Maksimov and Kolovsky, Equation (3)

Percentage Accurate: 72.4% → 99.2%

Time: 11.7s

Alternatives: 7

Speedup: 1.9×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \left(\left(-2 \cdot J\right) \cdot t_0\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot t_0}\right)}^{2}} \end{array} \end{array} \]

FPCore

(FPCore (J K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))))
   (* (* (* -2.0 J) t_0) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) t_0)) 2.0))))))

C

double code(double J, double K, double U) {
	double t_0 = cos((K / 2.0));
	return ((-2.0 * J) * t_0) * sqrt((1.0 + pow((U / ((2.0 * J) * t_0)), 2.0)));
}

Fortran

real(8) function code(j, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    t_0 = cos((k / 2.0d0))
    code = (((-2.0d0) * j) * t_0) * sqrt((1.0d0 + ((u / ((2.0d0 * j) * t_0)) ** 2.0d0)))
end function

Java

public static double code(double J, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	return ((-2.0 * J) * t_0) * Math.sqrt((1.0 + Math.pow((U / ((2.0 * J) * t_0)), 2.0)));
}

Python

def code(J, K, U):
	t_0 = math.cos((K / 2.0))
	return ((-2.0 * J) * t_0) * math.sqrt((1.0 + math.pow((U / ((2.0 * J) * t_0)), 2.0)))

Julia

function code(J, K, U)
	t_0 = cos(Float64(K / 2.0))
	return Float64(Float64(Float64(-2.0 * J) * t_0) * sqrt(Float64(1.0 + (Float64(U / Float64(Float64(2.0 * J) * t_0)) ^ 2.0))))
end

MATLAB

function tmp = code(J, K, U)
	t_0 = cos((K / 2.0));
	tmp = ((-2.0 * J) * t_0) * sqrt((1.0 + ((U / ((2.0 * J) * t_0)) ^ 2.0)));
end

Wolfram

code[J_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(-2.0 * J), $MachinePrecision] * t$95$0), $MachinePrecision] * N[Sqrt[N[(1.0 + N[Power[N[(U / N[(N[(2.0 * J), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Initial Program: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ \left(\left(-2 \cdot J\right) \cdot t_0\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot t_0}\right)}^{2}} \end{array} \end{array} \]

FPCore

(FPCore (J K U)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))))
   (* (* (* -2.0 J) t_0) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) t_0)) 2.0))))))

C

double code(double J, double K, double U) {
	double t_0 = cos((K / 2.0));
	return ((-2.0 * J) * t_0) * sqrt((1.0 + pow((U / ((2.0 * J) * t_0)), 2.0)));
}

Fortran

real(8) function code(j, k, u)
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: u
    real(8) :: t_0
    t_0 = cos((k / 2.0d0))
    code = (((-2.0d0) * j) * t_0) * sqrt((1.0d0 + ((u / ((2.0d0 * j) * t_0)) ** 2.0d0)))
end function

Java

public static double code(double J, double K, double U) {
	double t_0 = Math.cos((K / 2.0));
	return ((-2.0 * J) * t_0) * Math.sqrt((1.0 + Math.pow((U / ((2.0 * J) * t_0)), 2.0)));
}

Python

def code(J, K, U):
	t_0 = math.cos((K / 2.0))
	return ((-2.0 * J) * t_0) * math.sqrt((1.0 + math.pow((U / ((2.0 * J) * t_0)), 2.0)))

Julia

function code(J, K, U)
	t_0 = cos(Float64(K / 2.0))
	return Float64(Float64(Float64(-2.0 * J) * t_0) * sqrt(Float64(1.0 + (Float64(U / Float64(Float64(2.0 * J) * t_0)) ^ 2.0))))
end

MATLAB

function tmp = code(J, K, U)
	t_0 = cos((K / 2.0));
	tmp = ((-2.0 * J) * t_0) * sqrt((1.0 + ((U / ((2.0 * J) * t_0)) ^ 2.0)));
end

Wolfram

code[J_, K_, U_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(-2.0 * J), $MachinePrecision] * t$95$0), $MachinePrecision] * N[Sqrt[N[(1.0 + N[Power[N[(U / N[(N[(2.0 * J), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} U_m = \left|U\right| \\ J_m = \left|J\right| \\ J_s = \mathsf{copysign}\left(1, J\right) \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ t_1 := J_m \cdot t_0\\ t_2 := \left(\left(-2 \cdot J_m\right) \cdot t_0\right) \cdot \sqrt{1 + {\left(\frac{U_m}{t_0 \cdot \left(J_m \cdot 2\right)}\right)}^{2}}\\ J_s \cdot \begin{array}{l} \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;-2 \cdot \left(U_m \cdot 0.5\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;-2 \cdot \left(t_1 \cdot \mathsf{hypot}\left(1, \frac{\frac{U_m}{2}}{t_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(U_m \cdot -0.5\right)\\ \end{array} \end{array} \end{array} \]

FPCore

U_m = (fabs.f64 U)
J_m = (fabs.f64 J)
J_s = (copysign.f64 1 J)
(FPCore (J_s J_m K U_m)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0)))
        (t_1 (* J_m t_0))
        (t_2
         (*
          (* (* -2.0 J_m) t_0)
          (sqrt (+ 1.0 (pow (/ U_m (* t_0 (* J_m 2.0))) 2.0))))))
   (*
    J_s
    (if (<= t_2 (- INFINITY))
      (* -2.0 (* U_m 0.5))
      (if (<= t_2 2e+289)
        (* -2.0 (* t_1 (hypot 1.0 (/ (/ U_m 2.0) t_1))))
        (* -2.0 (* U_m -0.5)))))))

C

U_m = fabs(U);
J_m = fabs(J);
J_s = copysign(1.0, J);
double code(double J_s, double J_m, double K, double U_m) {
	double t_0 = cos((K / 2.0));
	double t_1 = J_m * t_0;
	double t_2 = ((-2.0 * J_m) * t_0) * sqrt((1.0 + pow((U_m / (t_0 * (J_m * 2.0))), 2.0)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = -2.0 * (U_m * 0.5);
	} else if (t_2 <= 2e+289) {
		tmp = -2.0 * (t_1 * hypot(1.0, ((U_m / 2.0) / t_1)));
	} else {
		tmp = -2.0 * (U_m * -0.5);
	}
	return J_s * tmp;
}

Java

U_m = Math.abs(U);
J_m = Math.abs(J);
J_s = Math.copySign(1.0, J);
public static double code(double J_s, double J_m, double K, double U_m) {
	double t_0 = Math.cos((K / 2.0));
	double t_1 = J_m * t_0;
	double t_2 = ((-2.0 * J_m) * t_0) * Math.sqrt((1.0 + Math.pow((U_m / (t_0 * (J_m * 2.0))), 2.0)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 * (U_m * 0.5);
	} else if (t_2 <= 2e+289) {
		tmp = -2.0 * (t_1 * Math.hypot(1.0, ((U_m / 2.0) / t_1)));
	} else {
		tmp = -2.0 * (U_m * -0.5);
	}
	return J_s * tmp;
}

Python

U_m = math.fabs(U)
J_m = math.fabs(J)
J_s = math.copysign(1.0, J)
def code(J_s, J_m, K, U_m):
	t_0 = math.cos((K / 2.0))
	t_1 = J_m * t_0
	t_2 = ((-2.0 * J_m) * t_0) * math.sqrt((1.0 + math.pow((U_m / (t_0 * (J_m * 2.0))), 2.0)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = -2.0 * (U_m * 0.5)
	elif t_2 <= 2e+289:
		tmp = -2.0 * (t_1 * math.hypot(1.0, ((U_m / 2.0) / t_1)))
	else:
		tmp = -2.0 * (U_m * -0.5)
	return J_s * tmp

Julia

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0, J)
function code(J_s, J_m, K, U_m)
	t_0 = cos(Float64(K / 2.0))
	t_1 = Float64(J_m * t_0)
	t_2 = Float64(Float64(Float64(-2.0 * J_m) * t_0) * sqrt(Float64(1.0 + (Float64(U_m / Float64(t_0 * Float64(J_m * 2.0))) ^ 2.0))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(-2.0 * Float64(U_m * 0.5));
	elseif (t_2 <= 2e+289)
		tmp = Float64(-2.0 * Float64(t_1 * hypot(1.0, Float64(Float64(U_m / 2.0) / t_1))));
	else
		tmp = Float64(-2.0 * Float64(U_m * -0.5));
	end
	return Float64(J_s * tmp)
end

MATLAB

U_m = abs(U);
J_m = abs(J);
J_s = sign(J) * abs(1.0);
function tmp_2 = code(J_s, J_m, K, U_m)
	t_0 = cos((K / 2.0));
	t_1 = J_m * t_0;
	t_2 = ((-2.0 * J_m) * t_0) * sqrt((1.0 + ((U_m / (t_0 * (J_m * 2.0))) ^ 2.0)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = -2.0 * (U_m * 0.5);
	elseif (t_2 <= 2e+289)
		tmp = -2.0 * (t_1 * hypot(1.0, ((U_m / 2.0) / t_1)));
	else
		tmp = -2.0 * (U_m * -0.5);
	end
	tmp_2 = J_s * tmp;
end

Wolfram

U_m = N[Abs[U], $MachinePrecision]
J_m = N[Abs[J], $MachinePrecision]
J_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[J]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[J$95$s_, J$95$m_, K_, U$95$m_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(J$95$m * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-2.0 * J$95$m), $MachinePrecision] * t$95$0), $MachinePrecision] * N[Sqrt[N[(1.0 + N[Power[N[(U$95$m / N[(t$95$0 * N[(J$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(J$95$s * If[LessEqual[t$95$2, (-Infinity)], N[(-2.0 * N[(U$95$m * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+289], N[(-2.0 * N[(t$95$1 * N[Sqrt[1.0 ^ 2 + N[(N[(U$95$m / 2.0), $MachinePrecision] / t$95$1), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(U$95$m * -0.5), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 88.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} U_m = \left|U\right| \\ J_m = \left|J\right| \\ J_s = \mathsf{copysign}\left(1, J\right) \\ J_s \cdot \begin{array}{l} \mathbf{if}\;U_m \leq 8 \cdot 10^{+255}:\\ \;\;\;\;-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(J_m \cdot \mathsf{hypot}\left(1, \frac{0.5 \cdot \frac{U_m}{J_m}}{\cos \left(K \cdot 0.5\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(U_m \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

U_m = (fabs.f64 U)
J_m = (fabs.f64 J)
J_s = (copysign.f64 1 J)
(FPCore (J_s J_m K U_m)
 :precision binary64
 (*
  J_s
  (if (<= U_m 8e+255)
    (*
     -2.0
     (*
      (cos (/ K 2.0))
      (* J_m (hypot 1.0 (/ (* 0.5 (/ U_m J_m)) (cos (* K 0.5)))))))
    (* -2.0 (* U_m 0.5)))))

C

U_m = fabs(U);
J_m = fabs(J);
J_s = copysign(1.0, J);
double code(double J_s, double J_m, double K, double U_m) {
	double tmp;
	if (U_m <= 8e+255) {
		tmp = -2.0 * (cos((K / 2.0)) * (J_m * hypot(1.0, ((0.5 * (U_m / J_m)) / cos((K * 0.5))))));
	} else {
		tmp = -2.0 * (U_m * 0.5);
	}
	return J_s * tmp;
}

Java

U_m = Math.abs(U);
J_m = Math.abs(J);
J_s = Math.copySign(1.0, J);
public static double code(double J_s, double J_m, double K, double U_m) {
	double tmp;
	if (U_m <= 8e+255) {
		tmp = -2.0 * (Math.cos((K / 2.0)) * (J_m * Math.hypot(1.0, ((0.5 * (U_m / J_m)) / Math.cos((K * 0.5))))));
	} else {
		tmp = -2.0 * (U_m * 0.5);
	}
	return J_s * tmp;
}

Python

U_m = math.fabs(U)
J_m = math.fabs(J)
J_s = math.copysign(1.0, J)
def code(J_s, J_m, K, U_m):
	tmp = 0
	if U_m <= 8e+255:
		tmp = -2.0 * (math.cos((K / 2.0)) * (J_m * math.hypot(1.0, ((0.5 * (U_m / J_m)) / math.cos((K * 0.5))))))
	else:
		tmp = -2.0 * (U_m * 0.5)
	return J_s * tmp

Julia

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0, J)
function code(J_s, J_m, K, U_m)
	tmp = 0.0
	if (U_m <= 8e+255)
		tmp = Float64(-2.0 * Float64(cos(Float64(K / 2.0)) * Float64(J_m * hypot(1.0, Float64(Float64(0.5 * Float64(U_m / J_m)) / cos(Float64(K * 0.5)))))));
	else
		tmp = Float64(-2.0 * Float64(U_m * 0.5));
	end
	return Float64(J_s * tmp)
end

MATLAB

U_m = abs(U);
J_m = abs(J);
J_s = sign(J) * abs(1.0);
function tmp_2 = code(J_s, J_m, K, U_m)
	tmp = 0.0;
	if (U_m <= 8e+255)
		tmp = -2.0 * (cos((K / 2.0)) * (J_m * hypot(1.0, ((0.5 * (U_m / J_m)) / cos((K * 0.5))))));
	else
		tmp = -2.0 * (U_m * 0.5);
	end
	tmp_2 = J_s * tmp;
end

Wolfram

U_m = N[Abs[U], $MachinePrecision]
J_m = N[Abs[J], $MachinePrecision]
J_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[J]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[J$95$s_, J$95$m_, K_, U$95$m_] := N[(J$95$s * If[LessEqual[U$95$m, 8e+255], N[(-2.0 * N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(J$95$m * N[Sqrt[1.0 ^ 2 + N[(N[(0.5 * N[(U$95$m / J$95$m), $MachinePrecision]), $MachinePrecision] / N[Cos[N[(K * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(U$95$m * 0.5), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 88.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} U_m = \left|U\right| \\ J_m = \left|J\right| \\ J_s = \mathsf{copysign}\left(1, J\right) \\ \begin{array}{l} t_0 := \cos \left(\frac{K}{2}\right)\\ J_s \cdot \begin{array}{l} \mathbf{if}\;U_m \leq 1.3 \cdot 10^{+256}:\\ \;\;\;\;-2 \cdot \left(t_0 \cdot \left(J_m \cdot \mathsf{hypot}\left(1, \frac{\frac{U_m}{2}}{J_m \cdot t_0}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(U_m \cdot 0.5\right)\\ \end{array} \end{array} \end{array} \]

FPCore

U_m = (fabs.f64 U)
J_m = (fabs.f64 J)
J_s = (copysign.f64 1 J)
(FPCore (J_s J_m K U_m)
 :precision binary64
 (let* ((t_0 (cos (/ K 2.0))))
   (*
    J_s
    (if (<= U_m 1.3e+256)
      (* -2.0 (* t_0 (* J_m (hypot 1.0 (/ (/ U_m 2.0) (* J_m t_0))))))
      (* -2.0 (* U_m 0.5))))))

C

U_m = fabs(U);
J_m = fabs(J);
J_s = copysign(1.0, J);
double code(double J_s, double J_m, double K, double U_m) {
	double t_0 = cos((K / 2.0));
	double tmp;
	if (U_m <= 1.3e+256) {
		tmp = -2.0 * (t_0 * (J_m * hypot(1.0, ((U_m / 2.0) / (J_m * t_0)))));
	} else {
		tmp = -2.0 * (U_m * 0.5);
	}
	return J_s * tmp;
}

Java

U_m = Math.abs(U);
J_m = Math.abs(J);
J_s = Math.copySign(1.0, J);
public static double code(double J_s, double J_m, double K, double U_m) {
	double t_0 = Math.cos((K / 2.0));
	double tmp;
	if (U_m <= 1.3e+256) {
		tmp = -2.0 * (t_0 * (J_m * Math.hypot(1.0, ((U_m / 2.0) / (J_m * t_0)))));
	} else {
		tmp = -2.0 * (U_m * 0.5);
	}
	return J_s * tmp;
}

Python

U_m = math.fabs(U)
J_m = math.fabs(J)
J_s = math.copysign(1.0, J)
def code(J_s, J_m, K, U_m):
	t_0 = math.cos((K / 2.0))
	tmp = 0
	if U_m <= 1.3e+256:
		tmp = -2.0 * (t_0 * (J_m * math.hypot(1.0, ((U_m / 2.0) / (J_m * t_0)))))
	else:
		tmp = -2.0 * (U_m * 0.5)
	return J_s * tmp

Julia

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0, J)
function code(J_s, J_m, K, U_m)
	t_0 = cos(Float64(K / 2.0))
	tmp = 0.0
	if (U_m <= 1.3e+256)
		tmp = Float64(-2.0 * Float64(t_0 * Float64(J_m * hypot(1.0, Float64(Float64(U_m / 2.0) / Float64(J_m * t_0))))));
	else
		tmp = Float64(-2.0 * Float64(U_m * 0.5));
	end
	return Float64(J_s * tmp)
end

MATLAB

U_m = abs(U);
J_m = abs(J);
J_s = sign(J) * abs(1.0);
function tmp_2 = code(J_s, J_m, K, U_m)
	t_0 = cos((K / 2.0));
	tmp = 0.0;
	if (U_m <= 1.3e+256)
		tmp = -2.0 * (t_0 * (J_m * hypot(1.0, ((U_m / 2.0) / (J_m * t_0)))));
	else
		tmp = -2.0 * (U_m * 0.5);
	end
	tmp_2 = J_s * tmp;
end

Wolfram

U_m = N[Abs[U], $MachinePrecision]
J_m = N[Abs[J], $MachinePrecision]
J_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[J]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[J$95$s_, J$95$m_, K_, U$95$m_] := Block[{t$95$0 = N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]}, N[(J$95$s * If[LessEqual[U$95$m, 1.3e+256], N[(-2.0 * N[(t$95$0 * N[(J$95$m * N[Sqrt[1.0 ^ 2 + N[(N[(U$95$m / 2.0), $MachinePrecision] / N[(J$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(U$95$m * 0.5), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 76.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} U_m = \left|U\right| \\ J_m = \left|J\right| \\ J_s = \mathsf{copysign}\left(1, J\right) \\ J_s \cdot \begin{array}{l} \mathbf{if}\;J_m \leq 3.5 \cdot 10^{-86}:\\ \;\;\;\;-2 \cdot \left(U_m \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(J_m \cdot \mathsf{hypot}\left(1, 0.5 \cdot \frac{U_m}{J_m}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

U_m = (fabs.f64 U)
J_m = (fabs.f64 J)
J_s = (copysign.f64 1 J)
(FPCore (J_s J_m K U_m)
 :precision binary64
 (*
  J_s
  (if (<= J_m 3.5e-86)
    (* -2.0 (* U_m 0.5))
    (* -2.0 (* (cos (/ K 2.0)) (* J_m (hypot 1.0 (* 0.5 (/ U_m J_m)))))))))

C

U_m = fabs(U);
J_m = fabs(J);
J_s = copysign(1.0, J);
double code(double J_s, double J_m, double K, double U_m) {
	double tmp;
	if (J_m <= 3.5e-86) {
		tmp = -2.0 * (U_m * 0.5);
	} else {
		tmp = -2.0 * (cos((K / 2.0)) * (J_m * hypot(1.0, (0.5 * (U_m / J_m)))));
	}
	return J_s * tmp;
}

Java

U_m = Math.abs(U);
J_m = Math.abs(J);
J_s = Math.copySign(1.0, J);
public static double code(double J_s, double J_m, double K, double U_m) {
	double tmp;
	if (J_m <= 3.5e-86) {
		tmp = -2.0 * (U_m * 0.5);
	} else {
		tmp = -2.0 * (Math.cos((K / 2.0)) * (J_m * Math.hypot(1.0, (0.5 * (U_m / J_m)))));
	}
	return J_s * tmp;
}

Python

U_m = math.fabs(U)
J_m = math.fabs(J)
J_s = math.copysign(1.0, J)
def code(J_s, J_m, K, U_m):
	tmp = 0
	if J_m <= 3.5e-86:
		tmp = -2.0 * (U_m * 0.5)
	else:
		tmp = -2.0 * (math.cos((K / 2.0)) * (J_m * math.hypot(1.0, (0.5 * (U_m / J_m)))))
	return J_s * tmp

Julia

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0, J)
function code(J_s, J_m, K, U_m)
	tmp = 0.0
	if (J_m <= 3.5e-86)
		tmp = Float64(-2.0 * Float64(U_m * 0.5));
	else
		tmp = Float64(-2.0 * Float64(cos(Float64(K / 2.0)) * Float64(J_m * hypot(1.0, Float64(0.5 * Float64(U_m / J_m))))));
	end
	return Float64(J_s * tmp)
end

MATLAB

U_m = abs(U);
J_m = abs(J);
J_s = sign(J) * abs(1.0);
function tmp_2 = code(J_s, J_m, K, U_m)
	tmp = 0.0;
	if (J_m <= 3.5e-86)
		tmp = -2.0 * (U_m * 0.5);
	else
		tmp = -2.0 * (cos((K / 2.0)) * (J_m * hypot(1.0, (0.5 * (U_m / J_m)))));
	end
	tmp_2 = J_s * tmp;
end

Wolfram

U_m = N[Abs[U], $MachinePrecision]
J_m = N[Abs[J], $MachinePrecision]
J_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[J]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[J$95$s_, J$95$m_, K_, U$95$m_] := N[(J$95$s * If[LessEqual[J$95$m, 3.5e-86], N[(-2.0 * N[(U$95$m * 0.5), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision] * N[(J$95$m * N[Sqrt[1.0 ^ 2 + N[(0.5 * N[(U$95$m / J$95$m), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 46.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} U_m = \left|U\right| \\ J_m = \left|J\right| \\ J_s = \mathsf{copysign}\left(1, J\right) \\ \begin{array}{l} t_0 := -2 \cdot \left(J_m \cdot {1}^{0.3333333333333333}\right)\\ t_1 := -2 \cdot \left(U_m \cdot 0.5\right)\\ J_s \cdot \begin{array}{l} \mathbf{if}\;J_m \leq 6 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;J_m \leq 1.85 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;J_m \leq 2.3 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

U_m = (fabs.f64 U)
J_m = (fabs.f64 J)
J_s = (copysign.f64 1 J)
(FPCore (J_s J_m K U_m)
 :precision binary64
 (let* ((t_0 (* -2.0 (* J_m (pow 1.0 0.3333333333333333))))
        (t_1 (* -2.0 (* U_m 0.5))))
   (*
    J_s
    (if (<= J_m 6e-79)
      t_1
      (if (<= J_m 1.85e+58) t_0 (if (<= J_m 2.3e+103) t_1 t_0))))))

C

U_m = fabs(U);
J_m = fabs(J);
J_s = copysign(1.0, J);
double code(double J_s, double J_m, double K, double U_m) {
	double t_0 = -2.0 * (J_m * pow(1.0, 0.3333333333333333));
	double t_1 = -2.0 * (U_m * 0.5);
	double tmp;
	if (J_m <= 6e-79) {
		tmp = t_1;
	} else if (J_m <= 1.85e+58) {
		tmp = t_0;
	} else if (J_m <= 2.3e+103) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return J_s * tmp;
}

Fortran

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0d0, J)
real(8) function code(j_s, j_m, k, u_m)
    real(8), intent (in) :: j_s
    real(8), intent (in) :: j_m
    real(8), intent (in) :: k
    real(8), intent (in) :: u_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-2.0d0) * (j_m * (1.0d0 ** 0.3333333333333333d0))
    t_1 = (-2.0d0) * (u_m * 0.5d0)
    if (j_m <= 6d-79) then
        tmp = t_1
    else if (j_m <= 1.85d+58) then
        tmp = t_0
    else if (j_m <= 2.3d+103) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = j_s * tmp
end function

Java

U_m = Math.abs(U);
J_m = Math.abs(J);
J_s = Math.copySign(1.0, J);
public static double code(double J_s, double J_m, double K, double U_m) {
	double t_0 = -2.0 * (J_m * Math.pow(1.0, 0.3333333333333333));
	double t_1 = -2.0 * (U_m * 0.5);
	double tmp;
	if (J_m <= 6e-79) {
		tmp = t_1;
	} else if (J_m <= 1.85e+58) {
		tmp = t_0;
	} else if (J_m <= 2.3e+103) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return J_s * tmp;
}

Python

U_m = math.fabs(U)
J_m = math.fabs(J)
J_s = math.copysign(1.0, J)
def code(J_s, J_m, K, U_m):
	t_0 = -2.0 * (J_m * math.pow(1.0, 0.3333333333333333))
	t_1 = -2.0 * (U_m * 0.5)
	tmp = 0
	if J_m <= 6e-79:
		tmp = t_1
	elif J_m <= 1.85e+58:
		tmp = t_0
	elif J_m <= 2.3e+103:
		tmp = t_1
	else:
		tmp = t_0
	return J_s * tmp

Julia

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0, J)
function code(J_s, J_m, K, U_m)
	t_0 = Float64(-2.0 * Float64(J_m * (1.0 ^ 0.3333333333333333)))
	t_1 = Float64(-2.0 * Float64(U_m * 0.5))
	tmp = 0.0
	if (J_m <= 6e-79)
		tmp = t_1;
	elseif (J_m <= 1.85e+58)
		tmp = t_0;
	elseif (J_m <= 2.3e+103)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return Float64(J_s * tmp)
end

MATLAB

U_m = abs(U);
J_m = abs(J);
J_s = sign(J) * abs(1.0);
function tmp_2 = code(J_s, J_m, K, U_m)
	t_0 = -2.0 * (J_m * (1.0 ^ 0.3333333333333333));
	t_1 = -2.0 * (U_m * 0.5);
	tmp = 0.0;
	if (J_m <= 6e-79)
		tmp = t_1;
	elseif (J_m <= 1.85e+58)
		tmp = t_0;
	elseif (J_m <= 2.3e+103)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = J_s * tmp;
end

Wolfram

U_m = N[Abs[U], $MachinePrecision]
J_m = N[Abs[J], $MachinePrecision]
J_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[J]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[J$95$s_, J$95$m_, K_, U$95$m_] := Block[{t$95$0 = N[(-2.0 * N[(J$95$m * N[Power[1.0, 0.3333333333333333], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-2.0 * N[(U$95$m * 0.5), $MachinePrecision]), $MachinePrecision]}, N[(J$95$s * If[LessEqual[J$95$m, 6e-79], t$95$1, If[LessEqual[J$95$m, 1.85e+58], t$95$0, If[LessEqual[J$95$m, 2.3e+103], t$95$1, t$95$0]]]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 65.3% accurate, 3.9× speedup

Math

\[\begin{array}{l} U_m = \left|U\right| \\ J_m = \left|J\right| \\ J_s = \mathsf{copysign}\left(1, J\right) \\ J_s \cdot \begin{array}{l} \mathbf{if}\;J_m \leq 1.95 \cdot 10^{-86}:\\ \;\;\;\;-2 \cdot \left(U_m \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(J_m \cdot \cos \left(\frac{K}{2}\right)\right)\\ \end{array} \end{array} \]

FPCore

U_m = (fabs.f64 U)
J_m = (fabs.f64 J)
J_s = (copysign.f64 1 J)
(FPCore (J_s J_m K U_m)
 :precision binary64
 (*
  J_s
  (if (<= J_m 1.95e-86)
    (* -2.0 (* U_m 0.5))
    (* -2.0 (* J_m (cos (/ K 2.0)))))))

C

U_m = fabs(U);
J_m = fabs(J);
J_s = copysign(1.0, J);
double code(double J_s, double J_m, double K, double U_m) {
	double tmp;
	if (J_m <= 1.95e-86) {
		tmp = -2.0 * (U_m * 0.5);
	} else {
		tmp = -2.0 * (J_m * cos((K / 2.0)));
	}
	return J_s * tmp;
}

Fortran

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0d0, J)
real(8) function code(j_s, j_m, k, u_m)
    real(8), intent (in) :: j_s
    real(8), intent (in) :: j_m
    real(8), intent (in) :: k
    real(8), intent (in) :: u_m
    real(8) :: tmp
    if (j_m <= 1.95d-86) then
        tmp = (-2.0d0) * (u_m * 0.5d0)
    else
        tmp = (-2.0d0) * (j_m * cos((k / 2.0d0)))
    end if
    code = j_s * tmp
end function

Java

U_m = Math.abs(U);
J_m = Math.abs(J);
J_s = Math.copySign(1.0, J);
public static double code(double J_s, double J_m, double K, double U_m) {
	double tmp;
	if (J_m <= 1.95e-86) {
		tmp = -2.0 * (U_m * 0.5);
	} else {
		tmp = -2.0 * (J_m * Math.cos((K / 2.0)));
	}
	return J_s * tmp;
}

Python

U_m = math.fabs(U)
J_m = math.fabs(J)
J_s = math.copysign(1.0, J)
def code(J_s, J_m, K, U_m):
	tmp = 0
	if J_m <= 1.95e-86:
		tmp = -2.0 * (U_m * 0.5)
	else:
		tmp = -2.0 * (J_m * math.cos((K / 2.0)))
	return J_s * tmp

Julia

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0, J)
function code(J_s, J_m, K, U_m)
	tmp = 0.0
	if (J_m <= 1.95e-86)
		tmp = Float64(-2.0 * Float64(U_m * 0.5));
	else
		tmp = Float64(-2.0 * Float64(J_m * cos(Float64(K / 2.0))));
	end
	return Float64(J_s * tmp)
end

MATLAB

U_m = abs(U);
J_m = abs(J);
J_s = sign(J) * abs(1.0);
function tmp_2 = code(J_s, J_m, K, U_m)
	tmp = 0.0;
	if (J_m <= 1.95e-86)
		tmp = -2.0 * (U_m * 0.5);
	else
		tmp = -2.0 * (J_m * cos((K / 2.0)));
	end
	tmp_2 = J_s * tmp;
end

Wolfram

U_m = N[Abs[U], $MachinePrecision]
J_m = N[Abs[J], $MachinePrecision]
J_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[J]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[J$95$s_, J$95$m_, K_, U$95$m_] := N[(J$95$s * If[LessEqual[J$95$m, 1.95e-86], N[(-2.0 * N[(U$95$m * 0.5), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(J$95$m * N[Cos[N[(K / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 40.0% accurate, 84.0× speedup

Math

\[\begin{array}{l} U_m = \left|U\right| \\ J_m = \left|J\right| \\ J_s = \mathsf{copysign}\left(1, J\right) \\ J_s \cdot \left(-2 \cdot \left(U_m \cdot 0.5\right)\right) \end{array} \]

FPCore

U_m = (fabs.f64 U)
J_m = (fabs.f64 J)
J_s = (copysign.f64 1 J)
(FPCore (J_s J_m K U_m) :precision binary64 (* J_s (* -2.0 (* U_m 0.5))))

C

U_m = fabs(U);
J_m = fabs(J);
J_s = copysign(1.0, J);
double code(double J_s, double J_m, double K, double U_m) {
	return J_s * (-2.0 * (U_m * 0.5));
}

Fortran

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0d0, J)
real(8) function code(j_s, j_m, k, u_m)
    real(8), intent (in) :: j_s
    real(8), intent (in) :: j_m
    real(8), intent (in) :: k
    real(8), intent (in) :: u_m
    code = j_s * ((-2.0d0) * (u_m * 0.5d0))
end function

Java

U_m = Math.abs(U);
J_m = Math.abs(J);
J_s = Math.copySign(1.0, J);
public static double code(double J_s, double J_m, double K, double U_m) {
	return J_s * (-2.0 * (U_m * 0.5));
}

Python

U_m = math.fabs(U)
J_m = math.fabs(J)
J_s = math.copysign(1.0, J)
def code(J_s, J_m, K, U_m):
	return J_s * (-2.0 * (U_m * 0.5))

Julia

U_m = abs(U)
J_m = abs(J)
J_s = copysign(1.0, J)
function code(J_s, J_m, K, U_m)
	return Float64(J_s * Float64(-2.0 * Float64(U_m * 0.5)))
end

MATLAB

U_m = abs(U);
J_m = abs(J);
J_s = sign(J) * abs(1.0);
function tmp = code(J_s, J_m, K, U_m)
	tmp = J_s * (-2.0 * (U_m * 0.5));
end

Wolfram

U_m = N[Abs[U], $MachinePrecision]
J_m = N[Abs[J], $MachinePrecision]
J_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[J]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[J$95$s_, J$95$m_, K_, U$95$m_] := N[(J$95$s * N[(-2.0 * N[(U$95$m * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023348 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  :precision binary64
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))