Maksimov and Kolovsky, Equation (4)

Percentage Accurate: 85.9% → 99.4%

Time: 10.2s

Alternatives: 10

Speedup: 1.4×

• 50.2% 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: 85.9% 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: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)\right) + U \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (+ (* 2.0 (* J (log1p (expm1 (* l (cos (* K 0.5))))))) U))

C

double code(double J, double l, double K, double U) {
	return (2.0 * (J * log1p(expm1((l * cos((K * 0.5))))))) + U;
}

Java

public static double code(double J, double l, double K, double U) {
	return (2.0 * (J * Math.log1p(Math.expm1((l * Math.cos((K * 0.5))))))) + U;
}

Python

def code(J, l, K, U):
	return (2.0 * (J * math.log1p(math.expm1((l * math.cos((K * 0.5))))))) + U

Julia

function code(J, l, K, U)
	return Float64(Float64(2.0 * Float64(J * log1p(expm1(Float64(l * cos(Float64(K * 0.5))))))) + U)
end

Wolfram

code[J_, l_, K_, U_] := N[(N[(2.0 * N[(J * N[Log[1 + N[(Exp[N[(l * N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in l around 0 65.5%

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

   1. log1p-expm1-u 99.5%

      \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)}\right) + U \]

   2. *-commutative 99.5%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot 0.5\right)}\right)\right)\right) + U \]

   3. metadata-eval 99.5%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) + U \]

   4. div-inv 99.5%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(\frac{K}{2}\right)}\right)\right)\right) + U \]

   5. div-inv 99.5%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot \frac{1}{2}\right)}\right)\right)\right) + U \]

   6. metadata-eval 99.5%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{0.5}\right)\right)\right)\right) + U \]

5. Applied egg-rr 99.5%

   \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)}\right) + U \]
6. Add Preprocessing

Alternative 2: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq 0.05:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell\right)\right)\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) 0.05)
   (+ (* 2.0 (* J (* l (cos (* 0.5 K))))) U)
   (+ (* 2.0 (* J (log1p (expm1 l)))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= 0.05) {
		tmp = (2.0 * (J * (l * cos((0.5 * K))))) + U;
	} else {
		tmp = (2.0 * (J * log1p(expm1(l)))) + U;
	}
	return tmp;
}

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (Math.cos((K / 2.0)) <= 0.05) {
		tmp = (2.0 * (J * (l * Math.cos((0.5 * K))))) + U;
	} else {
		tmp = (2.0 * (J * Math.log1p(Math.expm1(l)))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= 0.05:
		tmp = (2.0 * (J * (l * math.cos((0.5 * K))))) + U
	else:
		tmp = (2.0 * (J * math.log1p(math.expm1(l)))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= 0.05)
		tmp = Float64(Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K))))) + U);
	else
		tmp = Float64(Float64(2.0 * Float64(J * log1p(expm1(l)))) + U);
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], 0.05], N[(N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(N[(2.0 * N[(J * N[Log[1 + N[(Exp[l] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < 0.050000000000000003

   1. Initial program 83.7%

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

   3. Taylor expanded in l around 0 67.7%

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

   if 0.050000000000000003 < (cos.f64 (/.f64 K 2))

   1. Initial program 88.1%

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

   3. Taylor expanded in l around 0 64.6%

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

      1. log1p-expm1-u 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)}\right) + U \]

      2. *-commutative 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot 0.5\right)}\right)\right)\right) + U \]

      3. metadata-eval 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) + U \]

      4. div-inv 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(\frac{K}{2}\right)}\right)\right)\right) + U \]

      5. div-inv 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot \frac{1}{2}\right)}\right)\right)\right) + U \]

      6. metadata-eval 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{0.5}\right)\right)\right)\right) + U \]

   5. Applied egg-rr 100.0%

      \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)}\right) + U \]

   6. Taylor expanded in K around 0 97.3%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{\ell}\right)\right)\right) + U \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 94.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ t_1 := 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell\right)\right)\right) + U\\ \mathbf{if}\;\ell \leq -2.5 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\ell \leq -21500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\ell \leq 2.15 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right) + U\\ \mathbf{elif}\;\ell \leq 6 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (let* ((t_0
         (+ (* (* J (* 0.3333333333333333 (pow l 3.0))) (cos (/ K 2.0))) U))
        (t_1 (+ (* 2.0 (* J (log1p (expm1 l)))) U)))
   (if (<= l -2.5e+108)
     t_0
     (if (<= l -21500000.0)
       t_1
       (if (<= l 2.15e-16)
         (+ (* 2.0 (* J (* l (cos (* 0.5 K))))) U)
         (if (<= l 6e+83) t_1 t_0))))))

C

double code(double J, double l, double K, double U) {
	double t_0 = ((J * (0.3333333333333333 * pow(l, 3.0))) * cos((K / 2.0))) + U;
	double t_1 = (2.0 * (J * log1p(expm1(l)))) + U;
	double tmp;
	if (l <= -2.5e+108) {
		tmp = t_0;
	} else if (l <= -21500000.0) {
		tmp = t_1;
	} else if (l <= 2.15e-16) {
		tmp = (2.0 * (J * (l * cos((0.5 * K))))) + U;
	} else if (l <= 6e+83) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double J, double l, double K, double U) {
	double t_0 = ((J * (0.3333333333333333 * Math.pow(l, 3.0))) * Math.cos((K / 2.0))) + U;
	double t_1 = (2.0 * (J * Math.log1p(Math.expm1(l)))) + U;
	double tmp;
	if (l <= -2.5e+108) {
		tmp = t_0;
	} else if (l <= -21500000.0) {
		tmp = t_1;
	} else if (l <= 2.15e-16) {
		tmp = (2.0 * (J * (l * Math.cos((0.5 * K))))) + U;
	} else if (l <= 6e+83) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	t_0 = ((J * (0.3333333333333333 * math.pow(l, 3.0))) * math.cos((K / 2.0))) + U
	t_1 = (2.0 * (J * math.log1p(math.expm1(l)))) + U
	tmp = 0
	if l <= -2.5e+108:
		tmp = t_0
	elif l <= -21500000.0:
		tmp = t_1
	elif l <= 2.15e-16:
		tmp = (2.0 * (J * (l * math.cos((0.5 * K))))) + U
	elif l <= 6e+83:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(J, l, K, U)
	t_0 = Float64(Float64(Float64(J * Float64(0.3333333333333333 * (l ^ 3.0))) * cos(Float64(K / 2.0))) + U)
	t_1 = Float64(Float64(2.0 * Float64(J * log1p(expm1(l)))) + U)
	tmp = 0.0
	if (l <= -2.5e+108)
		tmp = t_0;
	elseif (l <= -21500000.0)
		tmp = t_1;
	elseif (l <= 2.15e-16)
		tmp = Float64(Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K))))) + U);
	elseif (l <= 6e+83)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := Block[{t$95$0 = N[(N[(N[(J * N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * N[(J * N[Log[1 + N[(Exp[l] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]}, If[LessEqual[l, -2.5e+108], t$95$0, If[LessEqual[l, -21500000.0], t$95$1, If[LessEqual[l, 2.15e-16], N[(N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], If[LessEqual[l, 6e+83], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -2.49999999999999995e108 or 5.9999999999999999e83 < 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 l around 0 100.0%

      \[\leadsto \left(J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3} + 2 \cdot \ell\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   4. Taylor expanded in l around inf 100.0%

      \[\leadsto \left(J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3}\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   if -2.49999999999999995e108 < l < -2.15e7 or 2.1499999999999999e-16 < l < 5.9999999999999999e83

   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 l around 0 15.1%

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

      1. log1p-expm1-u 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)}\right) + U \]

      2. *-commutative 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot 0.5\right)}\right)\right)\right) + U \]

      3. metadata-eval 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) + U \]

      4. div-inv 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(\frac{K}{2}\right)}\right)\right)\right) + U \]

      5. div-inv 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot \frac{1}{2}\right)}\right)\right)\right) + U \]

      6. metadata-eval 100.0%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{0.5}\right)\right)\right)\right) + U \]

   5. Applied egg-rr 100.0%

      \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)}\right) + U \]

   6. Taylor expanded in K around 0 76.9%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{\ell}\right)\right)\right) + U \]

   if -2.15e7 < l < 2.1499999999999999e-16

   1. Initial program 74.2%

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

   3. Taylor expanded in l around 0 98.3%

      \[\leadsto \color{blue}{2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)} + U \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{K}{2} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell\right)\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;\left(J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (/ K 2.0) 2e-10)
   (+ (* 2.0 (* J (log1p (expm1 l)))) U)
   (+
    (* (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* 2.0 l))) (cos (/ K 2.0)))
    U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if ((K / 2.0) <= 2e-10) {
		tmp = (2.0 * (J * log1p(expm1(l)))) + U;
	} else {
		tmp = ((J * ((0.3333333333333333 * pow(l, 3.0)) + (2.0 * l))) * cos((K / 2.0))) + U;
	}
	return tmp;
}

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if ((K / 2.0) <= 2e-10) {
		tmp = (2.0 * (J * Math.log1p(Math.expm1(l)))) + U;
	} else {
		tmp = ((J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (2.0 * l))) * Math.cos((K / 2.0))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if (K / 2.0) <= 2e-10:
		tmp = (2.0 * (J * math.log1p(math.expm1(l)))) + U
	else:
		tmp = ((J * ((0.3333333333333333 * math.pow(l, 3.0)) + (2.0 * l))) * math.cos((K / 2.0))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (Float64(K / 2.0) <= 2e-10)
		tmp = Float64(Float64(2.0 * Float64(J * log1p(expm1(l)))) + U);
	else
		tmp = Float64(Float64(Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(2.0 * l))) * cos(Float64(K / 2.0))) + U);
	end
	return tmp
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[(K / 2.0), $MachinePrecision], 2e-10], N[(N[(2.0 * N[(J * N[Log[1 + N[(Exp[l] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(N[(N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 K 2) < 2.00000000000000007e-10

   1. Initial program 86.8%

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

   3. Taylor expanded in l around 0 65.5%

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

      1. log1p-expm1-u 99.9%

         \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)}\right) + U \]

      2. *-commutative 99.9%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot 0.5\right)}\right)\right)\right) + U \]

      3. metadata-eval 99.9%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) + U \]

      4. div-inv 99.9%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(\frac{K}{2}\right)}\right)\right)\right) + U \]

      5. div-inv 99.9%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \color{blue}{\left(K \cdot \frac{1}{2}\right)}\right)\right)\right) + U \]

      6. metadata-eval 99.9%

         \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot \color{blue}{0.5}\right)\right)\right)\right) + U \]

   5. Applied egg-rr 99.9%

      \[\leadsto 2 \cdot \left(J \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\ell \cdot \cos \left(K \cdot 0.5\right)\right)\right)}\right) + U \]

   6. Taylor expanded in K around 0 86.1%

      \[\leadsto 2 \cdot \left(J \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{\ell}\right)\right)\right) + U \]

   if 2.00000000000000007e-10 < (/.f64 K 2)

   1. Initial program 87.1%

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

   3. Taylor expanded in l around 0 85.8%

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

Alternative 5: 79.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos \left(\frac{K}{2}\right) \leq -0.02:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right) + U\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(0.3333333333333333 \cdot {\ell}^{3} + 2 \cdot \ell\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= (cos (/ K 2.0)) -0.02)
   (+ (* 2.0 (* J (* l (cos (* 0.5 K))))) U)
   (+ (* J (+ (* 0.3333333333333333 (pow l 3.0)) (* 2.0 l))) U)))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (cos((K / 2.0)) <= -0.02) {
		tmp = (2.0 * (J * (l * cos((0.5 * K))))) + U;
	} else {
		tmp = (J * ((0.3333333333333333 * pow(l, 3.0)) + (2.0 * l))) + 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 (cos((k / 2.0d0)) <= (-0.02d0)) then
        tmp = (2.0d0 * (j * (l * cos((0.5d0 * k))))) + u
    else
        tmp = (j * ((0.3333333333333333d0 * (l ** 3.0d0)) + (2.0d0 * l))) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (Math.cos((K / 2.0)) <= -0.02) {
		tmp = (2.0 * (J * (l * Math.cos((0.5 * K))))) + U;
	} else {
		tmp = (J * ((0.3333333333333333 * Math.pow(l, 3.0)) + (2.0 * l))) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if math.cos((K / 2.0)) <= -0.02:
		tmp = (2.0 * (J * (l * math.cos((0.5 * K))))) + U
	else:
		tmp = (J * ((0.3333333333333333 * math.pow(l, 3.0)) + (2.0 * l))) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (cos(Float64(K / 2.0)) <= -0.02)
		tmp = Float64(Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K))))) + U);
	else
		tmp = Float64(Float64(J * Float64(Float64(0.3333333333333333 * (l ^ 3.0)) + Float64(2.0 * l))) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (cos((K / 2.0)) <= -0.02)
		tmp = (2.0 * (J * (l * cos((0.5 * K))))) + U;
	else
		tmp = (J * ((0.3333333333333333 * (l ^ 3.0)) + (2.0 * l))) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision], -0.02], N[(N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(N[(J * N[(N[(0.3333333333333333 * N[Power[l, 3.0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (/.f64 K 2)) < -0.0200000000000000004

   1. Initial program 85.4%

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

   3. Taylor expanded in l around 0 68.6%

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

   if -0.0200000000000000004 < (cos.f64 (/.f64 K 2))

   1. Initial program 87.4%

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

   3. Taylor expanded in l around 0 84.2%

      \[\leadsto \left(J \cdot \color{blue}{\left(0.3333333333333333 \cdot {\ell}^{3} + 2 \cdot \ell\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   4. Taylor expanded in K around 0 80.7%

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

Alternative 6: 55.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)\\ \mathbf{elif}\;\ell \leq -800:\\ \;\;\;\;-4 \cdot \left(J + -0.125 \cdot \left(J \cdot {K}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(J \cdot \ell\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -3e+47)
   (* 2.0 (* J (* l (cos (* 0.5 K)))))
   (if (<= l -800.0)
     (* -4.0 (+ J (* -0.125 (* J (pow K 2.0)))))
     (+ (* 2.0 (* J l)) U))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -3e+47) {
		tmp = 2.0 * (J * (l * cos((0.5 * K))));
	} else if (l <= -800.0) {
		tmp = -4.0 * (J + (-0.125 * (J * pow(K, 2.0))));
	} else {
		tmp = (2.0 * (J * l)) + 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 <= (-3d+47)) then
        tmp = 2.0d0 * (j * (l * cos((0.5d0 * k))))
    else if (l <= (-800.0d0)) then
        tmp = (-4.0d0) * (j + ((-0.125d0) * (j * (k ** 2.0d0))))
    else
        tmp = (2.0d0 * (j * l)) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -3e+47) {
		tmp = 2.0 * (J * (l * Math.cos((0.5 * K))));
	} else if (l <= -800.0) {
		tmp = -4.0 * (J + (-0.125 * (J * Math.pow(K, 2.0))));
	} else {
		tmp = (2.0 * (J * l)) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -3e+47:
		tmp = 2.0 * (J * (l * math.cos((0.5 * K))))
	elif l <= -800.0:
		tmp = -4.0 * (J + (-0.125 * (J * math.pow(K, 2.0))))
	else:
		tmp = (2.0 * (J * l)) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -3e+47)
		tmp = Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K)))));
	elseif (l <= -800.0)
		tmp = Float64(-4.0 * Float64(J + Float64(-0.125 * Float64(J * (K ^ 2.0)))));
	else
		tmp = Float64(Float64(2.0 * Float64(J * l)) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -3e+47)
		tmp = 2.0 * (J * (l * cos((0.5 * K))));
	elseif (l <= -800.0)
		tmp = -4.0 * (J + (-0.125 * (J * (K ^ 2.0))));
	else
		tmp = (2.0 * (J * l)) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -3e+47], N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, -800.0], N[(-4.0 * N[(J + N[(-0.125 * N[(J * N[Power[K, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(J * l), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -3.0000000000000001e47

   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 l around 0 40.6%

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

   4. Taylor expanded in J around inf 40.3%

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

   if -3.0000000000000001e47 < l < -800

   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 3.2%

      \[\leadsto \left(J \cdot \color{blue}{-4}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Taylor expanded in J around inf 3.4%

      \[\leadsto \color{blue}{-4 \cdot \left(J \cdot \cos \left(0.5 \cdot K\right)\right)} \]

   6. Taylor expanded in K around 0 37.9%

      \[\leadsto -4 \cdot \color{blue}{\left(J + -0.125 \cdot \left(J \cdot {K}^{2}\right)\right)} \]

   if -800 < l

   1. Initial program 82.4%

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

   3. Taylor expanded in l around 0 77.3%

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

   4. Taylor expanded in K around 0 66.9%

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

Alternative 7: 55.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -4.5 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right)\\ \mathbf{elif}\;\ell \leq -620:\\ \;\;\;\;0.5 \cdot \left(J \cdot {K}^{2}\right) + U\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(J \cdot \ell\right) + U\\ \end{array} \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (if (<= l -4.5e+47)
   (* 2.0 (* J (* l (cos (* 0.5 K)))))
   (if (<= l -620.0) (+ (* 0.5 (* J (pow K 2.0))) U) (+ (* 2.0 (* J l)) U))))

C

double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -4.5e+47) {
		tmp = 2.0 * (J * (l * cos((0.5 * K))));
	} else if (l <= -620.0) {
		tmp = (0.5 * (J * pow(K, 2.0))) + U;
	} else {
		tmp = (2.0 * (J * l)) + 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 <= (-4.5d+47)) then
        tmp = 2.0d0 * (j * (l * cos((0.5d0 * k))))
    else if (l <= (-620.0d0)) then
        tmp = (0.5d0 * (j * (k ** 2.0d0))) + u
    else
        tmp = (2.0d0 * (j * l)) + u
    end if
    code = tmp
end function

Java

public static double code(double J, double l, double K, double U) {
	double tmp;
	if (l <= -4.5e+47) {
		tmp = 2.0 * (J * (l * Math.cos((0.5 * K))));
	} else if (l <= -620.0) {
		tmp = (0.5 * (J * Math.pow(K, 2.0))) + U;
	} else {
		tmp = (2.0 * (J * l)) + U;
	}
	return tmp;
}

Python

def code(J, l, K, U):
	tmp = 0
	if l <= -4.5e+47:
		tmp = 2.0 * (J * (l * math.cos((0.5 * K))))
	elif l <= -620.0:
		tmp = (0.5 * (J * math.pow(K, 2.0))) + U
	else:
		tmp = (2.0 * (J * l)) + U
	return tmp

Julia

function code(J, l, K, U)
	tmp = 0.0
	if (l <= -4.5e+47)
		tmp = Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K)))));
	elseif (l <= -620.0)
		tmp = Float64(Float64(0.5 * Float64(J * (K ^ 2.0))) + U);
	else
		tmp = Float64(Float64(2.0 * Float64(J * l)) + U);
	end
	return tmp
end

MATLAB

function tmp_2 = code(J, l, K, U)
	tmp = 0.0;
	if (l <= -4.5e+47)
		tmp = 2.0 * (J * (l * cos((0.5 * K))));
	elseif (l <= -620.0)
		tmp = (0.5 * (J * (K ^ 2.0))) + U;
	else
		tmp = (2.0 * (J * l)) + U;
	end
	tmp_2 = tmp;
end

Wolfram

code[J_, l_, K_, U_] := If[LessEqual[l, -4.5e+47], N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, -620.0], N[(N[(0.5 * N[(J * N[Power[K, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision], N[(N[(2.0 * N[(J * l), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -4.49999999999999979e47

   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 l around 0 40.6%

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

   4. Taylor expanded in J around inf 40.3%

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

   if -4.49999999999999979e47 < l < -620

   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 3.2%

      \[\leadsto \left(J \cdot \color{blue}{-4}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

   5. Taylor expanded in K around 0 37.7%

      \[\leadsto \color{blue}{\left(-4 \cdot J + 0.5 \cdot \left(J \cdot {K}^{2}\right)\right)} + U \]

   6. Taylor expanded in K around inf 37.2%

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

   if -620 < l

   1. Initial program 82.4%

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

   3. Taylor expanded in l around 0 77.3%

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

   4. Taylor expanded in K around 0 66.9%

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

Alternative 8: 63.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(J \cdot \left(\ell \cdot \cos \left(0.5 \cdot K\right)\right)\right) + U \end{array} \]

FPCore

(FPCore (J l K U)
 :precision binary64
 (+ (* 2.0 (* J (* l (cos (* 0.5 K))))) U))

C

double code(double J, double l, double K, double U) {
	return (2.0 * (J * (l * cos((0.5 * K))))) + 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 = (2.0d0 * (j * (l * cos((0.5d0 * k))))) + u
end function

Java

public static double code(double J, double l, double K, double U) {
	return (2.0 * (J * (l * Math.cos((0.5 * K))))) + U;
}

Python

def code(J, l, K, U):
	return (2.0 * (J * (l * math.cos((0.5 * K))))) + U

Julia

function code(J, l, K, U)
	return Float64(Float64(2.0 * Float64(J * Float64(l * cos(Float64(0.5 * K))))) + U)
end

MATLAB

function tmp = code(J, l, K, U)
	tmp = (2.0 * (J * (l * cos((0.5 * K))))) + U;
end

Wolfram

code[J_, l_, K_, U_] := N[(N[(2.0 * N[(J * N[(l * N[Cos[N[(0.5 * K), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + U), $MachinePrecision]

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in l around 0 65.5%

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

Alternative 9: 53.3% accurate, 44.6× speedup

Math

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

FPCore

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

C

double code(double J, double l, double K, double U) {
	return (2.0 * (J * l)) + 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 = (2.0d0 * (j * l)) + u
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in l around 0 65.5%

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

4. Taylor expanded in K around 0 54.9%

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

Alternative 10: 35.7% 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 86.9%

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

4. Applied egg-rr 27.7%

   \[\leadsto \left(J \cdot \color{blue}{-4}\right) \cdot \cos \left(\frac{K}{2}\right) + U \]

5. Taylor expanded in J around 0 38.7%

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

Reproduce

herbie shell --seed 2024034 -o generate:simplify
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))