Complex division, real part

Percentage Accurate: 61.9% → 86.0%

Time: 11.0s

Alternatives: 9

Speedup: 2.1×

Specification

Math

\[\begin{array}{l} \\ \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))

C

double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = ((a * c) + (b * d)) / ((c * c) + (d * d))
end function

Java

public static double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Python

def code(a, b, c, d):
	return ((a * c) + (b * d)) / ((c * c) + (d * d))

Julia

function code(a, b, c, d)
	return Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))

C

double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = ((a * c) + (b * d)) / ((c * c) + (d * d))
end function

Java

public static double code(double a, double b, double c, double d) {
	return ((a * c) + (b * d)) / ((c * c) + (d * d));
}

Python

def code(a, b, c, d):
	return ((a * c) + (b * d)) / ((c * c) + (d * d))

Julia

function code(a, b, c, d)
	return Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 86.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b}{\frac{c}{d}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) 5e+292)
   (* (/ 1.0 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
   (* (/ 1.0 c) (+ a (/ b (/ c d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((a * c) + (b * d)) / ((c * c) + (d * d))) <= 5e+292) {
		tmp = (1.0 / hypot(c, d)) * (fma(a, c, (b * d)) / hypot(c, d));
	} else {
		tmp = (1.0 / c) * (a + (b / (c / d)));
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d))) <= 5e+292)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(fma(a, c, Float64(b * d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(1.0 / c) * Float64(a + Float64(b / Float64(c / d))));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+292], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 75.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;\frac{d}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{b}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(d, \frac{b}{c}, a\right)}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -4.2e+86)
   (* (+ a (/ b (/ c d))) (/ -1.0 (hypot c d)))
   (if (<= c -5.2e-102)
     (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
     (if (<= c 1.08e+71)
       (* (/ d (hypot c d)) (/ b (hypot c d)))
       (/ (fma d (/ b c) a) (hypot c d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -4.2e+86) {
		tmp = (a + (b / (c / d))) * (-1.0 / hypot(c, d));
	} else if (c <= -5.2e-102) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 1.08e+71) {
		tmp = (d / hypot(c, d)) * (b / hypot(c, d));
	} else {
		tmp = fma(d, (b / c), a) / hypot(c, d);
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -4.2e+86)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) * Float64(-1.0 / hypot(c, d)));
	elseif (c <= -5.2e-102)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 1.08e+71)
		tmp = Float64(Float64(d / hypot(c, d)) * Float64(b / hypot(c, d)));
	else
		tmp = Float64(fma(d, Float64(b / c), a) / hypot(c, d));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -4.2e+86], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.2e-102], N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.08e+71], N[(N[(d / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(b / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(d * N[(b / c), $MachinePrecision] + a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 3: 78.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b}{\frac{c}{d}}\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-246}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + b \cdot \frac{d}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -4.2e+86)
     (* (/ 1.0 c) (+ a (/ b (/ c d))))
     (if (<= c -1.7e-106)
       t_0
       (if (<= c 1.7e-246)
         (/ b d)
         (if (<= c 4.1e+60)
           t_0
           (* (/ 1.0 (hypot c d)) (+ a (* b (/ d c))))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double tmp;
	if (c <= -4.2e+86) {
		tmp = (1.0 / c) * (a + (b / (c / d)));
	} else if (c <= -1.7e-106) {
		tmp = t_0;
	} else if (c <= 1.7e-246) {
		tmp = b / d;
	} else if (c <= 4.1e+60) {
		tmp = t_0;
	} else {
		tmp = (1.0 / hypot(c, d)) * (a + (b * (d / c)));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double tmp;
	if (c <= -4.2e+86) {
		tmp = (1.0 / c) * (a + (b / (c / d)));
	} else if (c <= -1.7e-106) {
		tmp = t_0;
	} else if (c <= 1.7e-246) {
		tmp = b / d;
	} else if (c <= 4.1e+60) {
		tmp = t_0;
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * (a + (b * (d / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -4.2e+86:
		tmp = (1.0 / c) * (a + (b / (c / d)))
	elif c <= -1.7e-106:
		tmp = t_0
	elif c <= 1.7e-246:
		tmp = b / d
	elif c <= 4.1e+60:
		tmp = t_0
	else:
		tmp = (1.0 / math.hypot(c, d)) * (a + (b * (d / c)))
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (c <= -4.2e+86)
		tmp = Float64(Float64(1.0 / c) * Float64(a + Float64(b / Float64(c / d))));
	elseif (c <= -1.7e-106)
		tmp = t_0;
	elseif (c <= 1.7e-246)
		tmp = Float64(b / d);
	elseif (c <= 4.1e+60)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(a + Float64(b * Float64(d / c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (c <= -4.2e+86)
		tmp = (1.0 / c) * (a + (b / (c / d)));
	elseif (c <= -1.7e-106)
		tmp = t_0;
	elseif (c <= 1.7e-246)
		tmp = b / d;
	elseif (c <= 4.1e+60)
		tmp = t_0;
	else
		tmp = (1.0 / hypot(c, d)) * (a + (b * (d / c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+86], N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.7e-106], t$95$0, If[LessEqual[c, 1.7e-246], N[(b / d), $MachinePrecision], If[LessEqual[c, 4.1e+60], t$95$0, N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 78.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := a + \frac{b}{\frac{c}{d}}\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;\frac{1}{c} \cdot t_1\\ \mathbf{elif}\;c \leq -9.8 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-246}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (+ a (/ b (/ c d)))))
   (if (<= c -4.2e+86)
     (* (/ 1.0 c) t_1)
     (if (<= c -9.8e-107)
       t_0
       (if (<= c 1.2e-246)
         (/ b d)
         (if (<= c 3.6e+57) t_0 (* (/ 1.0 (hypot c d)) t_1)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double t_1 = a + (b / (c / d));
	double tmp;
	if (c <= -4.2e+86) {
		tmp = (1.0 / c) * t_1;
	} else if (c <= -9.8e-107) {
		tmp = t_0;
	} else if (c <= 1.2e-246) {
		tmp = b / d;
	} else if (c <= 3.6e+57) {
		tmp = t_0;
	} else {
		tmp = (1.0 / hypot(c, d)) * t_1;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double t_1 = a + (b / (c / d));
	double tmp;
	if (c <= -4.2e+86) {
		tmp = (1.0 / c) * t_1;
	} else if (c <= -9.8e-107) {
		tmp = t_0;
	} else if (c <= 1.2e-246) {
		tmp = b / d;
	} else if (c <= 3.6e+57) {
		tmp = t_0;
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * t_1;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	t_1 = a + (b / (c / d))
	tmp = 0
	if c <= -4.2e+86:
		tmp = (1.0 / c) * t_1
	elif c <= -9.8e-107:
		tmp = t_0
	elif c <= 1.2e-246:
		tmp = b / d
	elif c <= 3.6e+57:
		tmp = t_0
	else:
		tmp = (1.0 / math.hypot(c, d)) * t_1
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
	t_1 = Float64(a + Float64(b / Float64(c / d)))
	tmp = 0.0
	if (c <= -4.2e+86)
		tmp = Float64(Float64(1.0 / c) * t_1);
	elseif (c <= -9.8e-107)
		tmp = t_0;
	elseif (c <= 1.2e-246)
		tmp = Float64(b / d);
	elseif (c <= 3.6e+57)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	t_1 = a + (b / (c / d));
	tmp = 0.0;
	if (c <= -4.2e+86)
		tmp = (1.0 / c) * t_1;
	elseif (c <= -9.8e-107)
		tmp = t_0;
	elseif (c <= 1.2e-246)
		tmp = b / d;
	elseif (c <= 3.6e+57)
		tmp = t_0;
	else
		tmp = (1.0 / hypot(c, d)) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+86], N[(N[(1.0 / c), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[c, -9.8e-107], t$95$0, If[LessEqual[c, 1.2e-246], N[(b / d), $MachinePrecision], If[LessEqual[c, 3.6e+57], t$95$0, N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]

Derivation

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

Alternative 5: 81.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := b + \frac{a}{\frac{d}{c}}\\ \mathbf{if}\;d \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;t_0 \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;d \leq -4 \cdot 10^{-100}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b}{\frac{c}{d}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (+ b (/ a (/ d c)))))
   (if (<= d -6.2e+93)
     (* t_0 (/ -1.0 (hypot c d)))
     (if (<= d -4e-100)
       (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
       (if (<= d 1.15e-9)
         (* (/ 1.0 c) (+ a (/ b (/ c d))))
         (* (/ 1.0 (hypot c d)) t_0))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = b + (a / (d / c));
	double tmp;
	if (d <= -6.2e+93) {
		tmp = t_0 * (-1.0 / hypot(c, d));
	} else if (d <= -4e-100) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 1.15e-9) {
		tmp = (1.0 / c) * (a + (b / (c / d)));
	} else {
		tmp = (1.0 / hypot(c, d)) * t_0;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = b + (a / (d / c));
	double tmp;
	if (d <= -6.2e+93) {
		tmp = t_0 * (-1.0 / Math.hypot(c, d));
	} else if (d <= -4e-100) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 1.15e-9) {
		tmp = (1.0 / c) * (a + (b / (c / d)));
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = b + (a / (d / c))
	tmp = 0
	if d <= -6.2e+93:
		tmp = t_0 * (-1.0 / math.hypot(c, d))
	elif d <= -4e-100:
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
	elif d <= 1.15e-9:
		tmp = (1.0 / c) * (a + (b / (c / d)))
	else:
		tmp = (1.0 / math.hypot(c, d)) * t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(b + Float64(a / Float64(d / c)))
	tmp = 0.0
	if (d <= -6.2e+93)
		tmp = Float64(t_0 * Float64(-1.0 / hypot(c, d)));
	elseif (d <= -4e-100)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 1.15e-9)
		tmp = Float64(Float64(1.0 / c) * Float64(a + Float64(b / Float64(c / d))));
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = b + (a / (d / c));
	tmp = 0.0;
	if (d <= -6.2e+93)
		tmp = t_0 * (-1.0 / hypot(c, d));
	elseif (d <= -4e-100)
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	elseif (d <= 1.15e-9)
		tmp = (1.0 / c) * (a + (b / (c / d)));
	else
		tmp = (1.0 / hypot(c, d)) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -6.2e+93], N[(t$95$0 * N[(-1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -4e-100], N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 1.15e-9], N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{1}{c} \cdot \left(a + \frac{b}{\frac{c}{d}}\right)\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-246}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+144}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (* (/ 1.0 c) (+ a (/ b (/ c d))))))
   (if (<= c -4.5e+86)
     t_1
     (if (<= c -1.1e-106)
       t_0
       (if (<= c 1.1e-246) (/ b d) (if (<= c 3.1e+144) t_0 t_1))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double t_1 = (1.0 / c) * (a + (b / (c / d)));
	double tmp;
	if (c <= -4.5e+86) {
		tmp = t_1;
	} else if (c <= -1.1e-106) {
		tmp = t_0;
	} else if (c <= 1.1e-246) {
		tmp = b / d;
	} else if (c <= 3.1e+144) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
    t_1 = (1.0d0 / c) * (a + (b / (c / d)))
    if (c <= (-4.5d+86)) then
        tmp = t_1
    else if (c <= (-1.1d-106)) then
        tmp = t_0
    else if (c <= 1.1d-246) then
        tmp = b / d
    else if (c <= 3.1d+144) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double t_1 = (1.0 / c) * (a + (b / (c / d)));
	double tmp;
	if (c <= -4.5e+86) {
		tmp = t_1;
	} else if (c <= -1.1e-106) {
		tmp = t_0;
	} else if (c <= 1.1e-246) {
		tmp = b / d;
	} else if (c <= 3.1e+144) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	t_1 = (1.0 / c) * (a + (b / (c / d)))
	tmp = 0
	if c <= -4.5e+86:
		tmp = t_1
	elif c <= -1.1e-106:
		tmp = t_0
	elif c <= 1.1e-246:
		tmp = b / d
	elif c <= 3.1e+144:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
	t_1 = Float64(Float64(1.0 / c) * Float64(a + Float64(b / Float64(c / d))))
	tmp = 0.0
	if (c <= -4.5e+86)
		tmp = t_1;
	elseif (c <= -1.1e-106)
		tmp = t_0;
	elseif (c <= 1.1e-246)
		tmp = Float64(b / d);
	elseif (c <= 3.1e+144)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	t_1 = (1.0 / c) * (a + (b / (c / d)));
	tmp = 0.0;
	if (c <= -4.5e+86)
		tmp = t_1;
	elseif (c <= -1.1e-106)
		tmp = t_0;
	elseif (c <= 1.1e-246)
		tmp = b / d;
	elseif (c <= 3.1e+144)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e+86], t$95$1, If[LessEqual[c, -1.1e-106], t$95$0, If[LessEqual[c, 1.1e-246], N[(b / d), $MachinePrecision], If[LessEqual[c, 3.1e+144], t$95$0, t$95$1]]]]]]

Derivation

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

Alternative 7: 68.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.4 \cdot 10^{-50} \lor \neg \left(c \leq 4.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b}{\frac{c}{d}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -6.4e-50) (not (<= c 4.2e+54)))
   (* (/ 1.0 c) (+ a (/ b (/ c d))))
   (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -6.4e-50) || !(c <= 4.2e+54)) {
		tmp = (1.0 / c) * (a + (b / (c / d)));
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((c <= (-6.4d-50)) .or. (.not. (c <= 4.2d+54))) then
        tmp = (1.0d0 / c) * (a + (b / (c / d)))
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -6.4e-50) || !(c <= 4.2e+54)) {
		tmp = (1.0 / c) * (a + (b / (c / d)));
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -6.4e-50) or not (c <= 4.2e+54):
		tmp = (1.0 / c) * (a + (b / (c / d)))
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -6.4e-50) || !(c <= 4.2e+54))
		tmp = Float64(Float64(1.0 / c) * Float64(a + Float64(b / Float64(c / d))));
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -6.4e-50) || ~((c <= 4.2e+54)))
		tmp = (1.0 / c) * (a + (b / (c / d)));
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -6.4e-50], N[Not[LessEqual[c, 4.2e+54]], $MachinePrecision]], N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

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

Alternative 8: 63.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-14} \lor \neg \left(c \leq 1.7 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -4e-14) (not (<= c 1.7e+72))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4e-14) || !(c <= 1.7e+72)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((c <= (-4d-14)) .or. (.not. (c <= 1.7d+72))) then
        tmp = a / c
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4e-14) || !(c <= 1.7e+72)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -4e-14) or not (c <= 1.7e+72):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -4e-14) || !(c <= 1.7e+72))
		tmp = Float64(a / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -4e-14) || ~((c <= 1.7e+72)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -4e-14], N[Not[LessEqual[c, 1.7e+72]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

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

Alternative 9: 43.7% accurate, 5.0× speedup

Math

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

FPCore

(FPCore (a b c d) :precision binary64 (/ a c))

C

double code(double a, double b, double c, double d) {
	return a / c;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = a / c
end function

Java

public static double code(double a, double b, double c, double d) {
	return a / c;
}

Python

def code(a, b, c, d):
	return a / c

Julia

function code(a, b, c, d)
	return Float64(a / c)
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = a / c;
end

Wolfram

code[a_, b_, c_, d_] := N[(a / c), $MachinePrecision]

Derivation

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

Developer target: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left|d\right| < \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (< (fabs d) (fabs c))
   (/ (+ a (* b (/ d c))) (+ c (* d (/ d c))))
   (/ (+ b (* a (/ c d))) (+ d (* c (/ c d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (fabs(d) < fabs(c)) {
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)));
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (abs(d) < abs(c)) then
        tmp = (a + (b * (d / c))) / (c + (d * (d / c)))
    else
        tmp = (b + (a * (c / d))) / (d + (c * (c / d)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (Math.abs(d) < Math.abs(c)) {
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if math.fabs(d) < math.fabs(c):
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)))
	else:
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (abs(d) < abs(c))
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / Float64(c + Float64(d * Float64(d / c))));
	else
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / Float64(d + Float64(c * Float64(c / d))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (abs(d) < abs(c))
		tmp = (a + (b * (d / c))) / (c + (d * (d / c)));
	else
		tmp = (b + (a * (c / d))) / (d + (c * (c / d)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Less[N[Abs[d], $MachinePrecision], N[Abs[c], $MachinePrecision]], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c + N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(d + N[(c * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023350 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :herbie-target
  (if (< (fabs d) (fabs c)) (/ (+ a (* b (/ d c))) (+ c (* d (/ d c)))) (/ (+ b (* a (/ c d))) (+ d (* c (/ c d)))))

  (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))