Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 86.2% → 99.5%

Time: 11.0s

Alternatives: 17

Speedup: 2.6×

• 49.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))

C

double code(double J, double l, double K, double U) {
	return ((J * (exp(l) - exp(-l))) * cos((K / 2.0))) + U;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = ((j * (exp(l) - exp(-l))) * cos((k / 2.0d0))) + u
end function

Java

public static double code(double J, double l, double K, double U) {
	return ((J * (Math.exp(l) - Math.exp(-l))) * Math.cos((K / 2.0))) + U;
}

Python

def code(J, l, K, U):
	return ((J * (math.exp(l) - math.exp(-l))) * math.cos((K / 2.0))) + U

Julia

function code(J, l, K, U)
	return Float64(Float64(Float64(J * Float64(exp(l) - exp(Float64(-l)))) * cos(Float64(K / 2.0))) + U)
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = ((J * (exp(l) - exp(-l))) * cos((K / 2.0))) + U;
end

Wolfram

code[J_, l_, K_, U_] := N[(N[(N[(J * N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]

Initial Program: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))

C

double code(double J, double l, double K, double U) {
	return ((J * (exp(l) - exp(-l))) * cos((K / 2.0))) + U;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = ((j * (exp(l) - exp(-l))) * cos((k / 2.0d0))) + u
end function

Java

public static double code(double J, double l, double K, double U) {
	return ((J * (Math.exp(l) - Math.exp(-l))) * Math.cos((K / 2.0))) + U;
}

Python

def code(J, l, K, U):
	return ((J * (math.exp(l) - math.exp(-l))) * math.cos((K / 2.0))) + U

Julia

function code(J, l, K, U)
	return Float64(Float64(Float64(J * Float64(exp(l) - exp(Float64(-l)))) * cos(Float64(K / 2.0))) + U)
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = ((J * (exp(l) - exp(-l))) * cos((K / 2.0))) + U;
end

Wolfram

code[J_, l_, K_, U_] := N[(N[(N[(J * N[(N[Exp[l], $MachinePrecision] - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := e^{-\ell}\\ t_2 := e^{\ell} - t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(J \cdot \left(27 - t\_1\right)\right) \cdot t\_0 + U\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\ell, \cos \left(K \cdot 0.5\right) \cdot \left(J \cdot \mathsf{fma}\left(0.3333333333333333, {\ell}^{2}, 2\right)\right), U\right)\\ \mathbf{else}:\\ \;\;\;\;U + t\_0 \cdot \left(t\_2 \cdot J\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))) (t_1 (exp (- l))) (t_2 (- (exp l) t_1)))
   (if (<= t_2 (- INFINITY))
     (+ (* (* J (- 27.0 t_1)) t_0) U)
     (if (<= t_2 0.0)
       (fma
        l
        (* (cos (* K 0.5)) (* J (fma 0.3333333333333333 (pow l 2.0) 2.0)))
        U)
       (+ U (* t_0 (* t_2 J)))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = exp(-l);
	double t_2 = exp(l) - t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((J * (27.0 - t_1)) * t_0) + U;
	} else if (t_2 <= 0.0) {
		tmp = fma(l, (cos((K * 0.5)) * (J * fma(0.3333333333333333, pow(l, 2.0), 2.0))), U);
	} else {
		tmp = U + (t_0 * (t_2 * J));
	}
	return tmp;
}

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = exp(Float64(-l))
	t_2 = Float64(exp(l) - t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(J * Float64(27.0 - t_1)) * t_0) + U);
	elseif (t_2 <= 0.0)
		tmp = fma(l, Float64(cos(Float64(K * 0.5)) * Float64(J * fma(0.3333333333333333, (l ^ 2.0), 2.0))), U);
	else
		tmp = Float64(U + Float64(t_0 * Float64(t_2 * J)));
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-l)], $MachinePrecision]}, Block[{t$95$2 = N[(N[Exp[l], $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(J * N[(27.0 - t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(l * N[(N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision] * N[(J * N[(0.3333333333333333 * N[Power[l, 2.0], $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(t$95$0 * N[(t$95$2 * J), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -inf.0

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   4. Applied egg-rr 100.0%

      \[\leadsto \left(J \cdot \left(\color{blue}{27} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   if -inf.0 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < 0.0

   1. Initial program 69.4%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 99.9%

      \[\leadsto \color{blue}{U + \ell \cdot \left(0.3333333333333333 \cdot \left(J \cdot \left({\ell}^{2} \cdot \cos \left(0.5 \cdot K\right)\right)\right) + 2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\ell \cdot \left(0.3333333333333333 \cdot \left(J \cdot \left({\ell}^{2} \cdot \cos \left(0.5 \cdot K\right)\right)\right) + 2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right) + U} \]

      2. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, 0.3333333333333333 \cdot \left(J \cdot \left({\ell}^{2} \cdot \cos \left(0.5 \cdot K\right)\right)\right) + 2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right), U\right)} \]

      3. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(\ell, 0.3333333333333333 \cdot \color{blue}{\left(\left(J \cdot {\ell}^{2}\right) \cdot \cos \left(0.5 \cdot K\right)\right)} + 2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right), U\right) \]

      4. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(\ell, \color{blue}{\left(0.3333333333333333 \cdot \left(J \cdot {\ell}^{2}\right)\right) \cdot \cos \left(0.5 \cdot K\right)} + 2 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right), U\right) \]

      5. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(\ell, \left(0.3333333333333333 \cdot \left(J \cdot {\ell}^{2}\right)\right) \cdot \cos \left(0.5 \cdot K\right) + \color{blue}{\left(2 \cdot J\right) \cdot \cos \left(0.5 \cdot K\right)}, U\right) \]

      6. distribute-rgt-out 99.9%

         \[\leadsto \mathsf{fma}\left(\ell, \color{blue}{\cos \left(0.5 \cdot K\right) \cdot \left(0.3333333333333333 \cdot \left(J \cdot {\ell}^{2}\right) + 2 \cdot J\right)}, U\right) \]

      7. *-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(\ell, \cos \left(0.5 \cdot K\right) \cdot \left(0.3333333333333333 \cdot \color{blue}{\left({\ell}^{2} \cdot J\right)} + 2 \cdot J\right), U\right) \]

      8. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(\ell, \cos \left(0.5 \cdot K\right) \cdot \left(\color{blue}{\left(0.3333333333333333 \cdot {\ell}^{2}\right) \cdot J} + 2 \cdot J\right), U\right) \]

      9. distribute-rgt-out 99.9%

         \[\leadsto \mathsf{fma}\left(\ell, \cos \left(0.5 \cdot K\right) \cdot \color{blue}{\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{2} + 2\right)\right)}, U\right) \]

      10. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(\ell, \cos \left(0.5 \cdot K\right) \cdot \left(J \cdot \color{blue}{\mathsf{fma}\left(0.3333333333333333, {\ell}^{2}, 2\right)}\right), U\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, \cos \left(0.5 \cdot K\right) \cdot \left(J \cdot \mathsf{fma}\left(0.3333333333333333, {\ell}^{2}, 2\right)\right), U\right)} \]

   if 0.0 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{\ell} - e^{-\ell} \leq -\infty:\\ \;\;\;\;\left(J \cdot \left(27 - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \mathbf{elif}\;e^{\ell} - e^{-\ell} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\ell, \cos \left(K \cdot 0.5\right) \cdot \left(J \cdot \mathsf{fma}\left(0.3333333333333333, {\ell}^{2}, 2\right)\right), U\right)\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := e^{-\ell}\\ t_2 := e^{\ell} - t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(J \cdot \left(27 - t\_1\right)\right) \cdot t\_0 + U\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + t\_0 \cdot \left(t\_2 \cdot J\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))) (t_1 (exp (- l))) (t_2 (- (exp l) t_1)))
   (if (<= t_2 (- INFINITY))
     (+ (* (* J (- 27.0 t_1)) t_0) U)
     (if (<= t_2 0.0)
       (+ U (* 2.0 (* l (* J (cos (* K 0.5))))))
       (+ U (* t_0 (* t_2 J)))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = exp(-l);
	double t_2 = exp(l) - t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((J * (27.0 - t_1)) * t_0) + U;
	} else if (t_2 <= 0.0) {
		tmp = U + (2.0 * (l * (J * cos((K * 0.5)))));
	} else {
		tmp = U + (t_0 * (t_2 * J));
	}
	return tmp;
}

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = Math.exp(-l);
	double t_2 = Math.exp(l) - t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((J * (27.0 - t_1)) * t_0) + U;
	} else if (t_2 <= 0.0) {
		tmp = U + (2.0 * (l * (J * Math.cos((K * 0.5)))));
	} else {
		tmp = U + (t_0 * (t_2 * J));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = math.exp(-l)
	t_2 = math.exp(l) - t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((J * (27.0 - t_1)) * t_0) + U
	elif t_2 <= 0.0:
		tmp = U + (2.0 * (l * (J * math.cos((K * 0.5)))))
	else:
		tmp = U + (t_0 * (t_2 * J))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = exp(Float64(-l))
	t_2 = Float64(exp(l) - t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(J * Float64(27.0 - t_1)) * t_0) + U);
	elseif (t_2 <= 0.0)
		tmp = Float64(U + Float64(2.0 * Float64(l * Float64(J * cos(Float64(K * 0.5))))));
	else
		tmp = Float64(U + Float64(t_0 * Float64(t_2 * J)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = exp(-l);
	t_2 = exp(l) - t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((J * (27.0 - t_1)) * t_0) + U;
	elseif (t_2 <= 0.0)
		tmp = U + (2.0 * (l * (J * cos((K * 0.5)))));
	else
		tmp = U + (t_0 * (t_2 * J));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-l)], $MachinePrecision]}, Block[{t$95$2 = N[(N[Exp[l], $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(J * N[(27.0 - t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(U + N[(2.0 * N[(l * N[(J * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(t$95$0 * N[(t$95$2 * J), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -inf.0

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   4. Applied egg-rr 100.0%

      \[\leadsto \left(J \cdot \left(\color{blue}{27} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   if -inf.0 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < 0.0

   1. Initial program 69.4%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 99.9%

      \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   6. Taylor expanded in J around 0 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\ell \cdot \cos \left(0.5 \cdot K\right)\right) \cdot J\right)} + U \]

      2. associate-*l* 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\ell \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\right)} + U \]

      3. *-commutative 99.9%

         \[\leadsto 2 \cdot \left(\ell \cdot \color{blue}{\left(J \cdot \cos \left(0.5 \cdot K\right)\right)}\right) + U \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]

   if 0.0 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{\ell} - e^{-\ell} \leq -\infty:\\ \;\;\;\;\left(J \cdot \left(27 - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \mathbf{elif}\;e^{\ell} - e^{-\ell} \leq 0:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot J\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := e^{-\ell}\\ \mathbf{if}\;e^{\ell} - t\_1 \leq -\infty:\\ \;\;\;\;\left(J \cdot \left(27 - t\_1\right)\right) \cdot t\_0 + U\\ \mathbf{else}:\\ \;\;\;\;U + t\_0 \cdot \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \left(\ell \cdot \ell\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))) (t_1 (exp (- l))))
   (if (<= (- (exp l) t_1) (- INFINITY))
     (+ (* (* J (- 27.0 t_1)) t_0) U)
     (+ U (* t_0 (* J (* l (+ 2.0 (* 0.3333333333333333 (* l l))))))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = cos((K / 2.0));
	double t_1 = exp(-l);
	double tmp;
	if ((exp(l) - t_1) <= -((double) INFINITY)) {
		tmp = ((J * (27.0 - t_1)) * t_0) + U;
	} else {
		tmp = U + (t_0 * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))));
	}
	return tmp;
}

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = Math.exp(-l);
	double tmp;
	if ((Math.exp(l) - t_1) <= -Double.POSITIVE_INFINITY) {
		tmp = ((J * (27.0 - t_1)) * t_0) + U;
	} else {
		tmp = U + (t_0 * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = math.cos((K / 2.0))
	t_1 = math.exp(-l)
	tmp = 0
	if (math.exp(l) - t_1) <= -math.inf:
		tmp = ((J * (27.0 - t_1)) * t_0) + U
	else:
		tmp = U + (t_0 * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))))
	return tmp

Julia

function code(J, l, K, U)
	t_0 = cos(Float64(K / 2.0))
	t_1 = exp(Float64(-l))
	tmp = 0.0
	if (Float64(exp(l) - t_1) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(J * Float64(27.0 - t_1)) * t_0) + U);
	else
		tmp = Float64(U + Float64(t_0 * Float64(J * Float64(l * Float64(2.0 + Float64(0.3333333333333333 * Float64(l * l)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	t_0 = cos((K / 2.0));
	t_1 = exp(-l);
	tmp = 0.0;
	if ((exp(l) - t_1) <= -Inf)
		tmp = ((J * (27.0 - t_1)) * t_0) + U;
	else
		tmp = U + (t_0 * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-l)], $MachinePrecision]}, If[LessEqual[N[(N[Exp[l], $MachinePrecision] - t$95$1), $MachinePrecision], (-Infinity)], N[(N[(N[(J * N[(27.0 - t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(t$95$0 * N[(J * N[(l * N[(2.0 + N[(0.3333333333333333 * N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) < -inf.0

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   4. Applied egg-rr 100.0%

      \[\leadsto \left(J \cdot \left(\color{blue}{27} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   if -inf.0 < (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

   1. Initial program 82.7%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 93.3%

      \[\leadsto \left(J \cdot \color{blue}{\left(\ell \cdot \left(2 + 0.3333333333333333 \cdot {\ell}^{2}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \color{blue}{\left(\ell \cdot \ell\right)}\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Applied egg-rr 93.3%

      \[\leadsto \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \color{blue}{\left(\ell \cdot \ell\right)}\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{\ell} - e^{-\ell} \leq -\infty:\\ \;\;\;\;\left(J \cdot \left(27 - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \mathbf{else}:\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \left(\ell \cdot \ell\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1.8 \cdot 10^{+113} \lor \neg \left(\ell \leq -2050000\right):\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \left(\ell \cdot \ell\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -1.8e+113) (not (<= l -2050000.0)))
   (+ U (* (cos (/ K 2.0)) (* J (* l (+ 2.0 (* 0.3333333333333333 (* l l)))))))
   (+ U (* J (- 0.3333333333333333 (exp (- l)))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -1.8e+113) || !(l <= -2050000.0)) {
		tmp = U + (cos((K / 2.0)) * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))));
	} else {
		tmp = U + (J * (0.3333333333333333 - exp(-l)));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if ((l <= (-1.8d+113)) .or. (.not. (l <= (-2050000.0d0)))) then
        tmp = u + (cos((k / 2.0d0)) * (j * (l * (2.0d0 + (0.3333333333333333d0 * (l * l))))))
    else
        tmp = u + (j * (0.3333333333333333d0 - exp(-l)))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -1.8e+113) || !(l <= -2050000.0)) {
		tmp = U + (Math.cos((K / 2.0)) * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))));
	} else {
		tmp = U + (J * (0.3333333333333333 - Math.exp(-l)));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -1.8e+113) or not (l <= -2050000.0):
		tmp = U + (math.cos((K / 2.0)) * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))))
	else:
		tmp = U + (J * (0.3333333333333333 - math.exp(-l)))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -1.8e+113) || !(l <= -2050000.0))
		tmp = Float64(U + Float64(cos(Float64(K / 2.0)) * Float64(J * Float64(l * Float64(2.0 + Float64(0.3333333333333333 * Float64(l * l)))))));
	else
		tmp = Float64(U + Float64(J * Float64(0.3333333333333333 - exp(Float64(-l)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -1.8e+113) || ~((l <= -2050000.0)))
		tmp = U + (cos((K / 2.0)) * (J * (l * (2.0 + (0.3333333333333333 * (l * l))))));
	else
		tmp = U + (J * (0.3333333333333333 - exp(-l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -1.8e+113], N[Not[LessEqual[l, -2050000.0]], $MachinePrecision]], N[(U + N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(J * N[(l * N[(2.0 + N[(0.3333333333333333 * N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(0.3333333333333333 - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -1.79999999999999996e113 or -2.05e6 < l

   1. Initial program 86.2%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 94.3%

      \[\leadsto \left(J \cdot \color{blue}{\left(\ell \cdot \left(2 + 0.3333333333333333 \cdot {\ell}^{2}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. unpow2 94.3%

         \[\leadsto \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \color{blue}{\left(\ell \cdot \ell\right)}\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Applied egg-rr 94.3%

      \[\leadsto \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \color{blue}{\left(\ell \cdot \ell\right)}\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   if -1.79999999999999996e113 < l < -2.05e6

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 88.5%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 88.5%

      \[\leadsto J \cdot \left(\color{blue}{0.3333333333333333} - e^{-\ell}\right) + U \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1.8 \cdot 10^{+113} \lor \neg \left(\ell \leq -2050000\right):\\ \;\;\;\;U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot \left(\ell \cdot \left(2 + 0.3333333333333333 \cdot \left(\ell \cdot \ell\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -0.95:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -0.95)
   (+ U (* J (- 0.3333333333333333 (exp (- l)))))
   (if (<= l 2.4e-17)
     (+ U (* 2.0 (* l (* J (cos (* K 0.5))))))
     (+ U (* J (- (exp l) 0.3333333333333333))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -0.95) {
		tmp = U + (J * (0.3333333333333333 - exp(-l)));
	} else if (l <= 2.4e-17) {
		tmp = U + (2.0 * (l * (J * cos((K * 0.5)))));
	} else {
		tmp = U + (J * (exp(l) - 0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if (l <= (-0.95d0)) then
        tmp = u + (j * (0.3333333333333333d0 - exp(-l)))
    else if (l <= 2.4d-17) then
        tmp = u + (2.0d0 * (l * (j * cos((k * 0.5d0)))))
    else
        tmp = u + (j * (exp(l) - 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -0.95) {
		tmp = U + (J * (0.3333333333333333 - Math.exp(-l)));
	} else if (l <= 2.4e-17) {
		tmp = U + (2.0 * (l * (J * Math.cos((K * 0.5)))));
	} else {
		tmp = U + (J * (Math.exp(l) - 0.3333333333333333));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -0.95:
		tmp = U + (J * (0.3333333333333333 - math.exp(-l)))
	elif l <= 2.4e-17:
		tmp = U + (2.0 * (l * (J * math.cos((K * 0.5)))))
	else:
		tmp = U + (J * (math.exp(l) - 0.3333333333333333))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -0.95)
		tmp = Float64(U + Float64(J * Float64(0.3333333333333333 - exp(Float64(-l)))));
	elseif (l <= 2.4e-17)
		tmp = Float64(U + Float64(2.0 * Float64(l * Float64(J * cos(Float64(K * 0.5))))));
	else
		tmp = Float64(U + Float64(J * Float64(exp(l) - 0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -0.95)
		tmp = U + (J * (0.3333333333333333 - exp(-l)));
	elseif (l <= 2.4e-17)
		tmp = U + (2.0 * (l * (J * cos((K * 0.5)))));
	else
		tmp = U + (J * (exp(l) - 0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -0.95], N[(U + N[(J * N[(0.3333333333333333 - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2.4e-17], N[(U + N[(2.0 * N[(l * N[(J * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(N[Exp[l], $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -0.94999999999999996

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 76.4%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 76.4%

      \[\leadsto J \cdot \left(\color{blue}{0.3333333333333333} - e^{-\ell}\right) + U \]

   if -0.94999999999999996 < l < 2.39999999999999986e-17

   1. Initial program 69.1%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 99.9%

      \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   6. Taylor expanded in J around 0 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]
   7. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\ell \cdot \cos \left(0.5 \cdot K\right)\right) \cdot J\right)} + U \]

      2. associate-*l* 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\ell \cdot \left(\cos \left(0.5 \cdot K\right) \cdot J\right)\right)} + U \]

      3. *-commutative 99.9%

         \[\leadsto 2 \cdot \left(\ell \cdot \color{blue}{\left(J \cdot \cos \left(0.5 \cdot K\right)\right)}\right) + U \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]

   if 2.39999999999999986e-17 < l

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 78.0%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 77.3%

      \[\leadsto J \cdot \left(e^{\ell} - \color{blue}{0.3333333333333333}\right) + U \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -0.95:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;U + 2 \cdot \left(\ell \cdot \left(J \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -0.95:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -0.95)
   (+ U (* J (- 0.3333333333333333 (exp (- l)))))
   (if (<= l 2.4e-17)
     (+ U (* 2.0 (* J (* l (cos (* K 0.5))))))
     (+ U (* J (- (exp l) 0.3333333333333333))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -0.95) {
		tmp = U + (J * (0.3333333333333333 - exp(-l)));
	} else if (l <= 2.4e-17) {
		tmp = U + (2.0 * (J * (l * cos((K * 0.5)))));
	} else {
		tmp = U + (J * (exp(l) - 0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if (l <= (-0.95d0)) then
        tmp = u + (j * (0.3333333333333333d0 - exp(-l)))
    else if (l <= 2.4d-17) then
        tmp = u + (2.0d0 * (j * (l * cos((k * 0.5d0)))))
    else
        tmp = u + (j * (exp(l) - 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -0.95) {
		tmp = U + (J * (0.3333333333333333 - Math.exp(-l)));
	} else if (l <= 2.4e-17) {
		tmp = U + (2.0 * (J * (l * Math.cos((K * 0.5)))));
	} else {
		tmp = U + (J * (Math.exp(l) - 0.3333333333333333));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -0.95:
		tmp = U + (J * (0.3333333333333333 - math.exp(-l)))
	elif l <= 2.4e-17:
		tmp = U + (2.0 * (J * (l * math.cos((K * 0.5)))))
	else:
		tmp = U + (J * (math.exp(l) - 0.3333333333333333))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -0.95)
		tmp = Float64(U + Float64(J * Float64(0.3333333333333333 - exp(Float64(-l)))));
	elseif (l <= 2.4e-17)
		tmp = Float64(U + Float64(2.0 * Float64(J * Float64(l * cos(Float64(K * 0.5))))));
	else
		tmp = Float64(U + Float64(J * Float64(exp(l) - 0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -0.95)
		tmp = U + (J * (0.3333333333333333 - exp(-l)));
	elseif (l <= 2.4e-17)
		tmp = U + (2.0 * (J * (l * cos((K * 0.5)))));
	else
		tmp = U + (J * (exp(l) - 0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -0.95], N[(U + N[(J * N[(0.3333333333333333 - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2.4e-17], N[(U + N[(2.0 * N[(J * N[(l * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(N[Exp[l], $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -0.94999999999999996

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 76.4%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 76.4%

      \[\leadsto J \cdot \left(\color{blue}{0.3333333333333333} - e^{-\ell}\right) + U \]

   if -0.94999999999999996 < l < 2.39999999999999986e-17

   1. Initial program 69.1%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]

   if 2.39999999999999986e-17 < l

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 78.0%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 77.3%

      \[\leadsto J \cdot \left(e^{\ell} - \color{blue}{0.3333333333333333}\right) + U \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -0.95:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;U + 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -0.76:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\ell, J \cdot 2, U\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -0.76)
   (+ U (* J (- 0.3333333333333333 (exp (- l)))))
   (if (<= l 2.4e-17)
     (fma l (* J 2.0) U)
     (+ U (* J (- (exp l) 0.3333333333333333))))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -0.76) {
		tmp = U + (J * (0.3333333333333333 - exp(-l)));
	} else if (l <= 2.4e-17) {
		tmp = fma(l, (J * 2.0), U);
	} else {
		tmp = U + (J * (exp(l) - 0.3333333333333333));
	}
	return tmp;
}

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -0.76)
		tmp = Float64(U + Float64(J * Float64(0.3333333333333333 - exp(Float64(-l)))));
	elseif (l <= 2.4e-17)
		tmp = fma(l, Float64(J * 2.0), U);
	else
		tmp = Float64(U + Float64(J * Float64(exp(l) - 0.3333333333333333)));
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -0.76], N[(U + N[(J * N[(0.3333333333333333 - N[Exp[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2.4e-17], N[(l * N[(J * 2.0), $MachinePrecision] + U), $MachinePrecision], N[(U + N[(J * N[(N[Exp[l], $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -0.76000000000000001

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 76.4%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 76.4%

      \[\leadsto J \cdot \left(\color{blue}{0.3333333333333333} - e^{-\ell}\right) + U \]

   if -0.76000000000000001 < l < 2.39999999999999986e-17

   1. Initial program 69.1%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 99.9%

      \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   6. Taylor expanded in K around 0 84.7%

      \[\leadsto \color{blue}{U + 2 \cdot \left(J \cdot \ell\right)} \]
   7. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right) + U} \]

      2. associate-*r* 84.7%

         \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

      3. *-commutative 84.7%

         \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot J\right)} + U \]

      4. fma-define 84.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, 2 \cdot J, U\right)} \]

   8. Simplified 84.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, 2 \cdot J, U\right)} \]

   if 2.39999999999999986e-17 < l

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 78.0%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 77.3%

      \[\leadsto J \cdot \left(e^{\ell} - \color{blue}{0.3333333333333333}\right) + U \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -0.76:\\ \;\;\;\;U + J \cdot \left(0.3333333333333333 - e^{-\ell}\right)\\ \mathbf{elif}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\ell, J \cdot 2, U\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;U \cdot \left(1 + J \cdot \frac{\ell \cdot 2}{U}\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l 2.4e-17)
   (* U (+ 1.0 (* J (/ (* l 2.0) U))))
   (+ U (* J (- (exp l) 0.3333333333333333)))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= 2.4e-17) {
		tmp = U * (1.0 + (J * ((l * 2.0) / U)));
	} else {
		tmp = U + (J * (exp(l) - 0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if (l <= 2.4d-17) then
        tmp = u * (1.0d0 + (j * ((l * 2.0d0) / u)))
    else
        tmp = u + (j * (exp(l) - 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= 2.4e-17) {
		tmp = U * (1.0 + (J * ((l * 2.0) / U)));
	} else {
		tmp = U + (J * (Math.exp(l) - 0.3333333333333333));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= 2.4e-17:
		tmp = U * (1.0 + (J * ((l * 2.0) / U)))
	else:
		tmp = U + (J * (math.exp(l) - 0.3333333333333333))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= 2.4e-17)
		tmp = Float64(U * Float64(1.0 + Float64(J * Float64(Float64(l * 2.0) / U))));
	else
		tmp = Float64(U + Float64(J * Float64(exp(l) - 0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= 2.4e-17)
		tmp = U * (1.0 + (J * ((l * 2.0) / U)));
	else
		tmp = U + (J * (exp(l) - 0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, 2.4e-17], N[(U * N[(1.0 + N[(J * N[(N[(l * 2.0), $MachinePrecision] / U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(U + N[(J * N[(N[Exp[l], $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < 2.39999999999999986e-17

   1. Initial program 81.8%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 72.6%

      \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. *-commutative 72.6%

         \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

      2. associate-*l* 72.6%

         \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Simplified 72.6%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   6. Taylor expanded in U around inf 74.7%

      \[\leadsto \color{blue}{U \cdot \left(1 + 2 \cdot \frac{J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)}{U}\right)} \]

   7. Taylor expanded in K around 0 62.6%

      \[\leadsto U \cdot \left(1 + \color{blue}{2 \cdot \frac{J \cdot \ell}{U}}\right) \]
   8. Step-by-step derivation

      1. *-commutative 62.6%

         \[\leadsto U \cdot \left(1 + \color{blue}{\frac{J \cdot \ell}{U} \cdot 2}\right) \]

      2. associate-/l* 64.2%

         \[\leadsto U \cdot \left(1 + \color{blue}{\left(J \cdot \frac{\ell}{U}\right)} \cdot 2\right) \]

      3. associate-*l* 64.2%

         \[\leadsto U \cdot \left(1 + \color{blue}{J \cdot \left(\frac{\ell}{U} \cdot 2\right)}\right) \]

      4. associate-*l/ 64.2%

         \[\leadsto U \cdot \left(1 + J \cdot \color{blue}{\frac{\ell \cdot 2}{U}}\right) \]

   9. Simplified 64.2%

      \[\leadsto U \cdot \left(1 + \color{blue}{J \cdot \frac{\ell \cdot 2}{U}}\right) \]

   if 2.39999999999999986e-17 < l

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in K around 0 78.0%

      \[\leadsto \color{blue}{J \cdot \left(e^{\ell} - e^{-\ell}\right)} + U \]

   5. Applied egg-rr 77.3%

      \[\leadsto J \cdot \left(e^{\ell} - \color{blue}{0.3333333333333333}\right) + U \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;U \cdot \left(1 + J \cdot \frac{\ell \cdot 2}{U}\right)\\ \mathbf{else}:\\ \;\;\;\;U + J \cdot \left(e^{\ell} - 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.3% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;K \leq 2.7 \cdot 10^{-157} \lor \neg \left(K \leq 1.95 \cdot 10^{-59}\right):\\ \;\;\;\;U \cdot \left(1 + 2 \cdot \left(\ell \cdot \frac{J}{U}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(\ell \cdot 2 + \frac{U}{J}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= K 2.7e-157) (not (<= K 1.95e-59)))
   (* U (+ 1.0 (* 2.0 (* l (/ J U)))))
   (* J (+ (* l 2.0) (/ U J)))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((K <= 2.7e-157) || !(K <= 1.95e-59)) {
		tmp = U * (1.0 + (2.0 * (l * (J / U))));
	} else {
		tmp = J * ((l * 2.0) + (U / J));
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if ((k <= 2.7d-157) .or. (.not. (k <= 1.95d-59))) then
        tmp = u * (1.0d0 + (2.0d0 * (l * (j / u))))
    else
        tmp = j * ((l * 2.0d0) + (u / j))
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((K <= 2.7e-157) || !(K <= 1.95e-59)) {
		tmp = U * (1.0 + (2.0 * (l * (J / U))));
	} else {
		tmp = J * ((l * 2.0) + (U / J));
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (K <= 2.7e-157) or not (K <= 1.95e-59):
		tmp = U * (1.0 + (2.0 * (l * (J / U))))
	else:
		tmp = J * ((l * 2.0) + (U / J))
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((K <= 2.7e-157) || !(K <= 1.95e-59))
		tmp = Float64(U * Float64(1.0 + Float64(2.0 * Float64(l * Float64(J / U)))));
	else
		tmp = Float64(J * Float64(Float64(l * 2.0) + Float64(U / J)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((K <= 2.7e-157) || ~((K <= 1.95e-59)))
		tmp = U * (1.0 + (2.0 * (l * (J / U))));
	else
		tmp = J * ((l * 2.0) + (U / J));
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[K, 2.7e-157], N[Not[LessEqual[K, 1.95e-59]], $MachinePrecision]], N[(U * N[(1.0 + N[(2.0 * N[(l * N[(J / U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(J * N[(N[(l * 2.0), $MachinePrecision] + N[(U / J), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if K < 2.7e-157 or 1.95000000000000009e-59 < K

   1. Initial program 88.6%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 61.2%

      \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. *-commutative 61.2%

         \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

      2. associate-*l* 61.2%

         \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   6. Taylor expanded in U around inf 66.7%

      \[\leadsto \color{blue}{U \cdot \left(1 + 2 \cdot \frac{J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)}{U}\right)} \]

   7. Taylor expanded in K around 0 55.1%

      \[\leadsto U \cdot \left(1 + 2 \cdot \color{blue}{\frac{J \cdot \ell}{U}}\right) \]
   8. Step-by-step derivation

      1. *-commutative 55.1%

         \[\leadsto U \cdot \left(1 + 2 \cdot \frac{\color{blue}{\ell \cdot J}}{U}\right) \]

      2. associate-/l* 53.2%

         \[\leadsto U \cdot \left(1 + 2 \cdot \color{blue}{\left(\ell \cdot \frac{J}{U}\right)}\right) \]

   9. Simplified 53.2%

      \[\leadsto U \cdot \left(1 + 2 \cdot \color{blue}{\left(\ell \cdot \frac{J}{U}\right)}\right) \]

   if 2.7e-157 < K < 1.95000000000000009e-59

   1. Initial program 75.6%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 51.5%

      \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. *-commutative 51.5%

         \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

      2. associate-*l* 51.5%

         \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Simplified 51.5%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   6. Taylor expanded in K around 0 51.5%

      \[\leadsto \color{blue}{U + 2 \cdot \left(J \cdot \ell\right)} \]
   7. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right) + U} \]

      2. associate-*r* 51.5%

         \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

      3. *-commutative 51.5%

         \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot J\right)} + U \]

      4. fma-define 51.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, 2 \cdot J, U\right)} \]

   8. Simplified 51.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, 2 \cdot J, U\right)} \]

   9. Taylor expanded in J around inf 51.4%

      \[\leadsto \color{blue}{J \cdot \left(2 \cdot \ell + \frac{U}{J}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;K \leq 2.7 \cdot 10^{-157} \lor \neg \left(K \leq 1.95 \cdot 10^{-59}\right):\\ \;\;\;\;U \cdot \left(1 + 2 \cdot \left(\ell \cdot \frac{J}{U}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(\ell \cdot 2 + \frac{U}{J}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.2% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;J \leq -2.5 \cdot 10^{+114} \lor \neg \left(J \leq 2.45 \cdot 10^{+53}\right):\\ \;\;\;\;\ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= J -2.5e+114) (not (<= J 2.45e+53))) (* l (* J 2.0)) U))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((J <= -2.5e+114) || !(J <= 2.45e+53)) {
		tmp = l * (J * 2.0);
	} else {
		tmp = U;
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if ((j <= (-2.5d+114)) .or. (.not. (j <= 2.45d+53))) then
        tmp = l * (j * 2.0d0)
    else
        tmp = u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((J <= -2.5e+114) || !(J <= 2.45e+53)) {
		tmp = l * (J * 2.0);
	} else {
		tmp = U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (J <= -2.5e+114) or not (J <= 2.45e+53):
		tmp = l * (J * 2.0)
	else:
		tmp = U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((J <= -2.5e+114) || !(J <= 2.45e+53))
		tmp = Float64(l * Float64(J * 2.0));
	else
		tmp = U;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((J <= -2.5e+114) || ~((J <= 2.45e+53)))
		tmp = l * (J * 2.0);
	else
		tmp = U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[J, -2.5e+114], N[Not[LessEqual[J, 2.45e+53]], $MachinePrecision]], N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision], U]

Derivation

1. Split input into 2 regimes

2. if J < -2.5e114 or 2.45000000000000009e53 < J

   1. Initial program 75.9%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in l around 0 74.8%

      \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
   4. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

      2. associate-*l* 74.8%

         \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Simplified 74.8%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   6. Taylor expanded in K around 0 58.3%

      \[\leadsto \color{blue}{U + 2 \cdot \left(J \cdot \ell\right)} \]
   7. Step-by-step derivation

      1. +-commutative 58.3%

         \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right) + U} \]

      2. associate-*r* 58.3%

         \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

      3. *-commutative 58.3%

         \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot J\right)} + U \]

      4. fma-define 58.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, 2 \cdot J, U\right)} \]

   8. Simplified 58.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\ell, 2 \cdot J, U\right)} \]

   9. Taylor expanded in l around inf 48.4%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 48.4%

          \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} \]

       2. *-commutative 48.4%

          \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot J\right)} \]

   11. Simplified 48.4%

       \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot J\right)} \]

   if -2.5e114 < J < 2.45000000000000009e53

   1. Initial program 95.1%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in J around 0 42.0%

      \[\leadsto \color{blue}{U} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;J \leq -2.5 \cdot 10^{+114} \lor \neg \left(J \leq 2.45 \cdot 10^{+53}\right):\\ \;\;\;\;\ell \cdot \left(J \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.6% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -750 \lor \neg \left(\ell \leq 2.9 \cdot 10^{+74}\right):\\ \;\;\;\;U \cdot U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (or (<= l -750.0) (not (<= l 2.9e+74))) (* U U) U))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -750.0) || !(l <= 2.9e+74)) {
		tmp = U * U;
	} else {
		tmp = U;
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if ((l <= (-750.0d0)) .or. (.not. (l <= 2.9d+74))) then
        tmp = u * u
    else
        tmp = u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((l <= -750.0) || !(l <= 2.9e+74)) {
		tmp = U * U;
	} else {
		tmp = U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (l <= -750.0) or not (l <= 2.9e+74):
		tmp = U * U
	else:
		tmp = U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if ((l <= -750.0) || !(l <= 2.9e+74))
		tmp = Float64(U * U);
	else
		tmp = U;
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if ((l <= -750.0) || ~((l <= 2.9e+74)))
		tmp = U * U;
	else
		tmp = U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[Or[LessEqual[l, -750.0], N[Not[LessEqual[l, 2.9e+74]], $MachinePrecision]], N[(U * U), $MachinePrecision], U]

Derivation

1. Split input into 2 regimes

2. if l < -750 or 2.9000000000000002e74 < l

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   4. Applied egg-rr 13.1%

      \[\leadsto \color{blue}{U \cdot U} \]

   if -750 < l < 2.9000000000000002e74

   1. Initial program 73.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in J around 0 62.8%

      \[\leadsto \color{blue}{U} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -750 \lor \neg \left(\ell \leq 2.9 \cdot 10^{+74}\right):\\ \;\;\;\;U \cdot U\\ \mathbf{else}:\\ \;\;\;\;U\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.6% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -760:\\ \;\;\;\;U \cdot \left(U - -4\right)\\ \mathbf{elif}\;\ell \leq 2.9 \cdot 10^{+74}:\\ \;\;\;\;U\\ \mathbf{else}:\\ \;\;\;\;U \cdot U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -760.0) (* U (- U -4.0)) (if (<= l 2.9e+74) U (* U U))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -760.0) {
		tmp = U * (U - -4.0);
	} else if (l <= 2.9e+74) {
		tmp = U;
	} else {
		tmp = U * U;
	}
	return tmp;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: tmp
    if (l <= (-760.0d0)) then
        tmp = u * (u - (-4.0d0))
    else if (l <= 2.9d+74) then
        tmp = u
    else
        tmp = u * u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -760.0) {
		tmp = U * (U - -4.0);
	} else if (l <= 2.9e+74) {
		tmp = U;
	} else {
		tmp = U * U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -760.0:
		tmp = U * (U - -4.0)
	elif l <= 2.9e+74:
		tmp = U
	else:
		tmp = U * U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -760.0)
		tmp = Float64(U * Float64(U - -4.0));
	elseif (l <= 2.9e+74)
		tmp = U;
	else
		tmp = Float64(U * U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -760.0)
		tmp = U * (U - -4.0);
	elseif (l <= 2.9e+74)
		tmp = U;
	else
		tmp = U * U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -760.0], N[(U * N[(U - -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2.9e+74], U, N[(U * U), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -760

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   4. Applied egg-rr 9.8%

      \[\leadsto \color{blue}{U \cdot \left(U - -4\right)} \]

   if -760 < l < 2.9000000000000002e74

   1. Initial program 73.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   3. Taylor expanded in J around 0 62.8%

      \[\leadsto \color{blue}{U} \]

   if 2.9000000000000002e74 < l

   1. Initial program 100.0%

      \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
   2. Add Preprocessing

   4. Applied egg-rr 16.8%

      \[\leadsto \color{blue}{U \cdot U} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 60.4% accurate, 28.4× speedup

Math

\[\begin{array}{l} \\ U \cdot \left(1 + J \cdot \frac{\ell \cdot 2}{U}\right) \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 (* U (+ 1.0 (* J (/ (* l 2.0) U)))))

C

double code(double J, double l, double K, double U) {
	return U * (1.0 + (J * ((l * 2.0) / U)));
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = u * (1.0d0 + (j * ((l * 2.0d0) / u)))
end function

Java

public static double code(double J, double l, double K, double U) {
	return U * (1.0 + (J * ((l * 2.0) / U)));
}

Python

def code(J, l, K, U):
	return U * (1.0 + (J * ((l * 2.0) / U)))

Julia

function code(J, l, K, U)
	return Float64(U * Float64(1.0 + Float64(J * Float64(Float64(l * 2.0) / U))))
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = U * (1.0 + (J * ((l * 2.0) / U)));
end

Wolfram

code[J_, l_, K_, U_] := N[(U * N[(1.0 + N[(J * N[(N[(l * 2.0), $MachinePrecision] / U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.6%

   \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
2. Add Preprocessing

3. Taylor expanded in l around 0 60.4%

   \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
4. Step-by-step derivation

   1. *-commutative 60.4%

      \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   2. associate-*l* 60.4%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

5. Simplified 60.4%

   \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

6. Taylor expanded in U around inf 64.8%

   \[\leadsto \color{blue}{U \cdot \left(1 + 2 \cdot \frac{J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)}{U}\right)} \]

7. Taylor expanded in K around 0 54.0%

   \[\leadsto U \cdot \left(1 + \color{blue}{2 \cdot \frac{J \cdot \ell}{U}}\right) \]
8. Step-by-step derivation

   1. *-commutative 54.0%

      \[\leadsto U \cdot \left(1 + \color{blue}{\frac{J \cdot \ell}{U} \cdot 2}\right) \]

   2. associate-/l* 57.0%

      \[\leadsto U \cdot \left(1 + \color{blue}{\left(J \cdot \frac{\ell}{U}\right)} \cdot 2\right) \]

   3. associate-*l* 57.0%

      \[\leadsto U \cdot \left(1 + \color{blue}{J \cdot \left(\frac{\ell}{U} \cdot 2\right)}\right) \]

   4. associate-*l/ 57.0%

      \[\leadsto U \cdot \left(1 + J \cdot \color{blue}{\frac{\ell \cdot 2}{U}}\right) \]

9. Simplified 57.0%

   \[\leadsto U \cdot \left(1 + \color{blue}{J \cdot \frac{\ell \cdot 2}{U}}\right) \]
10. Add Preprocessing

Alternative 14: 57.6% accurate, 28.4× speedup

Math

\[\begin{array}{l} \\ U \cdot \left(1 + 2 \cdot \frac{\ell \cdot J}{U}\right) \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 (* U (+ 1.0 (* 2.0 (/ (* l J) U)))))

C

double code(double J, double l, double K, double U) {
	return U * (1.0 + (2.0 * ((l * J) / U)));
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = u * (1.0d0 + (2.0d0 * ((l * j) / u)))
end function

Java

public static double code(double J, double l, double K, double U) {
	return U * (1.0 + (2.0 * ((l * J) / U)));
}

Python

def code(J, l, K, U):
	return U * (1.0 + (2.0 * ((l * J) / U)))

Julia

function code(J, l, K, U)
	return Float64(U * Float64(1.0 + Float64(2.0 * Float64(Float64(l * J) / U))))
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = U * (1.0 + (2.0 * ((l * J) / U)));
end

Wolfram

code[J_, l_, K_, U_] := N[(U * N[(1.0 + N[(2.0 * N[(N[(l * J), $MachinePrecision] / U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.6%

   \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
2. Add Preprocessing

3. Taylor expanded in l around 0 60.4%

   \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
4. Step-by-step derivation

   1. *-commutative 60.4%

      \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   2. associate-*l* 60.4%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

5. Simplified 60.4%

   \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

6. Taylor expanded in U around inf 64.8%

   \[\leadsto \color{blue}{U \cdot \left(1 + 2 \cdot \frac{J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)}{U}\right)} \]

7. Taylor expanded in K around 0 54.0%

   \[\leadsto U \cdot \left(1 + \color{blue}{2 \cdot \frac{J \cdot \ell}{U}}\right) \]
8. Step-by-step derivation

   1. *-commutative 54.0%

      \[\leadsto U \cdot \left(1 + 2 \cdot \frac{\color{blue}{\ell \cdot J}}{U}\right) \]

9. Simplified 54.0%

   \[\leadsto U \cdot \left(1 + \color{blue}{2 \cdot \frac{\ell \cdot J}{U}}\right) \]
10. Add Preprocessing

Alternative 15: 54.5% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ U + \ell \cdot \left(J \cdot 2\right) \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 (+ U (* l (* J 2.0))))

C

double code(double J, double l, double K, double U) {
	return U + (l * (J * 2.0));
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = u + (l * (j * 2.0d0))
end function

Java

public static double code(double J, double l, double K, double U) {
	return U + (l * (J * 2.0));
}

Python

def code(J, l, K, U):
	return U + (l * (J * 2.0))

Julia

function code(J, l, K, U)
	return Float64(U + Float64(l * Float64(J * 2.0)))
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = U + (l * (J * 2.0));
end

Wolfram

code[J_, l_, K_, U_] := N[(U + N[(l * N[(J * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.6%

   \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
2. Add Preprocessing

3. Taylor expanded in l around 0 60.4%

   \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]
4. Step-by-step derivation

   1. *-commutative 60.4%

      \[\leadsto \color{blue}{\left(\left(J \cdot \ell\right) \cdot 2\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

   2. associate-*l* 60.4%

      \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

5. Simplified 60.4%

   \[\leadsto \color{blue}{\left(J \cdot \left(\ell \cdot 2\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U \]

6. Taylor expanded in K around 0 50.1%

   \[\leadsto \color{blue}{2 \cdot \left(J \cdot \ell\right)} + U \]
7. Step-by-step derivation

   1. associate-*r* 50.1%

      \[\leadsto \color{blue}{\left(2 \cdot J\right) \cdot \ell} + U \]

   2. *-commutative 50.1%

      \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot J\right)} + U \]

8. Simplified 50.1%

   \[\leadsto \color{blue}{\ell \cdot \left(2 \cdot J\right)} + U \]

9. Final simplification 50.1%

   \[\leadsto U + \ell \cdot \left(J \cdot 2\right) \]
10. Add Preprocessing

Alternative 16: 37.6% accurate, 312.0× speedup

Math

\[\begin{array}{l} \\ U \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 U)

C

double code(double J, double l, double K, double U) {
	return U;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = u
end function

Java

public static double code(double J, double l, double K, double U) {
	return U;
}

Python

def code(J, l, K, U):
	return U

Julia

function code(J, l, K, U)
	return U
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = U;
end

Wolfram

code[J_, l_, K_, U_] := U

Derivation

1. Initial program 87.6%

   \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
2. Add Preprocessing

3. Taylor expanded in J around 0 30.1%

   \[\leadsto \color{blue}{U} \]
4. Add Preprocessing

Alternative 17: 2.7% accurate, 312.0× speedup

Math

\[\begin{array}{l} \\ -4 \end{array} \]

FPCore

(FPCore (J l K U) :precision binary64 -4.0)

C

double code(double J, double l, double K, double U) {
	return -4.0;
}

Fortran

real(8) function code(j, l, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    code = -4.0d0
end function

Java

public static double code(double J, double l, double K, double U) {
	return -4.0;
}

Python

def code(J, l, K, U):
	return -4.0

Julia

function code(J, l, K, U)
	return -4.0
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = -4.0;
end

Wolfram

code[J_, l_, K_, U_] := -4.0

Derivation

1. Initial program 87.6%

   \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U \]
2. Add Preprocessing

4. Applied egg-rr 2.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-3, U, -4\right)} \]
5. Step-by-step derivation

   1. fma-undefine 2.5%

      \[\leadsto \color{blue}{-3 \cdot U + -4} \]

   2. *-commutative 2.5%

      \[\leadsto \color{blue}{U \cdot -3} + -4 \]

   3. fma-define 2.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(U, -3, -4\right)} \]

6. Simplified 2.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(U, -3, -4\right)} \]

7. Taylor expanded in U around 0 2.6%

   \[\leadsto \color{blue}{-4} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024158 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))