Toniolo and Linder, Equation (10-)

Percentage Accurate: 35.5% → 95.4%

Time: 24.5s

Alternatives: 9

Speedup: 3.8×

• 39.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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))))

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));
}

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

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));
}

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))

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

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

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]

Initial Program: 35.5% accurate, 1.0× speedup

Math

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

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))))

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));
}

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

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));
}

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))

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

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

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]

Alternative 1: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;k\_m \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot {\left(\frac{\sqrt{\frac{\cos k\_m}{t\_m}}}{\sin k\_m} \cdot \frac{\ell}{k\_m}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos k\_m \cdot \frac{\frac{\ell}{k\_m} \cdot \frac{\ell}{k\_m}}{t\_m \cdot {\sin k\_m}^{2}}\right)\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 5.8e-16)
    (* 2.0 (pow (* (/ (sqrt (/ (cos k_m) t_m)) (sin k_m)) (/ l k_m)) 2.0))
    (*
     2.0
     (* (cos k_m) (/ (* (/ l k_m) (/ l k_m)) (* t_m (pow (sin k_m) 2.0))))))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 5.8e-16) {
		tmp = 2.0 * pow(((sqrt((cos(k_m) / t_m)) / sin(k_m)) * (l / k_m)), 2.0);
	} else {
		tmp = 2.0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * pow(sin(k_m), 2.0))));
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 5.8d-16) then
        tmp = 2.0d0 * (((sqrt((cos(k_m) / t_m)) / sin(k_m)) * (l / k_m)) ** 2.0d0)
    else
        tmp = 2.0d0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * (sin(k_m) ** 2.0d0))))
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 5.8e-16) {
		tmp = 2.0 * Math.pow(((Math.sqrt((Math.cos(k_m) / t_m)) / Math.sin(k_m)) * (l / k_m)), 2.0);
	} else {
		tmp = 2.0 * (Math.cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * Math.pow(Math.sin(k_m), 2.0))));
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 5.8e-16:
		tmp = 2.0 * math.pow(((math.sqrt((math.cos(k_m) / t_m)) / math.sin(k_m)) * (l / k_m)), 2.0)
	else:
		tmp = 2.0 * (math.cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * math.pow(math.sin(k_m), 2.0))))
	return t_s * tmp

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 5.8e-16)
		tmp = Float64(2.0 * (Float64(Float64(sqrt(Float64(cos(k_m) / t_m)) / sin(k_m)) * Float64(l / k_m)) ^ 2.0));
	else
		tmp = Float64(2.0 * Float64(cos(k_m) * Float64(Float64(Float64(l / k_m) * Float64(l / k_m)) / Float64(t_m * (sin(k_m) ^ 2.0)))));
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 5.8e-16)
		tmp = 2.0 * (((sqrt((cos(k_m) / t_m)) / sin(k_m)) * (l / k_m)) ^ 2.0);
	else
		tmp = 2.0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * (sin(k_m) ^ 2.0))));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 5.8e-16], N[(2.0 * N[Power[N[(N[(N[Sqrt[N[(N[Cos[k$95$m], $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision] / N[Sin[k$95$m], $MachinePrecision]), $MachinePrecision] * N[(l / k$95$m), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Cos[k$95$m], $MachinePrecision] * N[(N[(N[(l / k$95$m), $MachinePrecision] * N[(l / k$95$m), $MachinePrecision]), $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k$95$m], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if k < 5.7999999999999996e-16

   1. Initial program 34.3%

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

   3. Simplified 38.7%

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

   5. Taylor expanded in t around 0 74.7%

      \[\leadsto \color{blue}{2 \cdot \frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 74.9%

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

   7. Simplified 74.9%

      \[\leadsto \color{blue}{2 \cdot \left(\frac{{\ell}^{2}}{{k}^{2}} \cdot \frac{\cos k}{t \cdot {\sin k}^{2}}\right)} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 53.3%

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

      2. pow2 53.3%

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

   9. Applied egg-rr 58.6%

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

   if 5.7999999999999996e-16 < k

   1. Initial program 23.7%

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

   3. Simplified 33.0%

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

   5. Taylor expanded in t around 0 75.5%

      \[\leadsto \color{blue}{2 \cdot \frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in l around 0 75.5%

      \[\leadsto 2 \cdot \color{blue}{\frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 75.5%

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

      2. associate-*r/ 75.6%

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

      3. associate-/r* 73.4%

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

      4. unpow2 73.4%

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

      5. unpow2 73.4%

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

      6. times-frac 92.7%

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

      7. unpow2 92.7%

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

   10. Simplified 92.7%

       \[\leadsto 2 \cdot \color{blue}{\left(\cos k \cdot \frac{{\left(\frac{\ell}{k}\right)}^{2}}{t \cdot {\sin k}^{2}}\right)} \]
   11. Step-by-step derivation

       1. unpow2 92.7%

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

   12. Applied egg-rr 92.7%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot {\left(\frac{\sqrt{\frac{\cos k}{t}}}{\sin k} \cdot \frac{\ell}{k}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos k \cdot \frac{\frac{\ell}{k} \cdot \frac{\ell}{k}}{t \cdot {\sin k}^{2}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;k\_m \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot {\left(\sqrt{\frac{\cos k\_m}{t\_m}} \cdot \frac{\frac{\ell}{k\_m}}{\sin k\_m}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos k\_m \cdot \frac{\frac{\ell}{k\_m} \cdot \frac{\ell}{k\_m}}{t\_m \cdot {\sin k\_m}^{2}}\right)\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 5.8e-16)
    (* 2.0 (pow (* (sqrt (/ (cos k_m) t_m)) (/ (/ l k_m) (sin k_m))) 2.0))
    (*
     2.0
     (* (cos k_m) (/ (* (/ l k_m) (/ l k_m)) (* t_m (pow (sin k_m) 2.0))))))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 5.8e-16) {
		tmp = 2.0 * pow((sqrt((cos(k_m) / t_m)) * ((l / k_m) / sin(k_m))), 2.0);
	} else {
		tmp = 2.0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * pow(sin(k_m), 2.0))));
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 5.8d-16) then
        tmp = 2.0d0 * ((sqrt((cos(k_m) / t_m)) * ((l / k_m) / sin(k_m))) ** 2.0d0)
    else
        tmp = 2.0d0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * (sin(k_m) ** 2.0d0))))
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 5.8e-16) {
		tmp = 2.0 * Math.pow((Math.sqrt((Math.cos(k_m) / t_m)) * ((l / k_m) / Math.sin(k_m))), 2.0);
	} else {
		tmp = 2.0 * (Math.cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * Math.pow(Math.sin(k_m), 2.0))));
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 5.8e-16:
		tmp = 2.0 * math.pow((math.sqrt((math.cos(k_m) / t_m)) * ((l / k_m) / math.sin(k_m))), 2.0)
	else:
		tmp = 2.0 * (math.cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * math.pow(math.sin(k_m), 2.0))))
	return t_s * tmp

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 5.8e-16)
		tmp = Float64(2.0 * (Float64(sqrt(Float64(cos(k_m) / t_m)) * Float64(Float64(l / k_m) / sin(k_m))) ^ 2.0));
	else
		tmp = Float64(2.0 * Float64(cos(k_m) * Float64(Float64(Float64(l / k_m) * Float64(l / k_m)) / Float64(t_m * (sin(k_m) ^ 2.0)))));
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 5.8e-16)
		tmp = 2.0 * ((sqrt((cos(k_m) / t_m)) * ((l / k_m) / sin(k_m))) ^ 2.0);
	else
		tmp = 2.0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * (sin(k_m) ^ 2.0))));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 5.8e-16], N[(2.0 * N[Power[N[(N[Sqrt[N[(N[Cos[k$95$m], $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision] * N[(N[(l / k$95$m), $MachinePrecision] / N[Sin[k$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Cos[k$95$m], $MachinePrecision] * N[(N[(N[(l / k$95$m), $MachinePrecision] * N[(l / k$95$m), $MachinePrecision]), $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k$95$m], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if k < 5.7999999999999996e-16

   1. Initial program 34.3%

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

   3. Simplified 38.7%

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

   5. Taylor expanded in t around 0 74.7%

      \[\leadsto \color{blue}{2 \cdot \frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 74.9%

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

   7. Simplified 74.9%

      \[\leadsto \color{blue}{2 \cdot \left(\frac{{\ell}^{2}}{{k}^{2}} \cdot \frac{\cos k}{t \cdot {\sin k}^{2}}\right)} \]
   8. Step-by-step derivation

      1. pow1 74.9%

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

   9. Applied egg-rr 58.6%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\frac{\sqrt{\frac{\cos k}{t}}}{\sin k} \cdot \frac{\ell}{k}\right)}^{2}\right)}^{1}} \]
   10. Step-by-step derivation

       1. unpow1 58.6%

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

       2. associate-*l/ 58.6%

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

       3. associate-/l* 58.6%

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

   11. Simplified 58.6%

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

   if 5.7999999999999996e-16 < k

   1. Initial program 23.7%

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

   3. Simplified 33.0%

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

   5. Taylor expanded in t around 0 75.5%

      \[\leadsto \color{blue}{2 \cdot \frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in l around 0 75.5%

      \[\leadsto 2 \cdot \color{blue}{\frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 75.5%

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

      2. associate-*r/ 75.6%

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

      3. associate-/r* 73.4%

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

      4. unpow2 73.4%

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

      5. unpow2 73.4%

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

      6. times-frac 92.7%

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

      7. unpow2 92.7%

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

   10. Simplified 92.7%

       \[\leadsto 2 \cdot \color{blue}{\left(\cos k \cdot \frac{{\left(\frac{\ell}{k}\right)}^{2}}{t \cdot {\sin k}^{2}}\right)} \]
   11. Step-by-step derivation

       1. unpow2 92.7%

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

   12. Applied egg-rr 92.7%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot {\left(\sqrt{\frac{\cos k}{t}} \cdot \frac{\frac{\ell}{k}}{\sin k}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos k \cdot \frac{\frac{\ell}{k} \cdot \frac{\ell}{k}}{t \cdot {\sin k}^{2}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;k\_m \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;{\left(\ell \cdot \frac{\sqrt{\frac{2}{t\_m}}}{{k\_m}^{2}}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos k\_m \cdot \frac{\frac{\ell}{k\_m} \cdot \frac{\ell}{k\_m}}{t\_m \cdot {\sin k\_m}^{2}}\right)\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 5.8e-16)
    (pow (* l (/ (sqrt (/ 2.0 t_m)) (pow k_m 2.0))) 2.0)
    (*
     2.0
     (* (cos k_m) (/ (* (/ l k_m) (/ l k_m)) (* t_m (pow (sin k_m) 2.0))))))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 5.8e-16) {
		tmp = pow((l * (sqrt((2.0 / t_m)) / pow(k_m, 2.0))), 2.0);
	} else {
		tmp = 2.0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * pow(sin(k_m), 2.0))));
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 5.8d-16) then
        tmp = (l * (sqrt((2.0d0 / t_m)) / (k_m ** 2.0d0))) ** 2.0d0
    else
        tmp = 2.0d0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * (sin(k_m) ** 2.0d0))))
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 5.8e-16) {
		tmp = Math.pow((l * (Math.sqrt((2.0 / t_m)) / Math.pow(k_m, 2.0))), 2.0);
	} else {
		tmp = 2.0 * (Math.cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * Math.pow(Math.sin(k_m), 2.0))));
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 5.8e-16:
		tmp = math.pow((l * (math.sqrt((2.0 / t_m)) / math.pow(k_m, 2.0))), 2.0)
	else:
		tmp = 2.0 * (math.cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * math.pow(math.sin(k_m), 2.0))))
	return t_s * tmp

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 5.8e-16)
		tmp = Float64(l * Float64(sqrt(Float64(2.0 / t_m)) / (k_m ^ 2.0))) ^ 2.0;
	else
		tmp = Float64(2.0 * Float64(cos(k_m) * Float64(Float64(Float64(l / k_m) * Float64(l / k_m)) / Float64(t_m * (sin(k_m) ^ 2.0)))));
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 5.8e-16)
		tmp = (l * (sqrt((2.0 / t_m)) / (k_m ^ 2.0))) ^ 2.0;
	else
		tmp = 2.0 * (cos(k_m) * (((l / k_m) * (l / k_m)) / (t_m * (sin(k_m) ^ 2.0))));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 5.8e-16], N[Power[N[(l * N[(N[Sqrt[N[(2.0 / t$95$m), $MachinePrecision]], $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[(2.0 * N[(N[Cos[k$95$m], $MachinePrecision] * N[(N[(N[(l / k$95$m), $MachinePrecision] * N[(l / k$95$m), $MachinePrecision]), $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k$95$m], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if k < 5.7999999999999996e-16

   1. Initial program 34.3%

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

   3. Simplified 38.7%

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

   5. Taylor expanded in k around 0 65.5%

      \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
   6. Step-by-step derivation

      1. *-commutative 65.5%

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

      2. associate-/r* 65.5%

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

   7. Simplified 65.5%

      \[\leadsto \color{blue}{\frac{\frac{2}{t}}{{k}^{4}}} \cdot \left(\ell \cdot \ell\right) \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 48.1%

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

      2. pow2 48.1%

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

      3. associate-/r* 48.1%

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

      4. *-commutative 48.1%

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

      5. sqrt-prod 46.0%

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

      6. sqrt-prod 27.2%

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

      7. add-sqr-sqrt 51.0%

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

      8. associate-/r* 51.0%

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

      9. sqrt-div 43.3%

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

      10. sqrt-pow1 44.8%

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

      11. metadata-eval 44.8%

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

   9. Applied egg-rr 44.8%

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

   if 5.7999999999999996e-16 < k

   1. Initial program 23.7%

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

   3. Simplified 33.0%

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

   5. Taylor expanded in t around 0 75.5%

      \[\leadsto \color{blue}{2 \cdot \frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in l around 0 75.5%

      \[\leadsto 2 \cdot \color{blue}{\frac{{\ell}^{2} \cdot \cos k}{{k}^{2} \cdot \left(t \cdot {\sin k}^{2}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 75.5%

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

      2. associate-*r/ 75.6%

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

      3. associate-/r* 73.4%

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

      4. unpow2 73.4%

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

      5. unpow2 73.4%

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

      6. times-frac 92.7%

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

      7. unpow2 92.7%

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

   10. Simplified 92.7%

       \[\leadsto 2 \cdot \color{blue}{\left(\cos k \cdot \frac{{\left(\frac{\ell}{k}\right)}^{2}}{t \cdot {\sin k}^{2}}\right)} \]
   11. Step-by-step derivation

       1. unpow2 92.7%

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

   12. Applied egg-rr 92.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;{\left(\ell \cdot \frac{\sqrt{\frac{2}{t}}}{{k}^{2}}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos k \cdot \frac{\frac{\ell}{k} \cdot \frac{\ell}{k}}{t \cdot {\sin k}^{2}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot {\left(\ell \cdot \frac{\sqrt{\frac{2}{t\_m}}}{{k\_m}^{2}}\right)}^{2} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (* t_s (pow (* l (/ (sqrt (/ 2.0 t_m)) (pow k_m 2.0))) 2.0)))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	return t_s * pow((l * (sqrt((2.0 / t_m)) / pow(k_m, 2.0))), 2.0);
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    code = t_s * ((l * (sqrt((2.0d0 / t_m)) / (k_m ** 2.0d0))) ** 2.0d0)
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	return t_s * Math.pow((l * (Math.sqrt((2.0 / t_m)) / Math.pow(k_m, 2.0))), 2.0);
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	return t_s * math.pow((l * (math.sqrt((2.0 / t_m)) / math.pow(k_m, 2.0))), 2.0)

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	return Float64(t_s * (Float64(l * Float64(sqrt(Float64(2.0 / t_m)) / (k_m ^ 2.0))) ^ 2.0))
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k_m)
	tmp = t_s * ((l * (sqrt((2.0 / t_m)) / (k_m ^ 2.0))) ^ 2.0);
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * N[Power[N[(l * N[(N[Sqrt[N[(2.0 / t$95$m), $MachinePrecision]], $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.5%

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

3. Simplified 37.2%

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

5. Taylor expanded in k around 0 61.7%

   \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
6. Step-by-step derivation

   1. *-commutative 61.7%

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

   2. associate-/r* 61.7%

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

7. Simplified 61.7%

   \[\leadsto \color{blue}{\frac{\frac{2}{t}}{{k}^{4}}} \cdot \left(\ell \cdot \ell\right) \]
8. Step-by-step derivation

   1. add-sqr-sqrt 48.4%

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

   2. pow2 48.4%

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

   3. associate-/r* 48.4%

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

   4. *-commutative 48.4%

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

   5. sqrt-prod 46.9%

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

   6. sqrt-prod 26.6%

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

   7. add-sqr-sqrt 50.7%

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

   8. associate-/r* 50.7%

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

   9. sqrt-div 39.5%

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

   10. sqrt-pow1 40.6%

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

   11. metadata-eval 40.6%

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

9. Applied egg-rr 40.6%

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

10. Final simplification 40.6%

    \[\leadsto {\left(\ell \cdot \frac{\sqrt{\frac{2}{t}}}{{k}^{2}}\right)}^{2} \]
11. Add Preprocessing

Alternative 5: 69.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;\left(\frac{2}{t\_m} \cdot {\ell}^{2}\right) \cdot {k\_m}^{-4}\\ \mathbf{elif}\;t\_m \leq 3.6 \cdot 10^{+127}:\\ \;\;\;\;\frac{2}{{\left(k\_m \cdot \left(\frac{k\_m}{t\_m} \cdot \frac{{t\_m}^{1.5}}{\ell}\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\left({k\_m}^{-2} \cdot \frac{\frac{2}{t\_m}}{{k\_m}^{2}}\right) \cdot \left(\ell \cdot \ell\right)\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= t_m 1.7e-217)
    (* (* (/ 2.0 t_m) (pow l 2.0)) (pow k_m -4.0))
    (if (<= t_m 3.6e+127)
      (/ 2.0 (pow (* k_m (* (/ k_m t_m) (/ (pow t_m 1.5) l))) 2.0))
      (* (* (pow k_m -2.0) (/ (/ 2.0 t_m) (pow k_m 2.0))) (* l l))))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (t_m <= 1.7e-217) {
		tmp = ((2.0 / t_m) * pow(l, 2.0)) * pow(k_m, -4.0);
	} else if (t_m <= 3.6e+127) {
		tmp = 2.0 / pow((k_m * ((k_m / t_m) * (pow(t_m, 1.5) / l))), 2.0);
	} else {
		tmp = (pow(k_m, -2.0) * ((2.0 / t_m) / pow(k_m, 2.0))) * (l * l);
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (t_m <= 1.7d-217) then
        tmp = ((2.0d0 / t_m) * (l ** 2.0d0)) * (k_m ** (-4.0d0))
    else if (t_m <= 3.6d+127) then
        tmp = 2.0d0 / ((k_m * ((k_m / t_m) * ((t_m ** 1.5d0) / l))) ** 2.0d0)
    else
        tmp = ((k_m ** (-2.0d0)) * ((2.0d0 / t_m) / (k_m ** 2.0d0))) * (l * l)
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (t_m <= 1.7e-217) {
		tmp = ((2.0 / t_m) * Math.pow(l, 2.0)) * Math.pow(k_m, -4.0);
	} else if (t_m <= 3.6e+127) {
		tmp = 2.0 / Math.pow((k_m * ((k_m / t_m) * (Math.pow(t_m, 1.5) / l))), 2.0);
	} else {
		tmp = (Math.pow(k_m, -2.0) * ((2.0 / t_m) / Math.pow(k_m, 2.0))) * (l * l);
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if t_m <= 1.7e-217:
		tmp = ((2.0 / t_m) * math.pow(l, 2.0)) * math.pow(k_m, -4.0)
	elif t_m <= 3.6e+127:
		tmp = 2.0 / math.pow((k_m * ((k_m / t_m) * (math.pow(t_m, 1.5) / l))), 2.0)
	else:
		tmp = (math.pow(k_m, -2.0) * ((2.0 / t_m) / math.pow(k_m, 2.0))) * (l * l)
	return t_s * tmp

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (t_m <= 1.7e-217)
		tmp = Float64(Float64(Float64(2.0 / t_m) * (l ^ 2.0)) * (k_m ^ -4.0));
	elseif (t_m <= 3.6e+127)
		tmp = Float64(2.0 / (Float64(k_m * Float64(Float64(k_m / t_m) * Float64((t_m ^ 1.5) / l))) ^ 2.0));
	else
		tmp = Float64(Float64((k_m ^ -2.0) * Float64(Float64(2.0 / t_m) / (k_m ^ 2.0))) * Float64(l * l));
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (t_m <= 1.7e-217)
		tmp = ((2.0 / t_m) * (l ^ 2.0)) * (k_m ^ -4.0);
	elseif (t_m <= 3.6e+127)
		tmp = 2.0 / ((k_m * ((k_m / t_m) * ((t_m ^ 1.5) / l))) ^ 2.0);
	else
		tmp = ((k_m ^ -2.0) * ((2.0 / t_m) / (k_m ^ 2.0))) * (l * l);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * If[LessEqual[t$95$m, 1.7e-217], N[(N[(N[(2.0 / t$95$m), $MachinePrecision] * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision] * N[Power[k$95$m, -4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 3.6e+127], N[(2.0 / N[Power[N[(k$95$m * N[(N[(k$95$m / t$95$m), $MachinePrecision] * N[(N[Power[t$95$m, 1.5], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[k$95$m, -2.0], $MachinePrecision] * N[(N[(2.0 / t$95$m), $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(l * l), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < 1.70000000000000008e-217

   1. Initial program 29.3%

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

   3. Simplified 33.2%

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

   5. Taylor expanded in k around 0 56.1%

      \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
   6. Step-by-step derivation

      1. *-commutative 56.1%

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

      2. associate-/r* 56.1%

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

   7. Simplified 56.1%

      \[\leadsto \color{blue}{\frac{\frac{2}{t}}{{k}^{4}}} \cdot \left(\ell \cdot \ell\right) \]
   8. Step-by-step derivation

      1. associate-/r* 56.1%

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

      2. pow1 56.1%

         \[\leadsto \color{blue}{{\left(\frac{2}{t \cdot {k}^{4}} \cdot \left(\ell \cdot \ell\right)\right)}^{1}} \]

      3. *-commutative 56.1%

         \[\leadsto {\color{blue}{\left(\left(\ell \cdot \ell\right) \cdot \frac{2}{t \cdot {k}^{4}}\right)}}^{1} \]

      4. pow2 56.1%

         \[\leadsto {\left(\color{blue}{{\ell}^{2}} \cdot \frac{2}{t \cdot {k}^{4}}\right)}^{1} \]

      5. metadata-eval 56.1%

         \[\leadsto {\left({\ell}^{2} \cdot \frac{\color{blue}{2 \cdot 1}}{t \cdot {k}^{4}}\right)}^{1} \]

      6. frac-times 56.1%

         \[\leadsto {\left({\ell}^{2} \cdot \color{blue}{\left(\frac{2}{t} \cdot \frac{1}{{k}^{4}}\right)}\right)}^{1} \]

      7. pow-flip 56.1%

         \[\leadsto {\left({\ell}^{2} \cdot \left(\frac{2}{t} \cdot \color{blue}{{k}^{\left(-4\right)}}\right)\right)}^{1} \]

      8. metadata-eval 56.1%

         \[\leadsto {\left({\ell}^{2} \cdot \left(\frac{2}{t} \cdot {k}^{\color{blue}{-4}}\right)\right)}^{1} \]

   9. Applied egg-rr 56.1%

      \[\leadsto \color{blue}{{\left({\ell}^{2} \cdot \left(\frac{2}{t} \cdot {k}^{-4}\right)\right)}^{1}} \]
   10. Step-by-step derivation

       1. unpow1 56.1%

          \[\leadsto \color{blue}{{\ell}^{2} \cdot \left(\frac{2}{t} \cdot {k}^{-4}\right)} \]

       2. associate-*r* 55.9%

          \[\leadsto \color{blue}{\left({\ell}^{2} \cdot \frac{2}{t}\right) \cdot {k}^{-4}} \]

   11. Simplified 55.9%

       \[\leadsto \color{blue}{\left({\ell}^{2} \cdot \frac{2}{t}\right) \cdot {k}^{-4}} \]

   if 1.70000000000000008e-217 < t < 3.59999999999999979e127

   1. Initial program 52.6%

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

   4. Applied egg-rr 40.5%

      \[\leadsto \frac{2}{\color{blue}{{\left(\frac{k}{t} \cdot \left(\frac{{t}^{1.5}}{\ell} \cdot \sqrt{\sin k \cdot \tan k}\right)\right)}^{2} + \left(\sin k \cdot \left(\tan k \cdot \left({t}^{3} \cdot {\ell}^{-2}\right)\right)\right) \cdot 0}} \]
   5. Step-by-step derivation

      1. mul0-rgt 60.9%

         \[\leadsto \frac{2}{{\left(\frac{k}{t} \cdot \left(\frac{{t}^{1.5}}{\ell} \cdot \sqrt{\sin k \cdot \tan k}\right)\right)}^{2} + \color{blue}{0}} \]

      2. +-rgt-identity 60.9%

         \[\leadsto \frac{2}{\color{blue}{{\left(\frac{k}{t} \cdot \left(\frac{{t}^{1.5}}{\ell} \cdot \sqrt{\sin k \cdot \tan k}\right)\right)}^{2}}} \]

      3. associate-*r* 60.9%

         \[\leadsto \frac{2}{{\color{blue}{\left(\left(\frac{k}{t} \cdot \frac{{t}^{1.5}}{\ell}\right) \cdot \sqrt{\sin k \cdot \tan k}\right)}}^{2}} \]

   6. Simplified 60.9%

      \[\leadsto \frac{2}{\color{blue}{{\left(\left(\frac{k}{t} \cdot \frac{{t}^{1.5}}{\ell}\right) \cdot \sqrt{\sin k \cdot \tan k}\right)}^{2}}} \]

   7. Taylor expanded in k around 0 73.4%

      \[\leadsto \frac{2}{{\left(\left(\frac{k}{t} \cdot \frac{{t}^{1.5}}{\ell}\right) \cdot \color{blue}{k}\right)}^{2}} \]

   if 3.59999999999999979e127 < t

   1. Initial program 6.5%

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

   3. Simplified 17.7%

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

   5. Taylor expanded in k around 0 74.1%

      \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
   6. Step-by-step derivation

      1. *-commutative 74.1%

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

      2. associate-/r* 74.1%

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

   7. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\frac{2}{t}}{{k}^{4}}} \cdot \left(\ell \cdot \ell\right) \]
   8. Step-by-step derivation

      1. *-un-lft-identity 74.1%

         \[\leadsto \frac{\color{blue}{1 \cdot \frac{2}{t}}}{{k}^{4}} \cdot \left(\ell \cdot \ell\right) \]

      2. metadata-eval 74.1%

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

      3. pow-prod-up 74.1%

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

      4. times-frac 76.1%

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

      5. pow-flip 76.1%

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

      6. metadata-eval 76.1%

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

   9. Applied egg-rr 76.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;\left(\frac{2}{t} \cdot {\ell}^{2}\right) \cdot {k}^{-4}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+127}:\\ \;\;\;\;\frac{2}{{\left(k \cdot \left(\frac{k}{t} \cdot \frac{{t}^{1.5}}{\ell}\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\left({k}^{-2} \cdot \frac{\frac{2}{t}}{{k}^{2}}\right) \cdot \left(\ell \cdot \ell\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \left(\left({k\_m}^{-2} \cdot \frac{\frac{2}{t\_m}}{{k\_m}^{2}}\right) \cdot \left(\ell \cdot \ell\right)\right) \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (* t_s (* (* (pow k_m -2.0) (/ (/ 2.0 t_m) (pow k_m 2.0))) (* l l))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	return t_s * ((pow(k_m, -2.0) * ((2.0 / t_m) / pow(k_m, 2.0))) * (l * l));
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    code = t_s * (((k_m ** (-2.0d0)) * ((2.0d0 / t_m) / (k_m ** 2.0d0))) * (l * l))
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	return t_s * ((Math.pow(k_m, -2.0) * ((2.0 / t_m) / Math.pow(k_m, 2.0))) * (l * l));
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	return t_s * ((math.pow(k_m, -2.0) * ((2.0 / t_m) / math.pow(k_m, 2.0))) * (l * l))

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	return Float64(t_s * Float64(Float64((k_m ^ -2.0) * Float64(Float64(2.0 / t_m) / (k_m ^ 2.0))) * Float64(l * l)))
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k_m)
	tmp = t_s * (((k_m ^ -2.0) * ((2.0 / t_m) / (k_m ^ 2.0))) * (l * l));
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * N[(N[(N[Power[k$95$m, -2.0], $MachinePrecision] * N[(N[(2.0 / t$95$m), $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.5%

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

3. Simplified 37.2%

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

5. Taylor expanded in k around 0 61.7%

   \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
6. Step-by-step derivation

   1. *-commutative 61.7%

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

   2. associate-/r* 61.7%

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

7. Simplified 61.7%

   \[\leadsto \color{blue}{\frac{\frac{2}{t}}{{k}^{4}}} \cdot \left(\ell \cdot \ell\right) \]
8. Step-by-step derivation

   1. *-un-lft-identity 61.7%

      \[\leadsto \frac{\color{blue}{1 \cdot \frac{2}{t}}}{{k}^{4}} \cdot \left(\ell \cdot \ell\right) \]

   2. metadata-eval 61.7%

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

   3. pow-prod-up 61.7%

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

   4. times-frac 62.8%

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

   5. pow-flip 62.8%

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

   6. metadata-eval 62.8%

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

9. Applied egg-rr 62.8%

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

10. Final simplification 62.8%

    \[\leadsto \left({k}^{-2} \cdot \frac{\frac{2}{t}}{{k}^{2}}\right) \cdot \left(\ell \cdot \ell\right) \]
11. Add Preprocessing

Alternative 7: 62.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \left(2 \cdot \frac{{\ell}^{2} \cdot {k\_m}^{-4}}{t\_m}\right) \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (* t_s (* 2.0 (/ (* (pow l 2.0) (pow k_m -4.0)) t_m))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	return t_s * (2.0 * ((pow(l, 2.0) * pow(k_m, -4.0)) / t_m));
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    code = t_s * (2.0d0 * (((l ** 2.0d0) * (k_m ** (-4.0d0))) / t_m))
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	return t_s * (2.0 * ((Math.pow(l, 2.0) * Math.pow(k_m, -4.0)) / t_m));
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	return t_s * (2.0 * ((math.pow(l, 2.0) * math.pow(k_m, -4.0)) / t_m))

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	return Float64(t_s * Float64(2.0 * Float64(Float64((l ^ 2.0) * (k_m ^ -4.0)) / t_m)))
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k_m)
	tmp = t_s * (2.0 * (((l ^ 2.0) * (k_m ^ -4.0)) / t_m));
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * N[(2.0 * N[(N[(N[Power[l, 2.0], $MachinePrecision] * N[Power[k$95$m, -4.0], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.5%

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

3. Simplified 37.2%

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

5. Taylor expanded in k around 0 61.7%

   \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
6. Step-by-step derivation

   1. *-commutative 61.7%

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

   2. associate-/r* 61.7%

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

7. Simplified 61.7%

   \[\leadsto \color{blue}{\frac{\frac{2}{t}}{{k}^{4}}} \cdot \left(\ell \cdot \ell\right) \]
8. Step-by-step derivation

   1. div-inv 61.7%

      \[\leadsto \color{blue}{\left(\frac{2}{t} \cdot \frac{1}{{k}^{4}}\right)} \cdot \left(\ell \cdot \ell\right) \]

   2. pow-flip 61.7%

      \[\leadsto \left(\frac{2}{t} \cdot \color{blue}{{k}^{\left(-4\right)}}\right) \cdot \left(\ell \cdot \ell\right) \]

   3. metadata-eval 61.7%

      \[\leadsto \left(\frac{2}{t} \cdot {k}^{\color{blue}{-4}}\right) \cdot \left(\ell \cdot \ell\right) \]

9. Applied egg-rr 61.7%

   \[\leadsto \color{blue}{\left(\frac{2}{t} \cdot {k}^{-4}\right)} \cdot \left(\ell \cdot \ell\right) \]
10. Step-by-step derivation

    1. associate-*l/ 61.7%

       \[\leadsto \color{blue}{\frac{2 \cdot {k}^{-4}}{t}} \cdot \left(\ell \cdot \ell\right) \]

    2. associate-/l* 61.7%

       \[\leadsto \color{blue}{\left(2 \cdot \frac{{k}^{-4}}{t}\right)} \cdot \left(\ell \cdot \ell\right) \]

11. Simplified 61.7%

    \[\leadsto \color{blue}{\left(2 \cdot \frac{{k}^{-4}}{t}\right)} \cdot \left(\ell \cdot \ell\right) \]
12. Step-by-step derivation

    1. pow1 61.7%

       \[\leadsto \color{blue}{{\left(\left(2 \cdot \frac{{k}^{-4}}{t}\right) \cdot \left(\ell \cdot \ell\right)\right)}^{1}} \]

    2. associate-*l* 61.7%

       \[\leadsto {\color{blue}{\left(2 \cdot \left(\frac{{k}^{-4}}{t} \cdot \left(\ell \cdot \ell\right)\right)\right)}}^{1} \]

    3. pow2 61.7%

       \[\leadsto {\left(2 \cdot \left(\frac{{k}^{-4}}{t} \cdot \color{blue}{{\ell}^{2}}\right)\right)}^{1} \]

13. Applied egg-rr 61.7%

    \[\leadsto \color{blue}{{\left(2 \cdot \left(\frac{{k}^{-4}}{t} \cdot {\ell}^{2}\right)\right)}^{1}} \]
14. Step-by-step derivation

    1. unpow1 61.7%

       \[\leadsto \color{blue}{2 \cdot \left(\frac{{k}^{-4}}{t} \cdot {\ell}^{2}\right)} \]

    2. *-commutative 61.7%

       \[\leadsto 2 \cdot \color{blue}{\left({\ell}^{2} \cdot \frac{{k}^{-4}}{t}\right)} \]

    3. associate-*r/ 62.4%

       \[\leadsto 2 \cdot \color{blue}{\frac{{\ell}^{2} \cdot {k}^{-4}}{t}} \]

15. Simplified 62.4%

    \[\leadsto \color{blue}{2 \cdot \frac{{\ell}^{2} \cdot {k}^{-4}}{t}} \]

16. Final simplification 62.4%

    \[\leadsto 2 \cdot \frac{{\ell}^{2} \cdot {k}^{-4}}{t} \]
17. Add Preprocessing

Alternative 8: 62.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \left(\left(\ell \cdot \ell\right) \cdot \left(2 \cdot \frac{{k\_m}^{-4}}{t\_m}\right)\right) \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (* t_s (* (* l l) (* 2.0 (/ (pow k_m -4.0) t_m)))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	return t_s * ((l * l) * (2.0 * (pow(k_m, -4.0) / t_m)));
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    code = t_s * ((l * l) * (2.0d0 * ((k_m ** (-4.0d0)) / t_m)))
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	return t_s * ((l * l) * (2.0 * (Math.pow(k_m, -4.0) / t_m)));
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	return t_s * ((l * l) * (2.0 * (math.pow(k_m, -4.0) / t_m)))

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	return Float64(t_s * Float64(Float64(l * l) * Float64(2.0 * Float64((k_m ^ -4.0) / t_m))))
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k_m)
	tmp = t_s * ((l * l) * (2.0 * ((k_m ^ -4.0) / t_m)));
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * N[(N[(l * l), $MachinePrecision] * N[(2.0 * N[(N[Power[k$95$m, -4.0], $MachinePrecision] / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.5%

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

3. Simplified 37.2%

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

5. Taylor expanded in k around 0 61.7%

   \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
6. Step-by-step derivation

   1. *-commutative 61.7%

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

   2. associate-/r* 61.7%

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

7. Simplified 61.7%

   \[\leadsto \color{blue}{\frac{\frac{2}{t}}{{k}^{4}}} \cdot \left(\ell \cdot \ell\right) \]
8. Step-by-step derivation

   1. div-inv 61.7%

      \[\leadsto \color{blue}{\left(\frac{2}{t} \cdot \frac{1}{{k}^{4}}\right)} \cdot \left(\ell \cdot \ell\right) \]

   2. pow-flip 61.7%

      \[\leadsto \left(\frac{2}{t} \cdot \color{blue}{{k}^{\left(-4\right)}}\right) \cdot \left(\ell \cdot \ell\right) \]

   3. metadata-eval 61.7%

      \[\leadsto \left(\frac{2}{t} \cdot {k}^{\color{blue}{-4}}\right) \cdot \left(\ell \cdot \ell\right) \]

9. Applied egg-rr 61.7%

   \[\leadsto \color{blue}{\left(\frac{2}{t} \cdot {k}^{-4}\right)} \cdot \left(\ell \cdot \ell\right) \]
10. Step-by-step derivation

    1. associate-*l/ 61.7%

       \[\leadsto \color{blue}{\frac{2 \cdot {k}^{-4}}{t}} \cdot \left(\ell \cdot \ell\right) \]

    2. associate-/l* 61.7%

       \[\leadsto \color{blue}{\left(2 \cdot \frac{{k}^{-4}}{t}\right)} \cdot \left(\ell \cdot \ell\right) \]

11. Simplified 61.7%

    \[\leadsto \color{blue}{\left(2 \cdot \frac{{k}^{-4}}{t}\right)} \cdot \left(\ell \cdot \ell\right) \]

12. Final simplification 61.7%

    \[\leadsto \left(\ell \cdot \ell\right) \cdot \left(2 \cdot \frac{{k}^{-4}}{t}\right) \]
13. Add Preprocessing

Alternative 9: 62.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \left(\left(\ell \cdot \ell\right) \cdot \frac{\frac{2}{t\_m}}{{k\_m}^{4}}\right) \end{array} \]

FPCore

k_m = (fabs.f64 k)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (* t_s (* (* l l) (/ (/ 2.0 t_m) (pow k_m 4.0)))))

C

k_m = fabs(k);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	return t_s * ((l * l) * ((2.0 / t_m) / pow(k_m, 4.0)));
}

Fortran

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    code = t_s * ((l * l) * ((2.0d0 / t_m) / (k_m ** 4.0d0)))
end function

Java

k_m = Math.abs(k);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k_m) {
	return t_s * ((l * l) * ((2.0 / t_m) / Math.pow(k_m, 4.0)));
}

Python

k_m = math.fabs(k)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	return t_s * ((l * l) * ((2.0 / t_m) / math.pow(k_m, 4.0)))

Julia

k_m = abs(k)
t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	return Float64(t_s * Float64(Float64(l * l) * Float64(Float64(2.0 / t_m) / (k_m ^ 4.0))))
end

MATLAB

k_m = abs(k);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k_m)
	tmp = t_s * ((l * l) * ((2.0 / t_m) / (k_m ^ 4.0)));
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k$95$m_] := N[(t$95$s * N[(N[(l * l), $MachinePrecision] * N[(N[(2.0 / t$95$m), $MachinePrecision] / N[Power[k$95$m, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.5%

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

3. Simplified 37.2%

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

5. Taylor expanded in k around 0 61.7%

   \[\leadsto \color{blue}{\frac{2}{{k}^{4} \cdot t}} \cdot \left(\ell \cdot \ell\right) \]
6. Step-by-step derivation

   1. *-commutative 61.7%

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

   2. associate-/r* 61.7%

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

7. Simplified 61.7%

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

8. Final simplification 61.7%

   \[\leadsto \left(\ell \cdot \ell\right) \cdot \frac{\frac{2}{t}}{{k}^{4}} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(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))))