Falkner and Boettcher, Appendix A

Percentage Accurate: 90.2% → 99.1%

Time: 9.6s

Alternatives: 11

Speedup: 1.1×

• 23.4% 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: 90.2% 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: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ \begin{array}{l} t_0 := a_m \cdot {k}^{m}\\ a_s \cdot \begin{array}{l} \mathbf{if}\;\frac{t_0}{k \cdot k + \left(1 + k \cdot 10\right)} \leq 10^{+202}:\\ \;\;\;\;\frac{-1}{\frac{-1}{t_0} - \frac{k}{a_m} \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (let* ((t_0 (* a_m (pow k m))))
   (*
    a_s
    (if (<= (/ t_0 (+ (* k k) (+ 1.0 (* k 10.0)))) 1e+202)
      (/ -1.0 (- (/ -1.0 t_0) (* (/ k a_m) (+ k 10.0))))
      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 = a_m * pow(k, m);
	double tmp;
	if ((t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 1e+202) {
		tmp = -1.0 / ((-1.0 / t_0) - ((k / a_m) * (k + 10.0)));
	} 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 = a_m * (k ** m)
    if ((t_0 / ((k * k) + (1.0d0 + (k * 10.0d0)))) <= 1d+202) then
        tmp = (-1.0d0) / (((-1.0d0) / t_0) - ((k / a_m) * (k + 10.0d0)))
    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 = a_m * Math.pow(k, m);
	double tmp;
	if ((t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 1e+202) {
		tmp = -1.0 / ((-1.0 / t_0) - ((k / a_m) * (k + 10.0)));
	} 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 = a_m * math.pow(k, m)
	tmp = 0
	if (t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 1e+202:
		tmp = -1.0 / ((-1.0 / t_0) - ((k / a_m) * (k + 10.0)))
	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(a_m * (k ^ m))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(k * k) + Float64(1.0 + Float64(k * 10.0)))) <= 1e+202)
		tmp = Float64(-1.0 / Float64(Float64(-1.0 / t_0) - Float64(Float64(k / a_m) * Float64(k + 10.0))));
	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 = a_m * (k ^ m);
	tmp = 0.0;
	if ((t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 1e+202)
		tmp = -1.0 / ((-1.0 / t_0) - ((k / a_m) * (k + 10.0)));
	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[(a$95$m * N[Power[k, m], $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(t$95$0 / N[(N[(k * k), $MachinePrecision] + N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+202], N[(-1.0 / N[(N[(-1.0 / t$95$0), $MachinePrecision] - N[(N[(k / a$95$m), $MachinePrecision] * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]), $MachinePrecision]]

Derivation

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

Alternative 2: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq 3.4:\\ \;\;\;\;\frac{a_m}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;a_m \cdot {k}^{m}\\ \end{array} \end{array} \]

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 3.4)
    (/ a_m (/ (+ 1.0 (* k (+ k 10.0))) (pow k m)))
    (* a_m (pow k 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 <= 3.4) {
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / pow(k, m));
	} else {
		tmp = a_m * pow(k, 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 <= 3.4d0) then
        tmp = a_m / ((1.0d0 + (k * (k + 10.0d0))) / (k ** m))
    else
        tmp = a_m * (k ** 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 <= 3.4) {
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / Math.pow(k, m));
	} else {
		tmp = a_m * Math.pow(k, 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 <= 3.4:
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / math.pow(k, m))
	else:
		tmp = a_m * math.pow(k, 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 <= 3.4)
		tmp = Float64(a_m / Float64(Float64(1.0 + Float64(k * Float64(k + 10.0))) / (k ^ m)));
	else
		tmp = Float64(a_m * (k ^ 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 <= 3.4)
		tmp = a_m / ((1.0 + (k * (k + 10.0))) / (k ^ m));
	else
		tmp = a_m * (k ^ 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, 3.4], N[(a$95$m / N[(N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[k, m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a$95$m * N[Power[k, m], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 3: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{a_m}{\frac{1 + k \cdot 10}{{k}^{m}}}\\ \mathbf{elif}\;m \leq 0.41:\\ \;\;\;\;\frac{a_m}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;a_m \cdot {k}^{m}\\ \end{array} \end{array} \]

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 -8.5e-16)
    (/ a_m (/ (+ 1.0 (* k 10.0)) (pow k m)))
    (if (<= m 0.41) (/ a_m (+ 1.0 (* k (+ k 10.0)))) (* a_m (pow k 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 <= -8.5e-16) {
		tmp = a_m / ((1.0 + (k * 10.0)) / pow(k, m));
	} else if (m <= 0.41) {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = a_m * pow(k, 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 <= (-8.5d-16)) then
        tmp = a_m / ((1.0d0 + (k * 10.0d0)) / (k ** m))
    else if (m <= 0.41d0) then
        tmp = a_m / (1.0d0 + (k * (k + 10.0d0)))
    else
        tmp = a_m * (k ** 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 <= -8.5e-16) {
		tmp = a_m / ((1.0 + (k * 10.0)) / Math.pow(k, m));
	} else if (m <= 0.41) {
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = a_m * Math.pow(k, 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 <= -8.5e-16:
		tmp = a_m / ((1.0 + (k * 10.0)) / math.pow(k, m))
	elif m <= 0.41:
		tmp = a_m / (1.0 + (k * (k + 10.0)))
	else:
		tmp = a_m * math.pow(k, 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 <= -8.5e-16)
		tmp = Float64(a_m / Float64(Float64(1.0 + Float64(k * 10.0)) / (k ^ m)));
	elseif (m <= 0.41)
		tmp = Float64(a_m / Float64(1.0 + Float64(k * Float64(k + 10.0))));
	else
		tmp = Float64(a_m * (k ^ 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 <= -8.5e-16)
		tmp = a_m / ((1.0 + (k * 10.0)) / (k ^ m));
	elseif (m <= 0.41)
		tmp = a_m / (1.0 + (k * (k + 10.0)));
	else
		tmp = a_m * (k ^ 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, -8.5e-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, 0.41], N[(a$95$m / N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a$95$m * N[Power[k, m], $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 4: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -0.0069 \lor \neg \left(m \leq 3.6 \cdot 10^{-7}\right):\\ \;\;\;\;a_m \cdot {k}^{m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a_m}{1 + k \cdot \left(k + 10\right)}\\ \end{array} \end{array} \]

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 -0.0069) (not (<= m 3.6e-7)))
    (* a_m (pow k 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 <= -0.0069) || !(m <= 3.6e-7)) {
		tmp = a_m * pow(k, 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 <= (-0.0069d0)) .or. (.not. (m <= 3.6d-7))) then
        tmp = a_m * (k ** 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 <= -0.0069) || !(m <= 3.6e-7)) {
		tmp = a_m * Math.pow(k, 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 <= -0.0069) or not (m <= 3.6e-7):
		tmp = a_m * math.pow(k, 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 <= -0.0069) || !(m <= 3.6e-7))
		tmp = Float64(a_m * (k ^ 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 <= -0.0069) || ~((m <= 3.6e-7)))
		tmp = a_m * (k ^ 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, -0.0069], N[Not[LessEqual[m, 3.6e-7]], $MachinePrecision]], N[(a$95$m * N[Power[k, m], $MachinePrecision]), $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 5: 29.0% accurate, 10.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;k \leq -6 \cdot 10^{+71} \lor \neg \left(k \leq 0.076\right):\\ \;\;\;\;a_m \cdot \frac{0.1}{k}\\ \mathbf{else}:\\ \;\;\;\;a_m \cdot \left(1 + k \cdot -10\right)\\ \end{array} \end{array} \]

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 (<= k -6e+71) (not (<= k 0.076)))
    (* a_m (/ 0.1 k))
    (* a_m (+ 1.0 (* 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 ((k <= -6e+71) || !(k <= 0.076)) {
		tmp = a_m * (0.1 / k);
	} else {
		tmp = a_m * (1.0 + (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 ((k <= (-6d+71)) .or. (.not. (k <= 0.076d0))) then
        tmp = a_m * (0.1d0 / k)
    else
        tmp = a_m * (1.0d0 + (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 ((k <= -6e+71) || !(k <= 0.076)) {
		tmp = a_m * (0.1 / k);
	} else {
		tmp = a_m * (1.0 + (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 (k <= -6e+71) or not (k <= 0.076):
		tmp = a_m * (0.1 / k)
	else:
		tmp = a_m * (1.0 + (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 ((k <= -6e+71) || !(k <= 0.076))
		tmp = Float64(a_m * Float64(0.1 / k));
	else
		tmp = Float64(a_m * Float64(1.0 + 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 ((k <= -6e+71) || ~((k <= 0.076)))
		tmp = a_m * (0.1 / k);
	else
		tmp = a_m * (1.0 + (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[k, -6e+71], N[Not[LessEqual[k, 0.076]], $MachinePrecision]], N[(a$95$m * N[(0.1 / k), $MachinePrecision]), $MachinePrecision], N[(a$95$m * N[(1.0 + N[(k * -10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 6: 29.0% accurate, 10.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;k \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;a_m \cdot \frac{0.1}{k}\\ \mathbf{elif}\;k \leq 0.076:\\ \;\;\;\;a_m \cdot \left(1 + k \cdot -10\right)\\ \mathbf{else}:\\ \;\;\;\;a_m \cdot \frac{1}{k \cdot 10}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (*
  a_s
  (if (<= k -4.8e+72)
    (* a_m (/ 0.1 k))
    (if (<= k 0.076) (* a_m (+ 1.0 (* k -10.0))) (* a_m (/ 1.0 (* 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 (k <= -4.8e+72) {
		tmp = a_m * (0.1 / k);
	} else if (k <= 0.076) {
		tmp = a_m * (1.0 + (k * -10.0));
	} else {
		tmp = a_m * (1.0 / (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 (k <= (-4.8d+72)) then
        tmp = a_m * (0.1d0 / k)
    else if (k <= 0.076d0) then
        tmp = a_m * (1.0d0 + (k * (-10.0d0)))
    else
        tmp = a_m * (1.0d0 / (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 (k <= -4.8e+72) {
		tmp = a_m * (0.1 / k);
	} else if (k <= 0.076) {
		tmp = a_m * (1.0 + (k * -10.0));
	} else {
		tmp = a_m * (1.0 / (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 k <= -4.8e+72:
		tmp = a_m * (0.1 / k)
	elif k <= 0.076:
		tmp = a_m * (1.0 + (k * -10.0))
	else:
		tmp = a_m * (1.0 / (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 (k <= -4.8e+72)
		tmp = Float64(a_m * Float64(0.1 / k));
	elseif (k <= 0.076)
		tmp = Float64(a_m * Float64(1.0 + Float64(k * -10.0)));
	else
		tmp = Float64(a_m * Float64(1.0 / 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 (k <= -4.8e+72)
		tmp = a_m * (0.1 / k);
	elseif (k <= 0.076)
		tmp = a_m * (1.0 + (k * -10.0));
	else
		tmp = a_m * (1.0 / (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[LessEqual[k, -4.8e+72], N[(a$95$m * N[(0.1 / k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 0.076], N[(a$95$m * N[(1.0 + N[(k * -10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a$95$m * N[(1.0 / N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 7: 28.6% accurate, 12.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;k \leq -6.2 \cdot 10^{+71} \lor \neg \left(k \leq 165\right):\\ \;\;\;\;0.1 \cdot \frac{a_m}{k}\\ \mathbf{else}:\\ \;\;\;\;a_m\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (* a_s (if (or (<= k -6.2e+71) (not (<= k 165.0))) (* 0.1 (/ a_m 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 ((k <= -6.2e+71) || !(k <= 165.0)) {
		tmp = 0.1 * (a_m / k);
	} else {
		tmp = 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 ((k <= (-6.2d+71)) .or. (.not. (k <= 165.0d0))) then
        tmp = 0.1d0 * (a_m / k)
    else
        tmp = 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 ((k <= -6.2e+71) || !(k <= 165.0)) {
		tmp = 0.1 * (a_m / k);
	} else {
		tmp = 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 (k <= -6.2e+71) or not (k <= 165.0):
		tmp = 0.1 * (a_m / k)
	else:
		tmp = 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 ((k <= -6.2e+71) || !(k <= 165.0))
		tmp = Float64(0.1 * Float64(a_m / k));
	else
		tmp = 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 ((k <= -6.2e+71) || ~((k <= 165.0)))
		tmp = 0.1 * (a_m / k);
	else
		tmp = 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[Or[LessEqual[k, -6.2e+71], N[Not[LessEqual[k, 165.0]], $MachinePrecision]], N[(0.1 * N[(a$95$m / k), $MachinePrecision]), $MachinePrecision], a$95$m]), $MachinePrecision]

Derivation

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

Alternative 8: 28.6% accurate, 12.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;k \leq -7.6 \cdot 10^{+70} \lor \neg \left(k \leq 165\right):\\ \;\;\;\;a_m \cdot \frac{0.1}{k}\\ \mathbf{else}:\\ \;\;\;\;a_m\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
(FPCore (a_s a_m k m)
 :precision binary64
 (* a_s (if (or (<= k -7.6e+70) (not (<= k 165.0))) (* a_m (/ 0.1 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 ((k <= -7.6e+70) || !(k <= 165.0)) {
		tmp = a_m * (0.1 / k);
	} else {
		tmp = 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 ((k <= (-7.6d+70)) .or. (.not. (k <= 165.0d0))) then
        tmp = a_m * (0.1d0 / k)
    else
        tmp = 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 ((k <= -7.6e+70) || !(k <= 165.0)) {
		tmp = a_m * (0.1 / k);
	} else {
		tmp = 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 (k <= -7.6e+70) or not (k <= 165.0):
		tmp = a_m * (0.1 / k)
	else:
		tmp = 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 ((k <= -7.6e+70) || !(k <= 165.0))
		tmp = Float64(a_m * Float64(0.1 / k));
	else
		tmp = 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 ((k <= -7.6e+70) || ~((k <= 165.0)))
		tmp = a_m * (0.1 / k);
	else
		tmp = 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[Or[LessEqual[k, -7.6e+70], N[Not[LessEqual[k, 165.0]], $MachinePrecision]], N[(a$95$m * N[(0.1 / k), $MachinePrecision]), $MachinePrecision], a$95$m]), $MachinePrecision]

Derivation

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

Alternative 9: 30.5% accurate, 12.6× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \begin{array}{l} \mathbf{if}\;m \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;a_m \cdot \frac{1}{k \cdot 10}\\ \mathbf{else}:\\ \;\;\;\;\frac{a_m}{1 + k \cdot 10}\\ \end{array} \end{array} \]

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 -1.05e+79) (* a_m (/ 1.0 (* k 10.0))) (/ a_m (+ 1.0 (* 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 <= -1.05e+79) {
		tmp = a_m * (1.0 / (k * 10.0));
	} else {
		tmp = a_m / (1.0 + (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 <= (-1.05d+79)) then
        tmp = a_m * (1.0d0 / (k * 10.0d0))
    else
        tmp = a_m / (1.0d0 + (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 <= -1.05e+79) {
		tmp = a_m * (1.0 / (k * 10.0));
	} else {
		tmp = a_m / (1.0 + (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 <= -1.05e+79:
		tmp = a_m * (1.0 / (k * 10.0))
	else:
		tmp = a_m / (1.0 + (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 <= -1.05e+79)
		tmp = Float64(a_m * Float64(1.0 / Float64(k * 10.0)));
	else
		tmp = Float64(a_m / Float64(1.0 + 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 <= -1.05e+79)
		tmp = a_m * (1.0 / (k * 10.0));
	else
		tmp = a_m / (1.0 + (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[LessEqual[m, -1.05e+79], N[(a$95$m * N[(1.0 / N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a$95$m / N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 10: 45.4% accurate, 12.7× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ a_s \cdot \frac{a_m}{1 + k \cdot \left(k + 10\right)} \end{array} \]

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 (+ 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) {
	return a_s * (a_m / (1.0 + (k * (k + 10.0))));
}

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 / (1.0d0 + (k * (k + 10.0d0))))
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 / (1.0 + (k * (k + 10.0))));
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
def code(a_s, a_m, k, m):
	return a_s * (a_m / (1.0 + (k * (k + 10.0))))

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
function code(a_s, a_m, k, m)
	return Float64(a_s * Float64(a_m / Float64(1.0 + Float64(k * Float64(k + 10.0)))))
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 * (a_m / (1.0 + (k * (k + 10.0))));
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[(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 11: 20.1% 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 2024008 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))