Falkner and Boettcher, Appendix A

Percentage Accurate: 90.3% → 97.7%

Time: 9.7s

Alternatives: 11

Speedup: 1.1×

• 23.5% 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: 90.3% 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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot {k}^{m}\\ t_1 := \frac{t_0}{\left(1 + k \cdot 10\right) + k \cdot k}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+211}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (* a (pow k m))) (t_1 (/ t_0 (+ (+ 1.0 (* k 10.0)) (* k k)))))
   (if (<= t_1 2e+211) t_1 t_0)))

C

double code(double a, double k, double m) {
	double t_0 = a * pow(k, m);
	double t_1 = t_0 / ((1.0 + (k * 10.0)) + (k * k));
	double tmp;
	if (t_1 <= 2e+211) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = a * (k ** m)
    t_1 = t_0 / ((1.0d0 + (k * 10.0d0)) + (k * k))
    if (t_1 <= 2d+211) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double t_0 = a * Math.pow(k, m);
	double t_1 = t_0 / ((1.0 + (k * 10.0)) + (k * k));
	double tmp;
	if (t_1 <= 2e+211) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = a * math.pow(k, m)
	t_1 = t_0 / ((1.0 + (k * 10.0)) + (k * k))
	tmp = 0
	if t_1 <= 2e+211:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(a * (k ^ m))
	t_1 = Float64(t_0 / Float64(Float64(1.0 + Float64(k * 10.0)) + Float64(k * k)))
	tmp = 0.0
	if (t_1 <= 2e+211)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = a * (k ^ m);
	t_1 = t_0 / ((1.0 + (k * 10.0)) + (k * k));
	tmp = 0.0;
	if (t_1 <= 2e+211)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := Block[{t$95$0 = N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 / N[(N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision] + N[(k * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+211], t$95$1, t$95$0]]]

Derivation

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

Alternative 2: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 3.9:\\ \;\;\;\;\frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot {k}^{m}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= m 3.9) (/ a (/ (+ 1.0 (* k (+ k 10.0))) (pow k m))) (* a (pow k m))))

C

double code(double a, double k, double m) {
	double tmp;
	if (m <= 3.9) {
		tmp = a / ((1.0 + (k * (k + 10.0))) / pow(k, m));
	} else {
		tmp = a * pow(k, m);
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= 3.9d0) then
        tmp = a / ((1.0d0 + (k * (k + 10.0d0))) / (k ** m))
    else
        tmp = a * (k ** m)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (m <= 3.9) {
		tmp = a / ((1.0 + (k * (k + 10.0))) / Math.pow(k, m));
	} else {
		tmp = a * Math.pow(k, m);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if m <= 3.9:
		tmp = a / ((1.0 + (k * (k + 10.0))) / math.pow(k, m))
	else:
		tmp = a * math.pow(k, m)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (m <= 3.9)
		tmp = Float64(a / Float64(Float64(1.0 + Float64(k * Float64(k + 10.0))) / (k ^ m)));
	else
		tmp = Float64(a * (k ^ m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (m <= 3.9)
		tmp = a / ((1.0 + (k * (k + 10.0))) / (k ^ m));
	else
		tmp = a * (k ^ m);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[m, 3.9], N[(a / N[(N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[k, m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.00075:\\ \;\;\;\;\frac{a}{\frac{1 + k \cdot 10}{{k}^{m}}}\\ \mathbf{elif}\;m \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot {k}^{m}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= m -0.00075)
   (/ a (/ (+ 1.0 (* k 10.0)) (pow k m)))
   (if (<= m 5.2e-5) (/ a (+ 1.0 (* k (+ k 10.0)))) (* a (pow k m)))))

C

double code(double a, double k, double m) {
	double tmp;
	if (m <= -0.00075) {
		tmp = a / ((1.0 + (k * 10.0)) / pow(k, m));
	} else if (m <= 5.2e-5) {
		tmp = a / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = a * pow(k, m);
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= (-0.00075d0)) then
        tmp = a / ((1.0d0 + (k * 10.0d0)) / (k ** m))
    else if (m <= 5.2d-5) then
        tmp = a / (1.0d0 + (k * (k + 10.0d0)))
    else
        tmp = a * (k ** m)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (m <= -0.00075) {
		tmp = a / ((1.0 + (k * 10.0)) / Math.pow(k, m));
	} else if (m <= 5.2e-5) {
		tmp = a / (1.0 + (k * (k + 10.0)));
	} else {
		tmp = a * Math.pow(k, m);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if m <= -0.00075:
		tmp = a / ((1.0 + (k * 10.0)) / math.pow(k, m))
	elif m <= 5.2e-5:
		tmp = a / (1.0 + (k * (k + 10.0)))
	else:
		tmp = a * math.pow(k, m)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (m <= -0.00075)
		tmp = Float64(a / Float64(Float64(1.0 + Float64(k * 10.0)) / (k ^ m)));
	elseif (m <= 5.2e-5)
		tmp = Float64(a / Float64(1.0 + Float64(k * Float64(k + 10.0))));
	else
		tmp = Float64(a * (k ^ m));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (m <= -0.00075)
		tmp = a / ((1.0 + (k * 10.0)) / (k ^ m));
	elseif (m <= 5.2e-5)
		tmp = a / (1.0 + (k * (k + 10.0)));
	else
		tmp = a * (k ^ m);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[m, -0.00075], N[(a / N[(N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision] / N[Power[k, m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 5.2e-5], N[(a / N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 97.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -0.00175 \lor \neg \left(m \leq 0.000225\right):\\ \;\;\;\;a \cdot {k}^{m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{1 + k \cdot \left(k + 10\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (or (<= m -0.00175) (not (<= m 0.000225)))
   (* a (pow k m))
   (/ a (+ 1.0 (* k (+ k 10.0))))))

C

double code(double a, double k, double m) {
	double tmp;
	if ((m <= -0.00175) || !(m <= 0.000225)) {
		tmp = a * pow(k, m);
	} else {
		tmp = a / (1.0 + (k * (k + 10.0)));
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if ((m <= (-0.00175d0)) .or. (.not. (m <= 0.000225d0))) then
        tmp = a * (k ** m)
    else
        tmp = a / (1.0d0 + (k * (k + 10.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if ((m <= -0.00175) || !(m <= 0.000225)) {
		tmp = a * Math.pow(k, m);
	} else {
		tmp = a / (1.0 + (k * (k + 10.0)));
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if (m <= -0.00175) or not (m <= 0.000225):
		tmp = a * math.pow(k, m)
	else:
		tmp = a / (1.0 + (k * (k + 10.0)))
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if ((m <= -0.00175) || !(m <= 0.000225))
		tmp = Float64(a * (k ^ m));
	else
		tmp = Float64(a / Float64(1.0 + Float64(k * Float64(k + 10.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if ((m <= -0.00175) || ~((m <= 0.000225)))
		tmp = a * (k ^ m);
	else
		tmp = a / (1.0 + (k * (k + 10.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[Or[LessEqual[m, -0.00175], N[Not[LessEqual[m, 0.000225]], $MachinePrecision]], N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision], N[(a / N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 46.2% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a}{k \cdot \left(k + 10\right)}\\ t_1 := -10 \cdot \left(a \cdot k\right)\\ \mathbf{if}\;k \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 0.075:\\ \;\;\;\;a + t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (/ a (* k (+ k 10.0)))) (t_1 (* -10.0 (* a k))))
   (if (<= k -4.2e+82)
     t_0
     (if (<= k -5e-310) t_1 (if (<= k 0.075) (+ a t_1) t_0)))))

C

double code(double a, double k, double m) {
	double t_0 = a / (k * (k + 10.0));
	double t_1 = -10.0 * (a * k);
	double tmp;
	if (k <= -4.2e+82) {
		tmp = t_0;
	} else if (k <= -5e-310) {
		tmp = t_1;
	} else if (k <= 0.075) {
		tmp = a + t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = a / (k * (k + 10.0d0))
    t_1 = (-10.0d0) * (a * k)
    if (k <= (-4.2d+82)) then
        tmp = t_0
    else if (k <= (-5d-310)) then
        tmp = t_1
    else if (k <= 0.075d0) then
        tmp = a + t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double t_0 = a / (k * (k + 10.0));
	double t_1 = -10.0 * (a * k);
	double tmp;
	if (k <= -4.2e+82) {
		tmp = t_0;
	} else if (k <= -5e-310) {
		tmp = t_1;
	} else if (k <= 0.075) {
		tmp = a + t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = a / (k * (k + 10.0))
	t_1 = -10.0 * (a * k)
	tmp = 0
	if k <= -4.2e+82:
		tmp = t_0
	elif k <= -5e-310:
		tmp = t_1
	elif k <= 0.075:
		tmp = a + t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(a / Float64(k * Float64(k + 10.0)))
	t_1 = Float64(-10.0 * Float64(a * k))
	tmp = 0.0
	if (k <= -4.2e+82)
		tmp = t_0;
	elseif (k <= -5e-310)
		tmp = t_1;
	elseif (k <= 0.075)
		tmp = Float64(a + t_1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = a / (k * (k + 10.0));
	t_1 = -10.0 * (a * k);
	tmp = 0.0;
	if (k <= -4.2e+82)
		tmp = t_0;
	elseif (k <= -5e-310)
		tmp = t_1;
	elseif (k <= 0.075)
		tmp = a + t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := Block[{t$95$0 = N[(a / N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-10.0 * N[(a * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -4.2e+82], t$95$0, If[LessEqual[k, -5e-310], t$95$1, If[LessEqual[k, 0.075], N[(a + t$95$1), $MachinePrecision], t$95$0]]]]]

Derivation

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

Alternative 6: 46.2% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a}{k \cdot \left(k + 10\right)}\\ \mathbf{if}\;k \leq -2.3 \cdot 10^{+87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{-308}:\\ \;\;\;\;-10 \cdot \left(a \cdot k\right)\\ \mathbf{elif}\;k \leq 1:\\ \;\;\;\;\frac{a}{1 + k \cdot 10}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (/ a (* k (+ k 10.0)))))
   (if (<= k -2.3e+87)
     t_0
     (if (<= k 1.5e-308)
       (* -10.0 (* a k))
       (if (<= k 1.0) (/ a (+ 1.0 (* k 10.0))) t_0)))))

C

double code(double a, double k, double m) {
	double t_0 = a / (k * (k + 10.0));
	double tmp;
	if (k <= -2.3e+87) {
		tmp = t_0;
	} else if (k <= 1.5e-308) {
		tmp = -10.0 * (a * k);
	} else if (k <= 1.0) {
		tmp = a / (1.0 + (k * 10.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (k * (k + 10.0d0))
    if (k <= (-2.3d+87)) then
        tmp = t_0
    else if (k <= 1.5d-308) then
        tmp = (-10.0d0) * (a * k)
    else if (k <= 1.0d0) then
        tmp = a / (1.0d0 + (k * 10.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double t_0 = a / (k * (k + 10.0));
	double tmp;
	if (k <= -2.3e+87) {
		tmp = t_0;
	} else if (k <= 1.5e-308) {
		tmp = -10.0 * (a * k);
	} else if (k <= 1.0) {
		tmp = a / (1.0 + (k * 10.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = a / (k * (k + 10.0))
	tmp = 0
	if k <= -2.3e+87:
		tmp = t_0
	elif k <= 1.5e-308:
		tmp = -10.0 * (a * k)
	elif k <= 1.0:
		tmp = a / (1.0 + (k * 10.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(a / Float64(k * Float64(k + 10.0)))
	tmp = 0.0
	if (k <= -2.3e+87)
		tmp = t_0;
	elseif (k <= 1.5e-308)
		tmp = Float64(-10.0 * Float64(a * k));
	elseif (k <= 1.0)
		tmp = Float64(a / Float64(1.0 + Float64(k * 10.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = a / (k * (k + 10.0));
	tmp = 0.0;
	if (k <= -2.3e+87)
		tmp = t_0;
	elseif (k <= 1.5e-308)
		tmp = -10.0 * (a * k);
	elseif (k <= 1.0)
		tmp = a / (1.0 + (k * 10.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := Block[{t$95$0 = N[(a / N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.3e+87], t$95$0, If[LessEqual[k, 1.5e-308], N[(-10.0 * N[(a * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.0], N[(a / N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 7: 52.7% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := k \cdot \left(k + 10\right)\\ \mathbf{if}\;m \leq -0.33:\\ \;\;\;\;\frac{a}{t_0}\\ \mathbf{elif}\;m \leq 0.95:\\ \;\;\;\;\frac{a}{1 + t_0}\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(a \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (* k (+ k 10.0))))
   (if (<= m -0.33)
     (/ a t_0)
     (if (<= m 0.95) (/ a (+ 1.0 t_0)) (* -10.0 (* a k))))))

C

double code(double a, double k, double m) {
	double t_0 = k * (k + 10.0);
	double tmp;
	if (m <= -0.33) {
		tmp = a / t_0;
	} else if (m <= 0.95) {
		tmp = a / (1.0 + t_0);
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = k * (k + 10.0d0)
    if (m <= (-0.33d0)) then
        tmp = a / t_0
    else if (m <= 0.95d0) then
        tmp = a / (1.0d0 + t_0)
    else
        tmp = (-10.0d0) * (a * k)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double t_0 = k * (k + 10.0);
	double tmp;
	if (m <= -0.33) {
		tmp = a / t_0;
	} else if (m <= 0.95) {
		tmp = a / (1.0 + t_0);
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = k * (k + 10.0)
	tmp = 0
	if m <= -0.33:
		tmp = a / t_0
	elif m <= 0.95:
		tmp = a / (1.0 + t_0)
	else:
		tmp = -10.0 * (a * k)
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(k * Float64(k + 10.0))
	tmp = 0.0
	if (m <= -0.33)
		tmp = Float64(a / t_0);
	elseif (m <= 0.95)
		tmp = Float64(a / Float64(1.0 + t_0));
	else
		tmp = Float64(-10.0 * Float64(a * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = k * (k + 10.0);
	tmp = 0.0;
	if (m <= -0.33)
		tmp = a / t_0;
	elseif (m <= 0.95)
		tmp = a / (1.0 + t_0);
	else
		tmp = -10.0 * (a * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := Block[{t$95$0 = N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[m, -0.33], N[(a / t$95$0), $MachinePrecision], If[LessEqual[m, 0.95], N[(a / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision], N[(-10.0 * N[(a * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 8: 32.0% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -3.2 \cdot 10^{-14}:\\ \;\;\;\;0.1 \cdot \frac{a}{k}\\ \mathbf{elif}\;m \leq 0.245:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(a \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= m -3.2e-14) (* 0.1 (/ a k)) (if (<= m 0.245) a (* -10.0 (* a k)))))

C

double code(double a, double k, double m) {
	double tmp;
	if (m <= -3.2e-14) {
		tmp = 0.1 * (a / k);
	} else if (m <= 0.245) {
		tmp = a;
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= (-3.2d-14)) then
        tmp = 0.1d0 * (a / k)
    else if (m <= 0.245d0) then
        tmp = a
    else
        tmp = (-10.0d0) * (a * k)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (m <= -3.2e-14) {
		tmp = 0.1 * (a / k);
	} else if (m <= 0.245) {
		tmp = a;
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if m <= -3.2e-14:
		tmp = 0.1 * (a / k)
	elif m <= 0.245:
		tmp = a
	else:
		tmp = -10.0 * (a * k)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (m <= -3.2e-14)
		tmp = Float64(0.1 * Float64(a / k));
	elseif (m <= 0.245)
		tmp = a;
	else
		tmp = Float64(-10.0 * Float64(a * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (m <= -3.2e-14)
		tmp = 0.1 * (a / k);
	elseif (m <= 0.245)
		tmp = a;
	else
		tmp = -10.0 * (a * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[m, -3.2e-14], N[(0.1 * N[(a / k), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 0.245], a, N[(-10.0 * N[(a * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 32.1% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -1 \cdot 10^{-13}:\\ \;\;\;\;\frac{0.1}{\frac{k}{a}}\\ \mathbf{elif}\;m \leq 0.22:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(a \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= m -1e-13) (/ 0.1 (/ k a)) (if (<= m 0.22) a (* -10.0 (* a k)))))

C

double code(double a, double k, double m) {
	double tmp;
	if (m <= -1e-13) {
		tmp = 0.1 / (k / a);
	} else if (m <= 0.22) {
		tmp = a;
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= (-1d-13)) then
        tmp = 0.1d0 / (k / a)
    else if (m <= 0.22d0) then
        tmp = a
    else
        tmp = (-10.0d0) * (a * k)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (m <= -1e-13) {
		tmp = 0.1 / (k / a);
	} else if (m <= 0.22) {
		tmp = a;
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if m <= -1e-13:
		tmp = 0.1 / (k / a)
	elif m <= 0.22:
		tmp = a
	else:
		tmp = -10.0 * (a * k)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (m <= -1e-13)
		tmp = Float64(0.1 / Float64(k / a));
	elseif (m <= 0.22)
		tmp = a;
	else
		tmp = Float64(-10.0 * Float64(a * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (m <= -1e-13)
		tmp = 0.1 / (k / a);
	elseif (m <= 0.22)
		tmp = a;
	else
		tmp = -10.0 * (a * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[m, -1e-13], N[(0.1 / N[(k / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 0.22], a, N[(-10.0 * N[(a * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 10: 26.2% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 0.4:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;-10 \cdot \left(a \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m) :precision binary64 (if (<= m 0.4) a (* -10.0 (* a k))))

C

double code(double a, double k, double m) {
	double tmp;
	if (m <= 0.4) {
		tmp = a;
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Fortran

real(8) function code(a, k, m)
    real(8), intent (in) :: a
    real(8), intent (in) :: k
    real(8), intent (in) :: m
    real(8) :: tmp
    if (m <= 0.4d0) then
        tmp = a
    else
        tmp = (-10.0d0) * (a * k)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (m <= 0.4) {
		tmp = a;
	} else {
		tmp = -10.0 * (a * k);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if m <= 0.4:
		tmp = a
	else:
		tmp = -10.0 * (a * k)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (m <= 0.4)
		tmp = a;
	else
		tmp = Float64(-10.0 * Float64(a * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (m <= 0.4)
		tmp = a;
	else
		tmp = -10.0 * (a * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[m, 0.4], a, N[(-10.0 * N[(a * k), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 20.2% accurate, 114.0× speedup

Math

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

FPCore

(FPCore (a k m) :precision binary64 a)

C

double code(double a, double k, double m) {
	return a;
}

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
end function

Java

public static double code(double a, double k, double m) {
	return a;
}

Python

def code(a, k, m):
	return a

Julia

function code(a, k, m)
	return a
end

MATLAB

function tmp = code(a, k, m)
	tmp = a;
end

Wolfram

code[a_, k_, m_] := a

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))