Falkner and Boettcher, Appendix A

Percentage Accurate: 90.0% → 98.8%

Time: 10.5s

Alternatives: 13

Speedup: 1.1×

• 23.6% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. a = -1.9999999999999999e-154
  2. k = 0.0
  3. m = -2.00000000000000007e154

Specification

Math

\[\begin{array}{l} \\ \frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

C

double code(double a, double k, double m) {
	return (a * pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k));
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    code = (a * (k ** m)) / ((1.0d0 + (10.0d0 * k)) + (k * k))
end function

Java

public static double code(double a, double k, double m) {
	return (a * Math.pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k));
}

Python

def code(a, k, m):
	return (a * math.pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k))

Julia

function code(a, k, m)
	return Float64(Float64(a * (k ^ m)) / Float64(Float64(1.0 + Float64(10.0 * k)) + Float64(k * k)))
end

MATLAB

function tmp = code(a, k, m)
	tmp = (a * (k ^ m)) / ((1.0 + (10.0 * k)) + (k * k));
end

Wolfram

code[a_, k_, m_] := N[(N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 + N[(10.0 * k), $MachinePrecision]), $MachinePrecision] + N[(k * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))

C

double code(double a, double k, double m) {
	return (a * pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k));
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    code = (a * (k ** m)) / ((1.0d0 + (10.0d0 * k)) + (k * k))
end function

Java

public static double code(double a, double k, double m) {
	return (a * Math.pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k));
}

Python

def code(a, k, m):
	return (a * math.pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k))

Julia

function code(a, k, m)
	return Float64(Float64(a * (k ^ m)) / Float64(Float64(1.0 + Float64(10.0 * k)) + Float64(k * k)))
end

MATLAB

function tmp = code(a, k, m)
	tmp = (a * (k ^ m)) / ((1.0 + (10.0 * k)) + (k * k));
end

Wolfram

code[a_, k_, m_] := N[(N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 + N[(10.0 * k), $MachinePrecision]), $MachinePrecision] + N[(k * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ \begin{array}{l} t_0 := {k}^{m} \cdot a_m\\ a_s \cdot \begin{array}{l} \mathbf{if}\;\frac{t_0}{\left(1 + k \cdot 10\right) + k \cdot k} \leq 5 \cdot 10^{+191}:\\ \;\;\;\;\frac{{k}^{m} \cdot \left(-\frac{a_m}{\mathsf{hypot}\left(1, k\right)}\right)}{-\mathsf{hypot}\left(1, k\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (let* ((t_0 (* (pow k m) a_m)))
   (*
    a_s
    (if (<= (/ t_0 (+ (+ 1.0 (* k 10.0)) (* k k))) 5e+191)
      (/ (* (pow k m) (- (/ a_m (hypot 1.0 k)))) (- (hypot 1.0 k)))
      t_0))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double t_0 = pow(k, m) * a_m;
	double tmp;
	if ((t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191) {
		tmp = (pow(k, m) * -(a_m / hypot(1.0, k))) / -hypot(1.0, k);
	} else {
		tmp = t_0;
	}
	return a_s * tmp;
}

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double t_0 = Math.pow(k, m) * a_m;
	double tmp;
	if ((t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191) {
		tmp = (Math.pow(k, m) * -(a_m / Math.hypot(1.0, k))) / -Math.hypot(1.0, k);
	} else {
		tmp = t_0;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	t_0 = math.pow(k, m) * a_m
	tmp = 0
	if (t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191:
		tmp = (math.pow(k, m) * -(a_m / math.hypot(1.0, k))) / -math.hypot(1.0, k)
	else:
		tmp = t_0
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	t_0 = Float64((k ^ m) * a_m)
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(1.0 + Float64(k * 10.0)) + Float64(k * k))) <= 5e+191)
		tmp = Float64(Float64((k ^ m) * Float64(-Float64(a_m / hypot(1.0, k)))) / Float64(-hypot(1.0, k)));
	else
		tmp = t_0;
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	t_0 = (k ^ m) * a_m;
	tmp = 0.0;
	if ((t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191)
		tmp = ((k ^ m) * -(a_m / hypot(1.0, k))) / -hypot(1.0, k);
	else
		tmp = t_0;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := Block[{t$95$0 = N[(N[Power[k, m], $MachinePrecision] * a$95$m), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(t$95$0 / N[(N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision] + N[(k * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+191], N[(N[(N[Power[k, m], $MachinePrecision] * (-N[(a$95$m / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision])), $MachinePrecision] / (-N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision])), $MachinePrecision], t$95$0]), $MachinePrecision]]

Derivation

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

Alternative 2: 99.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ \begin{array}{l} t_0 := \frac{\mathsf{hypot}\left(1, k\right)}{\sqrt{{k}^{m}}}\\ a_s \cdot \left(\frac{1}{t_0} \cdot \frac{a_m}{t_0}\right) \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (let* ((t_0 (/ (hypot 1.0 k) (sqrt (pow k m)))))
   (* a_s (* (/ 1.0 t_0) (/ a_m t_0)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double t_0 = hypot(1.0, k) / sqrt(pow(k, m));
	return a_s * ((1.0 / t_0) * (a_m / t_0));
}

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double t_0 = Math.hypot(1.0, k) / Math.sqrt(Math.pow(k, m));
	return a_s * ((1.0 / t_0) * (a_m / t_0));
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	t_0 = math.hypot(1.0, k) / math.sqrt(math.pow(k, m))
	return a_s * ((1.0 / t_0) * (a_m / t_0))

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	t_0 = Float64(hypot(1.0, k) / sqrt((k ^ m)))
	return Float64(a_s * Float64(Float64(1.0 / t_0) * Float64(a_m / t_0)))
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp = code(a_s, a_m, k, m)
	t_0 = hypot(1.0, k) / sqrt((k ^ m));
	tmp = a_s * ((1.0 / t_0) * (a_m / t_0));
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := Block[{t$95$0 = N[(N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision] / N[Sqrt[N[Power[k, m], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * N[(N[(1.0 / t$95$0), $MachinePrecision] * N[(a$95$m / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 98.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot {\left(\frac{\sqrt{a_m}}{\frac{\mathsf{hypot}\left(1, k\right)}{\sqrt{{k}^{m}}}}\right)}^{2} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (* a_s (pow (/ (sqrt a_m) (/ (hypot 1.0 k) (sqrt (pow k m)))) 2.0)))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	return a_s * pow((sqrt(a_m) / (hypot(1.0, k) / sqrt(pow(k, m)))), 2.0);
}

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	return a_s * Math.pow((Math.sqrt(a_m) / (Math.hypot(1.0, k) / Math.sqrt(Math.pow(k, m)))), 2.0);
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	return a_s * math.pow((math.sqrt(a_m) / (math.hypot(1.0, k) / math.sqrt(math.pow(k, m)))), 2.0)

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	return Float64(a_s * (Float64(sqrt(a_m) / Float64(hypot(1.0, k) / sqrt((k ^ m)))) ^ 2.0))
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp = code(a_s, a_m, k, m)
	tmp = a_s * ((sqrt(a_m) / (hypot(1.0, k) / sqrt((k ^ m)))) ^ 2.0);
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * N[Power[N[(N[Sqrt[a$95$m], $MachinePrecision] / N[(N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision] / N[Sqrt[N[Power[k, m], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ \begin{array}{l} t_0 := {k}^{m} \cdot a_m\\ a_s \cdot \begin{array}{l} \mathbf{if}\;\frac{t_0}{\left(1 + k \cdot 10\right) + k \cdot k} \leq 5 \cdot 10^{+191}:\\ \;\;\;\;\frac{a_m}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (let* ((t_0 (* (pow k m) a_m)))
   (*
    a_s
    (if (<= (/ t_0 (+ (+ 1.0 (* k 10.0)) (* k k))) 5e+191)
      (/ a_m (/ (+ 1.0 (* k (+ k 10.0))) (pow k m)))
      t_0))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double t_0 = pow(k, m) * a_m;
	double tmp;
	if ((t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191) {
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / pow(k, m));
	} else {
		tmp = t_0;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (k ** m) * a_m
    if ((t_0 / ((1.0d0 + (k * 10.0d0)) + (k * k))) <= 5d+191) then
        tmp = a_m / ((1.0d0 + (k * (k + 10.0d0))) / (k ** m))
    else
        tmp = t_0
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double t_0 = Math.pow(k, m) * a_m;
	double tmp;
	if ((t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191) {
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / Math.pow(k, m));
	} else {
		tmp = t_0;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	t_0 = math.pow(k, m) * a_m
	tmp = 0
	if (t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191:
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / math.pow(k, m))
	else:
		tmp = t_0
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	t_0 = Float64((k ^ m) * a_m)
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(1.0 + Float64(k * 10.0)) + Float64(k * k))) <= 5e+191)
		tmp = Float64(a_m / Float64(Float64(1.0 + Float64(k * Float64(k + 10.0))) / (k ^ m)));
	else
		tmp = t_0;
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	t_0 = (k ^ m) * a_m;
	tmp = 0.0;
	if ((t_0 / ((1.0 + (k * 10.0)) + (k * k))) <= 5e+191)
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / (k ^ m));
	else
		tmp = t_0;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := Block[{t$95$0 = N[(N[Power[k, m], $MachinePrecision] * a$95$m), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(t$95$0 / N[(N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision] + N[(k * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+191], N[(a$95$m / N[(N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[k, m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]), $MachinePrecision]]

Derivation

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

Alternative 5: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{a_m}{\frac{1 + k \cdot 10}{{k}^{m}}}\\ \mathbf{elif}\;m \leq 0.11:\\ \;\;\;\;\frac{a_m}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;{k}^{m} \cdot a_m\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (*
  a_s
  (if (<= m -1.95e-16)
    (/ a_m (/ (+ 1.0 (* k 10.0)) (pow k m)))
    (if (<= m 0.11) (/ a_m (+ 1.0 (* k (+ k 10.0)))) (* (pow k m) a_m)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -1.95e-16) {
		tmp = a_m / ((1.0 + (k * 10.0)) / pow(k, m));
	} else if (m <= 0.11) {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = pow(k, m) * a_m;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= (-1.95d-16)) then
        tmp = a_m / ((1.0d0 + (k * 10.0d0)) / (k ** m))
    else if (m <= 0.11d0) then
        tmp = a_m / (1.0d0 + (k * (k + 10.0d0)))
    else
        tmp = (k ** m) * a_m
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -1.95e-16) {
		tmp = a_m / ((1.0 + (k * 10.0)) / Math.pow(k, m));
	} else if (m <= 0.11) {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = Math.pow(k, m) * a_m;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if m <= -1.95e-16:
		tmp = a_m / ((1.0 + (k * 10.0)) / math.pow(k, m))
	elif m <= 0.11:
		tmp = a_m / (1.0 + (k * (k + 10.0)))
	else:
		tmp = math.pow(k, m) * a_m
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if (m <= -1.95e-16)
		tmp = Float64(a_m / Float64(Float64(1.0 + Float64(k * 10.0)) / (k ^ m)));
	elseif (m <= 0.11)
		tmp = Float64(a_m / Float64(1.0 + Float64(k * Float64(k + 10.0))));
	else
		tmp = Float64((k ^ m) * a_m);
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if (m <= -1.95e-16)
		tmp = a_m / ((1.0 + (k * 10.0)) / (k ^ m));
	elseif (m <= 0.11)
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	else
		tmp = (k ^ m) * a_m;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[LessEqual[m, -1.95e-16], N[(a$95$m / N[(N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision] / N[Power[k, m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 0.11], N[(a$95$m / N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[k, m], $MachinePrecision] * a$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 6: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq 4.2:\\ \;\;\;\;\frac{a_m}{\frac{1 + k \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;{k}^{m} \cdot a_m\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (*
  a_s
  (if (<= m 4.2) (/ a_m (/ (+ 1.0 (* k k)) (pow k m))) (* (pow k m) a_m))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= 4.2) {
		tmp = a_m / ((1.0 + (k * k)) / pow(k, m));
	} else {
		tmp = pow(k, m) * a_m;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= 4.2d0) then
        tmp = a_m / ((1.0d0 + (k * k)) / (k ** m))
    else
        tmp = (k ** m) * a_m
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= 4.2) {
		tmp = a_m / ((1.0 + (k * k)) / Math.pow(k, m));
	} else {
		tmp = Math.pow(k, m) * a_m;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if m <= 4.2:
		tmp = a_m / ((1.0 + (k * k)) / math.pow(k, m))
	else:
		tmp = math.pow(k, m) * a_m
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if (m <= 4.2)
		tmp = Float64(a_m / Float64(Float64(1.0 + Float64(k * k)) / (k ^ m)));
	else
		tmp = Float64((k ^ m) * a_m);
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if (m <= 4.2)
		tmp = a_m / ((1.0 + (k * k)) / (k ^ m));
	else
		tmp = (k ^ m) * a_m;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[LessEqual[m, 4.2], N[(a$95$m / N[(N[(1.0 + N[(k * k), $MachinePrecision]), $MachinePrecision] / N[Power[k, m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[k, m], $MachinePrecision] * a$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 96.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -1.95 \cdot 10^{-16} \lor \neg \left(m \leq 0.11\right):\\ \;\;\;\;{k}^{m} \cdot a_m\\ \mathbf{else}:\\ \;\;\;\;\frac{a_m}{1 + k \cdot \left(k + 10\right)}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (*
  a_s
  (if (or (<= m -1.95e-16) (not (<= m 0.11)))
    (* (pow k m) a_m)
    (/ a_m (+ 1.0 (* k (+ k 10.0)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if ((m <= -1.95e-16) || !(m <= 0.11)) {
		tmp = pow(k, m) * a_m;
	} else {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if ((m <= (-1.95d-16)) .or. (.not. (m <= 0.11d0))) then
        tmp = (k ** m) * a_m
    else
        tmp = a_m / (1.0d0 + (k * (k + 10.0d0)))
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if ((m <= -1.95e-16) || !(m <= 0.11)) {
		tmp = Math.pow(k, m) * a_m;
	} else {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if (m <= -1.95e-16) or not (m <= 0.11):
		tmp = math.pow(k, m) * a_m
	else:
		tmp = a_m / (1.0 + (k * (k + 10.0)))
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if ((m <= -1.95e-16) || !(m <= 0.11))
		tmp = Float64((k ^ m) * a_m);
	else
		tmp = Float64(a_m / Float64(1.0 + Float64(k * Float64(k + 10.0))));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if ((m <= -1.95e-16) || ~((m <= 0.11)))
		tmp = (k ^ m) * a_m;
	else
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[Or[LessEqual[m, -1.95e-16], N[Not[LessEqual[m, 0.11]], $MachinePrecision]], N[(N[Power[k, m], $MachinePrecision] * a$95$m), $MachinePrecision], N[(a$95$m / N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 37.0% accurate, 10.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -5.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\frac{k \cdot 10}{a_m}}\\ \mathbf{elif}\;m \leq 0.9:\\ \;\;\;\;\frac{a_m}{1 + k \cdot 10}\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(k \cdot a_m\right)\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (*
  a_s
  (if (<= m -5.5e+16)
    (/ 1.0 (/ (* k 10.0) a_m))
    (if (<= m 0.9) (/ a_m (+ 1.0 (* k 10.0))) (* -10.0 (* k a_m))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -5.5e+16) {
		tmp = 1.0 / ((k * 10.0) / a_m);
	} else if (m <= 0.9) {
		tmp = a_m / (1.0 + (k * 10.0));
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= (-5.5d+16)) then
        tmp = 1.0d0 / ((k * 10.0d0) / a_m)
    else if (m <= 0.9d0) then
        tmp = a_m / (1.0d0 + (k * 10.0d0))
    else
        tmp = (-10.0d0) * (k * a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -5.5e+16) {
		tmp = 1.0 / ((k * 10.0) / a_m);
	} else if (m <= 0.9) {
		tmp = a_m / (1.0 + (k * 10.0));
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if m <= -5.5e+16:
		tmp = 1.0 / ((k * 10.0) / a_m)
	elif m <= 0.9:
		tmp = a_m / (1.0 + (k * 10.0))
	else:
		tmp = -10.0 * (k * a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if (m <= -5.5e+16)
		tmp = Float64(1.0 / Float64(Float64(k * 10.0) / a_m));
	elseif (m <= 0.9)
		tmp = Float64(a_m / Float64(1.0 + Float64(k * 10.0)));
	else
		tmp = Float64(-10.0 * Float64(k * a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if (m <= -5.5e+16)
		tmp = 1.0 / ((k * 10.0) / a_m);
	elseif (m <= 0.9)
		tmp = a_m / (1.0 + (k * 10.0));
	else
		tmp = -10.0 * (k * a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[LessEqual[m, -5.5e+16], N[(1.0 / N[(N[(k * 10.0), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 0.9], N[(a$95$m / N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-10.0 * N[(k * a$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 9: 51.1% accurate, 10.3× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq 1.1:\\ \;\;\;\;\frac{a_m}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(k \cdot a_m\right)\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (* a_s (if (<= m 1.1) (/ a_m (+ 1.0 (* k (+ k 10.0)))) (* -10.0 (* k a_m)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= 1.1) {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= 1.1d0) then
        tmp = a_m / (1.0d0 + (k * (k + 10.0d0)))
    else
        tmp = (-10.0d0) * (k * a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= 1.1) {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if m <= 1.1:
		tmp = a_m / (1.0 + (k * (k + 10.0)))
	else:
		tmp = -10.0 * (k * a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if (m <= 1.1)
		tmp = Float64(a_m / Float64(1.0 + Float64(k * Float64(k + 10.0))));
	else
		tmp = Float64(-10.0 * Float64(k * a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if (m <= 1.1)
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	else
		tmp = -10.0 * (k * a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[LessEqual[m, 1.1], N[(a$95$m / N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-10.0 * N[(k * a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 10: 32.5% accurate, 12.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -0.00182:\\ \;\;\;\;0.1 \cdot \frac{a_m}{k}\\ \mathbf{elif}\;m \leq 0.47:\\ \;\;\;\;a_m\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(k \cdot a_m\right)\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (*
  a_s
  (if (<= m -0.00182)
    (* 0.1 (/ a_m k))
    (if (<= m 0.47) a_m (* -10.0 (* k a_m))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -0.00182) {
		tmp = 0.1 * (a_m / k);
	} else if (m <= 0.47) {
		tmp = a_m;
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= (-0.00182d0)) then
        tmp = 0.1d0 * (a_m / k)
    else if (m <= 0.47d0) then
        tmp = a_m
    else
        tmp = (-10.0d0) * (k * a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -0.00182) {
		tmp = 0.1 * (a_m / k);
	} else if (m <= 0.47) {
		tmp = a_m;
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if m <= -0.00182:
		tmp = 0.1 * (a_m / k)
	elif m <= 0.47:
		tmp = a_m
	else:
		tmp = -10.0 * (k * a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if (m <= -0.00182)
		tmp = Float64(0.1 * Float64(a_m / k));
	elseif (m <= 0.47)
		tmp = a_m;
	else
		tmp = Float64(-10.0 * Float64(k * a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if (m <= -0.00182)
		tmp = 0.1 * (a_m / k);
	elseif (m <= 0.47)
		tmp = a_m;
	else
		tmp = -10.0 * (k * a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[LessEqual[m, -0.00182], N[(0.1 * N[(a$95$m / k), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 0.47], a$95$m, N[(-10.0 * N[(k * a$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 11: 32.7% accurate, 12.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -0.0025:\\ \;\;\;\;\frac{1}{\frac{k \cdot 10}{a_m}}\\ \mathbf{elif}\;m \leq 0.55:\\ \;\;\;\;a_m\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(k \cdot a_m\right)\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (*
  a_s
  (if (<= m -0.0025)
    (/ 1.0 (/ (* k 10.0) a_m))
    (if (<= m 0.55) a_m (* -10.0 (* k a_m))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -0.0025) {
		tmp = 1.0 / ((k * 10.0) / a_m);
	} else if (m <= 0.55) {
		tmp = a_m;
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= (-0.0025d0)) then
        tmp = 1.0d0 / ((k * 10.0d0) / a_m)
    else if (m <= 0.55d0) then
        tmp = a_m
    else
        tmp = (-10.0d0) * (k * a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= -0.0025) {
		tmp = 1.0 / ((k * 10.0) / a_m);
	} else if (m <= 0.55) {
		tmp = a_m;
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if m <= -0.0025:
		tmp = 1.0 / ((k * 10.0) / a_m)
	elif m <= 0.55:
		tmp = a_m
	else:
		tmp = -10.0 * (k * a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if (m <= -0.0025)
		tmp = Float64(1.0 / Float64(Float64(k * 10.0) / a_m));
	elseif (m <= 0.55)
		tmp = a_m;
	else
		tmp = Float64(-10.0 * Float64(k * a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if (m <= -0.0025)
		tmp = 1.0 / ((k * 10.0) / a_m);
	elseif (m <= 0.55)
		tmp = a_m;
	else
		tmp = -10.0 * (k * a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[LessEqual[m, -0.0025], N[(1.0 / N[(N[(k * 10.0), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 0.55], a$95$m, N[(-10.0 * N[(k * a$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 12: 26.3% accurate, 16.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq 0.195:\\ \;\;\;\;a_m\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(k \cdot a_m\right)\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (* a_s (if (<= m 0.195) a_m (* -10.0 (* k a_m)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= 0.195) {
		tmp = a_m;
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= 0.195d0) then
        tmp = a_m
    else
        tmp = (-10.0d0) * (k * a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	double tmp;
	if (m <= 0.195) {
		tmp = a_m;
	} else {
		tmp = -10.0 * (k * a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	tmp = 0
	if m <= 0.195:
		tmp = a_m
	else:
		tmp = -10.0 * (k * a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	tmp = 0.0
	if (m <= 0.195)
		tmp = a_m;
	else
		tmp = Float64(-10.0 * Float64(k * a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp_2 = code(a_s, a_m, k, m)
	tmp = 0.0;
	if (m <= 0.195)
		tmp = a_m;
	else
		tmp = -10.0 * (k * a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * If[LessEqual[m, 0.195], a$95$m, N[(-10.0 * N[(k * a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 13: 20.4% accurate, 114.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot a_m \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m) :precision binary64 (* a_s a_m))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
double code(double a_s, double a_m, double k, double m) {
	return a_s * a_m;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
real(8) function code(a_s, a_m, k, m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: a_m
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    code = a_s * a_m
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
public static double code(double a_s, double a_m, double k, double m) {
	return a_s * a_m;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	return a_s * a_m

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	return Float64(a_s * a_m)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
function tmp = code(a_s, a_m, k, m)
	tmp = a_s * a_m;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[a$95$s_, a$95$m_, k_, m_] := N[(a$95$s * a$95$m), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023350 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))