Falkner and Boettcher, Appendix A

Percentage Accurate: 89.8% → 99.1%

Time: 13.3s

Alternatives: 19

Speedup: 1.0×

• 23.7% 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: 89.8% 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, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, k_, m_] := N[(N[(N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision] / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot {k}^{m}\\ \mathbf{if}\;\frac{t_0}{k \cdot k + \left(1 + k \cdot 10\right)} \leq 2 \cdot 10^{+217}:\\ \;\;\;\;\frac{{k}^{m}}{\mathsf{hypot}\left(1, k\right)} \cdot \frac{a}{\mathsf{hypot}\left(1, k\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (* a (pow k m))))
   (if (<= (/ t_0 (+ (* k k) (+ 1.0 (* k 10.0)))) 2e+217)
     (* (/ (pow k m) (hypot 1.0 k)) (/ a (hypot 1.0 k)))
     t_0)))

C

double code(double a, double k, double m) {
	double t_0 = a * pow(k, m);
	double tmp;
	if ((t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 2e+217) {
		tmp = (pow(k, m) / hypot(1.0, k)) * (a / hypot(1.0, k));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double a, double k, double m) {
	double t_0 = a * Math.pow(k, m);
	double tmp;
	if ((t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 2e+217) {
		tmp = (Math.pow(k, m) / Math.hypot(1.0, k)) * (a / Math.hypot(1.0, k));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = a * math.pow(k, m)
	tmp = 0
	if (t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 2e+217:
		tmp = (math.pow(k, m) / math.hypot(1.0, k)) * (a / math.hypot(1.0, k))
	else:
		tmp = t_0
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(a * (k ^ m))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(k * k) + Float64(1.0 + Float64(k * 10.0)))) <= 2e+217)
		tmp = Float64(Float64((k ^ m) / hypot(1.0, k)) * Float64(a / hypot(1.0, k)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = a * (k ^ m);
	tmp = 0.0;
	if ((t_0 / ((k * k) + (1.0 + (k * 10.0)))) <= 2e+217)
		tmp = ((k ^ m) / hypot(1.0, k)) * (a / hypot(1.0, k));
	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]}, If[LessEqual[N[(t$95$0 / N[(N[(k * k), $MachinePrecision] + N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+217], N[(N[(N[Power[k, m], $MachinePrecision] / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

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1. Add Preprocessing

Alternative 3: 83.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot {k}^{m}\\ \mathbf{if}\;m \leq -3.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{t_0}{1 + k \cdot k}\\ \mathbf{elif}\;m \leq 1.65 \cdot 10^{-8}:\\ \;\;\;\;{\left(\frac{\sqrt{a}}{\mathsf{hypot}\left(1, k\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (* a (pow k m))))
   (if (<= m -3.6e-35)
     (/ t_0 (+ 1.0 (* k k)))
     (if (<= m 1.65e-8) (pow (/ (sqrt a) (hypot 1.0 k)) 2.0) t_0))))

C

double code(double a, double k, double m) {
	double t_0 = a * pow(k, m);
	double tmp;
	if (m <= -3.6e-35) {
		tmp = t_0 / (1.0 + (k * k));
	} else if (m <= 1.65e-8) {
		tmp = pow((sqrt(a) / hypot(1.0, k)), 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double a, double k, double m) {
	double t_0 = a * Math.pow(k, m);
	double tmp;
	if (m <= -3.6e-35) {
		tmp = t_0 / (1.0 + (k * k));
	} else if (m <= 1.65e-8) {
		tmp = Math.pow((Math.sqrt(a) / Math.hypot(1.0, k)), 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = a * math.pow(k, m)
	tmp = 0
	if m <= -3.6e-35:
		tmp = t_0 / (1.0 + (k * k))
	elif m <= 1.65e-8:
		tmp = math.pow((math.sqrt(a) / math.hypot(1.0, k)), 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(a * (k ^ m))
	tmp = 0.0
	if (m <= -3.6e-35)
		tmp = Float64(t_0 / Float64(1.0 + Float64(k * k)));
	elseif (m <= 1.65e-8)
		tmp = Float64(sqrt(a) / hypot(1.0, k)) ^ 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = a * (k ^ m);
	tmp = 0.0;
	if (m <= -3.6e-35)
		tmp = t_0 / (1.0 + (k * k));
	elseif (m <= 1.65e-8)
		tmp = (sqrt(a) / hypot(1.0, k)) ^ 2.0;
	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]}, If[LessEqual[m, -3.6e-35], N[(t$95$0 / N[(1.0 + N[(k * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[m, 1.65e-8], N[Power[N[(N[Sqrt[a], $MachinePrecision] / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], t$95$0]]]

Derivation

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1. Add Preprocessing

Alternative 4: 99.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[a_, k_, m_] := N[(N[(a * N[(N[Power[k, m], $MachinePrecision] / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 5: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot {k}^{m}\\ t_1 := \frac{t_0}{k \cdot k + \left(1 + k \cdot 10\right)}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (* a (pow k m))) (t_1 (/ t_0 (+ (* k k) (+ 1.0 (* k 10.0))))))
   (if (<= t_1 2e+217) 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 / ((k * k) + (1.0 + (k * 10.0)));
	double tmp;
	if (t_1 <= 2e+217) {
		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 / ((k * k) + (1.0d0 + (k * 10.0d0)))
    if (t_1 <= 2d+217) 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 / ((k * k) + (1.0 + (k * 10.0)));
	double tmp;
	if (t_1 <= 2e+217) {
		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 / ((k * k) + (1.0 + (k * 10.0)))
	tmp = 0
	if t_1 <= 2e+217:
		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(k * k) + Float64(1.0 + Float64(k * 10.0))))
	tmp = 0.0
	if (t_1 <= 2e+217)
		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 / ((k * k) + (1.0 + (k * 10.0)));
	tmp = 0.0;
	if (t_1 <= 2e+217)
		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[(k * k), $MachinePrecision] + N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+217], t$95$1, t$95$0]]]

Derivation

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1. Add Preprocessing

Alternative 6: 96.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq 4.2 \cdot 10^{-9}:\\ \;\;\;\;a \cdot {k}^{m}\\ \mathbf{else}:\\ \;\;\;\;\frac{{k}^{m}}{\mathsf{hypot}\left(1, k\right)} \cdot \frac{a}{k}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= k 4.2e-9) (* a (pow k m)) (* (/ (pow k m) (hypot 1.0 k)) (/ a k))))

C

double code(double a, double k, double m) {
	double tmp;
	if (k <= 4.2e-9) {
		tmp = a * pow(k, m);
	} else {
		tmp = (pow(k, m) / hypot(1.0, k)) * (a / k);
	}
	return tmp;
}

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (k <= 4.2e-9) {
		tmp = a * Math.pow(k, m);
	} else {
		tmp = (Math.pow(k, m) / Math.hypot(1.0, k)) * (a / k);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if k <= 4.2e-9:
		tmp = a * math.pow(k, m)
	else:
		tmp = (math.pow(k, m) / math.hypot(1.0, k)) * (a / k)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (k <= 4.2e-9)
		tmp = Float64(a * (k ^ m));
	else
		tmp = Float64(Float64((k ^ m) / hypot(1.0, k)) * Float64(a / k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (k <= 4.2e-9)
		tmp = a * (k ^ m);
	else
		tmp = ((k ^ m) / hypot(1.0, k)) * (a / k);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[k, 4.2e-9], N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[k, m], $MachinePrecision] / N[Sqrt[1.0 ^ 2 + k ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / k), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;{k}^{m} \cdot \frac{a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot {k}^{m}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= m 6.5e-5)
   (* (pow k m) (/ a (+ 1.0 (* k (+ k 10.0)))))
   (* a (pow k m))))

C

double code(double a, double k, double m) {
	double tmp;
	if (m <= 6.5e-5) {
		tmp = pow(k, m) * (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 <= 6.5d-5) then
        tmp = (k ** m) * (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 <= 6.5e-5) {
		tmp = Math.pow(k, m) * (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 <= 6.5e-5:
		tmp = math.pow(k, m) * (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 <= 6.5e-5)
		tmp = Float64((k ^ m) * 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 <= 6.5e-5)
		tmp = (k ^ m) * (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, 6.5e-5], N[(N[Power[k, m], $MachinePrecision] * N[(a / N[(1.0 + N[(k * N[(k + 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot {k}^{m}\\ \mathbf{if}\;m \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t_0}{1 + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (* a (pow k m)))) (if (<= m 6.5e-5) (/ t_0 (+ 1.0 (* k k))) t_0)))

C

double code(double a, double k, double m) {
	double t_0 = a * pow(k, m);
	double tmp;
	if (m <= 6.5e-5) {
		tmp = t_0 / (1.0 + (k * k));
	} 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 ** m)
    if (m <= 6.5d-5) then
        tmp = t_0 / (1.0d0 + (k * k))
    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 tmp;
	if (m <= 6.5e-5) {
		tmp = t_0 / (1.0 + (k * k));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = a * math.pow(k, m)
	tmp = 0
	if m <= 6.5e-5:
		tmp = t_0 / (1.0 + (k * k))
	else:
		tmp = t_0
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(a * (k ^ m))
	tmp = 0.0
	if (m <= 6.5e-5)
		tmp = Float64(t_0 / Float64(1.0 + Float64(k * k)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = a * (k ^ m);
	tmp = 0.0;
	if (m <= 6.5e-5)
		tmp = t_0 / (1.0 + (k * k));
	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]}, If[LessEqual[m, 6.5e-5], N[(t$95$0 / N[(1.0 + N[(k * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

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

Alternative 9: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -5 \cdot 10^{-9} \lor \neg \left(m \leq 2.45 \cdot 10^{-5}\right):\\ \;\;\;\;a \cdot {k}^{m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{k \cdot k + \left(1 + k \cdot 10\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (or (<= m -5e-9) (not (<= m 2.45e-5)))
   (* a (pow k m))
   (/ a (+ (* k k) (+ 1.0 (* k 10.0))))))

C

double code(double a, double k, double m) {
	double tmp;
	if ((m <= -5e-9) || !(m <= 2.45e-5)) {
		tmp = a * pow(k, m);
	} else {
		tmp = a / ((k * k) + (1.0 + (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 <= (-5d-9)) .or. (.not. (m <= 2.45d-5))) then
        tmp = a * (k ** m)
    else
        tmp = a / ((k * k) + (1.0d0 + (k * 10.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if ((m <= -5e-9) || !(m <= 2.45e-5)) {
		tmp = a * Math.pow(k, m);
	} else {
		tmp = a / ((k * k) + (1.0 + (k * 10.0)));
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if (m <= -5e-9) or not (m <= 2.45e-5):
		tmp = a * math.pow(k, m)
	else:
		tmp = a / ((k * k) + (1.0 + (k * 10.0)))
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if ((m <= -5e-9) || !(m <= 2.45e-5))
		tmp = Float64(a * (k ^ m));
	else
		tmp = Float64(a / Float64(Float64(k * k) + Float64(1.0 + Float64(k * 10.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if ((m <= -5e-9) || ~((m <= 2.45e-5)))
		tmp = a * (k ^ m);
	else
		tmp = a / ((k * k) + (1.0 + (k * 10.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[Or[LessEqual[m, -5e-9], N[Not[LessEqual[m, 2.45e-5]], $MachinePrecision]], N[(a * N[Power[k, m], $MachinePrecision]), $MachinePrecision], N[(a / N[(N[(k * k), $MachinePrecision] + N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 46.9% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := k \cdot \left(k + 10\right)\\ \mathbf{if}\;m \leq -50:\\ \;\;\;\;\frac{a}{1 - t_0 \cdot t_0} \cdot \left(1 - k \cdot 10\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{k \cdot k + \left(1 + k \cdot 10\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (let* ((t_0 (* k (+ k 10.0))))
   (if (<= m -50.0)
     (* (/ a (- 1.0 (* t_0 t_0))) (- 1.0 (* k 10.0)))
     (/ a (+ (* k k) (+ 1.0 (* k 10.0)))))))

C

double code(double a, double k, double m) {
	double t_0 = k * (k + 10.0);
	double tmp;
	if (m <= -50.0) {
		tmp = (a / (1.0 - (t_0 * t_0))) * (1.0 - (k * 10.0));
	} else {
		tmp = a / ((k * k) + (1.0 + (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) :: t_0
    real(8) :: tmp
    t_0 = k * (k + 10.0d0)
    if (m <= (-50.0d0)) then
        tmp = (a / (1.0d0 - (t_0 * t_0))) * (1.0d0 - (k * 10.0d0))
    else
        tmp = a / ((k * k) + (1.0d0 + (k * 10.0d0)))
    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 <= -50.0) {
		tmp = (a / (1.0 - (t_0 * t_0))) * (1.0 - (k * 10.0));
	} else {
		tmp = a / ((k * k) + (1.0 + (k * 10.0)));
	}
	return tmp;
}

Python

def code(a, k, m):
	t_0 = k * (k + 10.0)
	tmp = 0
	if m <= -50.0:
		tmp = (a / (1.0 - (t_0 * t_0))) * (1.0 - (k * 10.0))
	else:
		tmp = a / ((k * k) + (1.0 + (k * 10.0)))
	return tmp

Julia

function code(a, k, m)
	t_0 = Float64(k * Float64(k + 10.0))
	tmp = 0.0
	if (m <= -50.0)
		tmp = Float64(Float64(a / Float64(1.0 - Float64(t_0 * t_0))) * Float64(1.0 - Float64(k * 10.0)));
	else
		tmp = Float64(a / Float64(Float64(k * k) + Float64(1.0 + Float64(k * 10.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	t_0 = k * (k + 10.0);
	tmp = 0.0;
	if (m <= -50.0)
		tmp = (a / (1.0 - (t_0 * t_0))) * (1.0 - (k * 10.0));
	else
		tmp = a / ((k * k) + (1.0 + (k * 10.0)));
	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, -50.0], N[(N[(a / N[(1.0 - N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a / N[(N[(k * k), $MachinePrecision] + N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 28.8% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\frac{a}{\frac{-k}{0.1}}\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{-9}:\\ \;\;\;\;a + -10 \cdot \left(a \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.1}{\frac{k}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= k -5e-311)
   (/ a (/ (- k) 0.1))
   (if (<= k 4.2e-9) (+ a (* -10.0 (* a k))) (/ 0.1 (/ k a)))))

C

double code(double a, double k, double m) {
	double tmp;
	if (k <= -5e-311) {
		tmp = a / (-k / 0.1);
	} else if (k <= 4.2e-9) {
		tmp = a + (-10.0 * (a * k));
	} else {
		tmp = 0.1 / (k / a);
	}
	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 (k <= (-5d-311)) then
        tmp = a / (-k / 0.1d0)
    else if (k <= 4.2d-9) then
        tmp = a + ((-10.0d0) * (a * k))
    else
        tmp = 0.1d0 / (k / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (k <= -5e-311) {
		tmp = a / (-k / 0.1);
	} else if (k <= 4.2e-9) {
		tmp = a + (-10.0 * (a * k));
	} else {
		tmp = 0.1 / (k / a);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if k <= -5e-311:
		tmp = a / (-k / 0.1)
	elif k <= 4.2e-9:
		tmp = a + (-10.0 * (a * k))
	else:
		tmp = 0.1 / (k / a)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (k <= -5e-311)
		tmp = Float64(a / Float64(Float64(-k) / 0.1));
	elseif (k <= 4.2e-9)
		tmp = Float64(a + Float64(-10.0 * Float64(a * k)));
	else
		tmp = Float64(0.1 / Float64(k / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (k <= -5e-311)
		tmp = a / (-k / 0.1);
	elseif (k <= 4.2e-9)
		tmp = a + (-10.0 * (a * k));
	else
		tmp = 0.1 / (k / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[k, -5e-311], N[(a / N[((-k) / 0.1), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.2e-9], N[(a + N[(-10.0 * N[(a * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.1 / N[(k / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 12: 27.0% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq 2.7 \cdot 10^{-303} \lor \neg \left(k \leq 59000000000\right):\\ \;\;\;\;\frac{a}{k} \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (or (<= k 2.7e-303) (not (<= k 59000000000.0))) (* (/ a k) 0.1) a))

C

double code(double a, double k, double m) {
	double tmp;
	if ((k <= 2.7e-303) || !(k <= 59000000000.0)) {
		tmp = (a / k) * 0.1;
	} else {
		tmp = a;
	}
	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 ((k <= 2.7d-303) .or. (.not. (k <= 59000000000.0d0))) then
        tmp = (a / k) * 0.1d0
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if ((k <= 2.7e-303) || !(k <= 59000000000.0)) {
		tmp = (a / k) * 0.1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if (k <= 2.7e-303) or not (k <= 59000000000.0):
		tmp = (a / k) * 0.1
	else:
		tmp = a
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if ((k <= 2.7e-303) || !(k <= 59000000000.0))
		tmp = Float64(Float64(a / k) * 0.1);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if ((k <= 2.7e-303) || ~((k <= 59000000000.0)))
		tmp = (a / k) * 0.1;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[Or[LessEqual[k, 2.7e-303], N[Not[LessEqual[k, 59000000000.0]], $MachinePrecision]], N[(N[(a / k), $MachinePrecision] * 0.1), $MachinePrecision], a]

Derivation

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

Alternative 13: 27.2% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq 2.7 \cdot 10^{-303}:\\ \;\;\;\;\frac{a}{k} \cdot 0.1\\ \mathbf{elif}\;k \leq 59000000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\frac{0.1}{\frac{k}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= k 2.7e-303)
   (* (/ a k) 0.1)
   (if (<= k 59000000000.0) a (/ 0.1 (/ k a)))))

C

double code(double a, double k, double m) {
	double tmp;
	if (k <= 2.7e-303) {
		tmp = (a / k) * 0.1;
	} else if (k <= 59000000000.0) {
		tmp = a;
	} else {
		tmp = 0.1 / (k / a);
	}
	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 (k <= 2.7d-303) then
        tmp = (a / k) * 0.1d0
    else if (k <= 59000000000.0d0) then
        tmp = a
    else
        tmp = 0.1d0 / (k / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (k <= 2.7e-303) {
		tmp = (a / k) * 0.1;
	} else if (k <= 59000000000.0) {
		tmp = a;
	} else {
		tmp = 0.1 / (k / a);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if k <= 2.7e-303:
		tmp = (a / k) * 0.1
	elif k <= 59000000000.0:
		tmp = a
	else:
		tmp = 0.1 / (k / a)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (k <= 2.7e-303)
		tmp = Float64(Float64(a / k) * 0.1);
	elseif (k <= 59000000000.0)
		tmp = a;
	else
		tmp = Float64(0.1 / Float64(k / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (k <= 2.7e-303)
		tmp = (a / k) * 0.1;
	elseif (k <= 59000000000.0)
		tmp = a;
	else
		tmp = 0.1 / (k / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[k, 2.7e-303], N[(N[(a / k), $MachinePrecision] * 0.1), $MachinePrecision], If[LessEqual[k, 59000000000.0], a, N[(0.1 / N[(k / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 14: 28.8% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\frac{a}{\frac{-k}{0.1}}\\ \mathbf{elif}\;k \leq 59000000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\frac{0.1}{\frac{k}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= k -5e-311)
   (/ a (/ (- k) 0.1))
   (if (<= k 59000000000.0) a (/ 0.1 (/ k a)))))

C

double code(double a, double k, double m) {
	double tmp;
	if (k <= -5e-311) {
		tmp = a / (-k / 0.1);
	} else if (k <= 59000000000.0) {
		tmp = a;
	} else {
		tmp = 0.1 / (k / a);
	}
	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 (k <= (-5d-311)) then
        tmp = a / (-k / 0.1d0)
    else if (k <= 59000000000.0d0) then
        tmp = a
    else
        tmp = 0.1d0 / (k / a)
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (k <= -5e-311) {
		tmp = a / (-k / 0.1);
	} else if (k <= 59000000000.0) {
		tmp = a;
	} else {
		tmp = 0.1 / (k / a);
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if k <= -5e-311:
		tmp = a / (-k / 0.1)
	elif k <= 59000000000.0:
		tmp = a
	else:
		tmp = 0.1 / (k / a)
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (k <= -5e-311)
		tmp = Float64(a / Float64(Float64(-k) / 0.1));
	elseif (k <= 59000000000.0)
		tmp = a;
	else
		tmp = Float64(0.1 / Float64(k / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (k <= -5e-311)
		tmp = a / (-k / 0.1);
	elseif (k <= 59000000000.0)
		tmp = a;
	else
		tmp = 0.1 / (k / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[k, -5e-311], N[(a / N[((-k) / 0.1), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 59000000000.0], a, N[(0.1 / N[(k / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 15: 29.5% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;m \leq -2.25 \cdot 10^{+51}:\\ \;\;\;\;\frac{a}{k} \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{1 + k \cdot 10}\\ \end{array} \end{array} \]

FPCore

(FPCore (a k m)
 :precision binary64
 (if (<= m -2.25e+51) (* (/ a k) 0.1) (/ a (+ 1.0 (* k 10.0)))))

C

double code(double a, double k, double m) {
	double tmp;
	if (m <= -2.25e+51) {
		tmp = (a / k) * 0.1;
	} else {
		tmp = a / (1.0 + (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 <= (-2.25d+51)) then
        tmp = (a / k) * 0.1d0
    else
        tmp = a / (1.0d0 + (k * 10.0d0))
    end if
    code = tmp
end function

Java

public static double code(double a, double k, double m) {
	double tmp;
	if (m <= -2.25e+51) {
		tmp = (a / k) * 0.1;
	} else {
		tmp = a / (1.0 + (k * 10.0));
	}
	return tmp;
}

Python

def code(a, k, m):
	tmp = 0
	if m <= -2.25e+51:
		tmp = (a / k) * 0.1
	else:
		tmp = a / (1.0 + (k * 10.0))
	return tmp

Julia

function code(a, k, m)
	tmp = 0.0
	if (m <= -2.25e+51)
		tmp = Float64(Float64(a / k) * 0.1);
	else
		tmp = Float64(a / Float64(1.0 + Float64(k * 10.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, k, m)
	tmp = 0.0;
	if (m <= -2.25e+51)
		tmp = (a / k) * 0.1;
	else
		tmp = a / (1.0 + (k * 10.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, k_, m_] := If[LessEqual[m, -2.25e+51], N[(N[(a / k), $MachinePrecision] * 0.1), $MachinePrecision], N[(a / N[(1.0 + N[(k * 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 16: 44.0% accurate, 10.4× speedup

Math

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

FPCore

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

C

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

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 * k) + (1.0d0 + (k * 10.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 17: 44.0% accurate, 12.7× speedup

Math

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

FPCore

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

C

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

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 / (1.0d0 + (k * (k + 10.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 18: 43.2% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \frac{a}{1 + k \cdot k} \end{array} \]

FPCore

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

C

double code(double a, double k, double m) {
	return a / (1.0 + (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 / (1.0d0 + (k * k))
end function

Java

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

Python

def code(a, k, m):
	return a / (1.0 + (k * k))

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 19: 19.8% 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

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1. Add Preprocessing

Reproduce

herbie shell --seed 2024006 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))