
Cost14736
\[\begin{array}{l} t_1 := \frac{2}{\frac{\left(k \cdot \left(t \cdot \frac{t}{\ell}\right)\right) \cdot \left(\left(2 + {\left(\frac{k}{t}\right)}^{2}\right) \cdot \tan k\right)}{\frac{\ell}{t}}}\\ t_2 := \left(2 \cdot \frac{\frac{\ell}{t \cdot k}}{k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{if}\;k \leq -1 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -2.5 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 10^{-190}:\\ \;\;\;\;\frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \mathbf{elif}\;k \leq 1150000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error12.5
Cost14024
\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{\ell}{\sin k}}{\tan k} \cdot \left(2 \cdot \frac{\frac{\ell}{k}}{t \cdot k}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]
Alternative 4
Error12.5
Cost14024
\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;\left(2 \cdot \frac{\frac{\ell}{t \cdot k}}{k}\right) \cdot \frac{\frac{\ell}{\sin k}}{\tan k}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]
Alternative 5
Error20.2
Cost13644
\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot k}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-50}:\\ \;\;\;\;\frac{\ell \cdot \frac{\ell}{k}}{k \cdot {t}^{3}}\\ \mathbf{elif}\;t \leq 10^{-40}:\\ \;\;\;\;\left(2 \cdot \left(t_1 \cdot \frac{1}{t}\right)\right) \cdot \left(t_1 + \ell \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k \cdot {t}^{1.5}}\right)}^{2}\\ \end{array} \]
Alternative 6
Error21.0
Cost7436
\[\begin{array}{l} t_1 := \frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ t_2 := \frac{\ell}{k \cdot k}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-50}:\\ \;\;\;\;\frac{\ell \cdot \frac{\ell}{k}}{k \cdot {t}^{3}}\\ \mathbf{elif}\;t \leq 10^{-60}:\\ \;\;\;\;\left(2 \cdot \left(t_2 \cdot \frac{1}{t}\right)\right) \cdot \left(t_2 + \ell \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Error21.4
Cost7304
\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot k}\\ t_2 := \frac{\ell}{\frac{t \cdot {\left(t \cdot k\right)}^{2}}{\ell}}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-60}:\\ \;\;\;\;\left(2 \cdot \left(t_1 \cdot \frac{1}{t}\right)\right) \cdot \left(t_1 + \ell \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 8
Error22.6
Cost1608
\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot k}\\ t_2 := \frac{\frac{\ell}{t} \cdot \frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-15}:\\ \;\;\;\;\left(2 \cdot \left(t_1 \cdot \frac{1}{t}\right)\right) \cdot \left(t_1 + \ell \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error25.3
Cost1352
\[\begin{array}{l} t_1 := \frac{2}{\frac{2 \cdot \left(t \cdot \frac{k \cdot k}{\frac{\ell}{t}}\right)}{\frac{\ell}{t}}}\\ \mathbf{if}\;k \leq -1 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 10^{-115}:\\ \;\;\;\;\frac{\frac{\ell}{t} \cdot \frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error23.7
Cost1352
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t} \cdot \frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-15}:\\ \;\;\;\;\left(\frac{2}{k \cdot k} + -0.3333333333333333\right) \cdot \left(\ell \cdot \frac{\ell}{k \cdot \left(t \cdot k\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error22.9
Cost1352
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t} \cdot \frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-15}:\\ \;\;\;\;\left(\frac{\ell}{t \cdot k} \cdot \frac{\ell}{k}\right) \cdot \left(\frac{2}{k \cdot k} + -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error30.5
Cost1096
\[\begin{array}{l} t_1 := \frac{\ell}{k \cdot k} \cdot \frac{\frac{\ell}{t}}{t \cdot t}\\ \mathbf{if}\;\ell \leq -7.90254837226343 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 2.0470367011658363 \cdot 10^{-35}:\\ \;\;\;\;\frac{\left(1 + \ell \cdot \left(\ell \cdot -0.11666666666666667\right)\right) + -1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error27.7
Cost1096
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{\left(t \cdot t\right) \cdot \frac{k}{\frac{\ell}{k}}}}{t}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{\left(1 + \ell \cdot \left(\ell \cdot -0.11666666666666667\right)\right) + -1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error25.7
Cost1096
\[\begin{array}{l} t_1 := \frac{\frac{\ell}{t} \cdot \frac{\ell}{k}}{k \cdot \left(t \cdot t\right)}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{\left(1 + \ell \cdot \left(\ell \cdot -0.11666666666666667\right)\right) + -1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Error34.0
Cost964
\[\begin{array}{l} \mathbf{if}\;\ell \cdot \ell \leq 2 \cdot 10^{-29}:\\ \;\;\;\;\frac{\left(1 + \ell \cdot \left(\ell \cdot -0.11666666666666667\right)\right) + -1}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{\ell \cdot \ell}{\frac{t}{-0.11666666666666667}}\right) + -1\\ \end{array} \]
Alternative 16
Error34.9
Cost704
\[\left(1 + \frac{\ell \cdot \ell}{\frac{t}{-0.11666666666666667}}\right) + -1 \]
Alternative 17
Error44.8
Cost448
\[\frac{\ell}{t} \cdot \left(\ell \cdot -0.11666666666666667\right) \]
Alternative 18
Error42.8
Cost448
\[\frac{-0.11666666666666667 \cdot \left(\ell \cdot \ell\right)}{t} \]

Error

Reproduce

herbie shell --seed 2022315 
(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))))