Complex division, real part

Percentage Accurate: 61.2% → 84.5%

Time: 11.0s

Alternatives: 12

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: 61.2% 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: 84.5% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) INFINITY)
   (/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
   (* (/ c (hypot c d)) (/ a (hypot c d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((a * c) + (b * d)) / ((c * c) + (d * d))) <= ((double) INFINITY)) {
		tmp = (fma(a, c, (b * d)) / hypot(c, d)) / hypot(c, d);
	} else {
		tmp = (c / hypot(c, d)) * (a / hypot(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))) <= Inf)
		tmp = Float64(Float64(fma(a, c, Float64(b * d)) / hypot(c, d)) / hypot(c, d));
	else
		tmp = Float64(Float64(c / hypot(c, d)) * Float64(a / hypot(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], Infinity], N[(N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], N[(N[(c / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 82.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{-b}{\frac{c}{d}} - a}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-134}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(a, c, b \cdot d\right) \cdot \frac{1}{{\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -4.5e+88)
   (/ (- (/ (- b) (/ c d)) a) (hypot c d))
   (if (<= c -1.05e-134)
     (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
     (if (<= c 7.2e-163)
       (* (/ 1.0 d) (+ b (/ (* a c) d)))
       (if (<= c 3.2e+68)
         (* (fma a c (* b d)) (/ 1.0 (pow (hypot c d) 2.0)))
         (* (/ c (hypot c d)) (/ a (hypot c d))))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -4.5e+88) {
		tmp = ((-b / (c / d)) - a) / hypot(c, d);
	} else if (c <= -1.05e-134) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 7.2e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 3.2e+68) {
		tmp = fma(a, c, (b * d)) * (1.0 / pow(hypot(c, d), 2.0));
	} else {
		tmp = (c / hypot(c, d)) * (a / hypot(c, d));
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -4.5e+88)
		tmp = Float64(Float64(Float64(Float64(-b) / Float64(c / d)) - a) / hypot(c, d));
	elseif (c <= -1.05e-134)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 7.2e-163)
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	elseif (c <= 3.2e+68)
		tmp = Float64(fma(a, c, Float64(b * d)) * Float64(1.0 / (hypot(c, d) ^ 2.0)));
	else
		tmp = Float64(Float64(c / hypot(c, d)) * Float64(a / hypot(c, d)));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -4.5e+88], N[(N[(N[((-b) / N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e-134], 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, 7.2e-163], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+68], N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 82.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{-b}{\frac{c}{d}} - a}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -1.15e+87)
     (/ (- (/ (- b) (/ c d)) a) (hypot c d))
     (if (<= c -1.6e-134)
       t_0
       (if (<= c 7.2e-163)
         (* (/ 1.0 d) (+ b (/ (* a c) d)))
         (if (<= c 3.3e+68) t_0 (* (/ c (hypot c d)) (/ a (hypot c d)))))))))

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 <= -1.15e+87) {
		tmp = ((-b / (c / d)) - a) / hypot(c, d);
	} else if (c <= -1.6e-134) {
		tmp = t_0;
	} else if (c <= 7.2e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 3.3e+68) {
		tmp = t_0;
	} else {
		tmp = (c / hypot(c, d)) * (a / hypot(c, d));
	}
	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 <= -1.15e+87) {
		tmp = ((-b / (c / d)) - a) / Math.hypot(c, d);
	} else if (c <= -1.6e-134) {
		tmp = t_0;
	} else if (c <= 7.2e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 3.3e+68) {
		tmp = t_0;
	} else {
		tmp = (c / Math.hypot(c, d)) * (a / Math.hypot(c, d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -1.15e+87:
		tmp = ((-b / (c / d)) - a) / math.hypot(c, d)
	elif c <= -1.6e-134:
		tmp = t_0
	elif c <= 7.2e-163:
		tmp = (1.0 / d) * (b + ((a * c) / d))
	elif c <= 3.3e+68:
		tmp = t_0
	else:
		tmp = (c / math.hypot(c, d)) * (a / math.hypot(c, d))
	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 <= -1.15e+87)
		tmp = Float64(Float64(Float64(Float64(-b) / Float64(c / d)) - a) / hypot(c, d));
	elseif (c <= -1.6e-134)
		tmp = t_0;
	elseif (c <= 7.2e-163)
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	elseif (c <= 3.3e+68)
		tmp = t_0;
	else
		tmp = Float64(Float64(c / hypot(c, d)) * Float64(a / hypot(c, d)));
	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 <= -1.15e+87)
		tmp = ((-b / (c / d)) - a) / hypot(c, d);
	elseif (c <= -1.6e-134)
		tmp = t_0;
	elseif (c <= 7.2e-163)
		tmp = (1.0 / d) * (b + ((a * c) / d));
	elseif (c <= 3.3e+68)
		tmp = t_0;
	else
		tmp = (c / hypot(c, d)) * (a / hypot(c, d));
	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, -1.15e+87], N[(N[(N[((-b) / N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.6e-134], t$95$0, If[LessEqual[c, 7.2e-163], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e+68], t$95$0, N[(N[(c / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 82.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{+89}:\\ \;\;\;\;\frac{a}{c} + d \cdot \frac{\frac{b}{c}}{c}\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -1.1e+89)
     (+ (/ a c) (* d (/ (/ b c) c)))
     (if (<= c -6e-135)
       t_0
       (if (<= c 7.2e-163)
         (* (/ 1.0 d) (+ b (/ (* a c) d)))
         (if (<= c 8e+102) t_0 (/ (+ a (/ b (/ c d))) (hypot c d))))))))

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 <= -1.1e+89) {
		tmp = (a / c) + (d * ((b / c) / c));
	} else if (c <= -6e-135) {
		tmp = t_0;
	} else if (c <= 7.2e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 8e+102) {
		tmp = t_0;
	} else {
		tmp = (a + (b / (c / d))) / hypot(c, d);
	}
	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 <= -1.1e+89) {
		tmp = (a / c) + (d * ((b / c) / c));
	} else if (c <= -6e-135) {
		tmp = t_0;
	} else if (c <= 7.2e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 8e+102) {
		tmp = t_0;
	} else {
		tmp = (a + (b / (c / d))) / Math.hypot(c, d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -1.1e+89:
		tmp = (a / c) + (d * ((b / c) / c))
	elif c <= -6e-135:
		tmp = t_0
	elif c <= 7.2e-163:
		tmp = (1.0 / d) * (b + ((a * c) / d))
	elif c <= 8e+102:
		tmp = t_0
	else:
		tmp = (a + (b / (c / d))) / math.hypot(c, d)
	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 <= -1.1e+89)
		tmp = Float64(Float64(a / c) + Float64(d * Float64(Float64(b / c) / c)));
	elseif (c <= -6e-135)
		tmp = t_0;
	elseif (c <= 7.2e-163)
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	elseif (c <= 8e+102)
		tmp = t_0;
	else
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / hypot(c, d));
	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 <= -1.1e+89)
		tmp = (a / c) + (d * ((b / c) / c));
	elseif (c <= -6e-135)
		tmp = t_0;
	elseif (c <= 7.2e-163)
		tmp = (1.0 / d) * (b + ((a * c) / d));
	elseif (c <= 8e+102)
		tmp = t_0;
	else
		tmp = (a + (b / (c / d))) / hypot(c, d);
	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, -1.1e+89], N[(N[(a / c), $MachinePrecision] + N[(d * N[(N[(b / c), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6e-135], t$95$0, If[LessEqual[c, 7.2e-163], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e+102], t$95$0, N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 82.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -2.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{-b}{\frac{c}{d}} - a}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -2.25e+86)
     (/ (- (/ (- b) (/ c d)) a) (hypot c d))
     (if (<= c -6e-135)
       t_0
       (if (<= c 7.2e-163)
         (* (/ 1.0 d) (+ b (/ (* a c) d)))
         (if (<= c 1.5e+102) t_0 (/ (+ a (/ b (/ c d))) (hypot c d))))))))

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 <= -2.25e+86) {
		tmp = ((-b / (c / d)) - a) / hypot(c, d);
	} else if (c <= -6e-135) {
		tmp = t_0;
	} else if (c <= 7.2e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 1.5e+102) {
		tmp = t_0;
	} else {
		tmp = (a + (b / (c / d))) / hypot(c, d);
	}
	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 <= -2.25e+86) {
		tmp = ((-b / (c / d)) - a) / Math.hypot(c, d);
	} else if (c <= -6e-135) {
		tmp = t_0;
	} else if (c <= 7.2e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 1.5e+102) {
		tmp = t_0;
	} else {
		tmp = (a + (b / (c / d))) / Math.hypot(c, d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -2.25e+86:
		tmp = ((-b / (c / d)) - a) / math.hypot(c, d)
	elif c <= -6e-135:
		tmp = t_0
	elif c <= 7.2e-163:
		tmp = (1.0 / d) * (b + ((a * c) / d))
	elif c <= 1.5e+102:
		tmp = t_0
	else:
		tmp = (a + (b / (c / d))) / math.hypot(c, d)
	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 <= -2.25e+86)
		tmp = Float64(Float64(Float64(Float64(-b) / Float64(c / d)) - a) / hypot(c, d));
	elseif (c <= -6e-135)
		tmp = t_0;
	elseif (c <= 7.2e-163)
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	elseif (c <= 1.5e+102)
		tmp = t_0;
	else
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / hypot(c, d));
	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 <= -2.25e+86)
		tmp = ((-b / (c / d)) - a) / hypot(c, d);
	elseif (c <= -6e-135)
		tmp = t_0;
	elseif (c <= 7.2e-163)
		tmp = (1.0 / d) * (b + ((a * c) / d));
	elseif (c <= 1.5e+102)
		tmp = t_0;
	else
		tmp = (a + (b / (c / d))) / hypot(c, d);
	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, -2.25e+86], N[(N[(N[((-b) / N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6e-135], t$95$0, If[LessEqual[c, 7.2e-163], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e+102], t$95$0, N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{a}{c} + d \cdot \frac{\frac{b}{c}}{c}\\ \mathbf{if}\;c \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-163}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (+ (/ a c) (* d (/ (/ b c) c)))))
   (if (<= c -2.3e+89)
     t_1
     (if (<= c -7.5e-135)
       t_0
       (if (<= c 6.8e-163)
         (* (/ 1.0 d) (+ b (/ (* a c) d)))
         (if (<= c 2.25e+101) 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 = (a / c) + (d * ((b / c) / c));
	double tmp;
	if (c <= -2.3e+89) {
		tmp = t_1;
	} else if (c <= -7.5e-135) {
		tmp = t_0;
	} else if (c <= 6.8e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 2.25e+101) {
		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 = (a / c) + (d * ((b / c) / c))
    if (c <= (-2.3d+89)) then
        tmp = t_1
    else if (c <= (-7.5d-135)) then
        tmp = t_0
    else if (c <= 6.8d-163) then
        tmp = (1.0d0 / d) * (b + ((a * c) / d))
    else if (c <= 2.25d+101) 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 = (a / c) + (d * ((b / c) / c));
	double tmp;
	if (c <= -2.3e+89) {
		tmp = t_1;
	} else if (c <= -7.5e-135) {
		tmp = t_0;
	} else if (c <= 6.8e-163) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else if (c <= 2.25e+101) {
		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 = (a / c) + (d * ((b / c) / c))
	tmp = 0
	if c <= -2.3e+89:
		tmp = t_1
	elif c <= -7.5e-135:
		tmp = t_0
	elif c <= 6.8e-163:
		tmp = (1.0 / d) * (b + ((a * c) / d))
	elif c <= 2.25e+101:
		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(a / c) + Float64(d * Float64(Float64(b / c) / c)))
	tmp = 0.0
	if (c <= -2.3e+89)
		tmp = t_1;
	elseif (c <= -7.5e-135)
		tmp = t_0;
	elseif (c <= 6.8e-163)
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	elseif (c <= 2.25e+101)
		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 = (a / c) + (d * ((b / c) / c));
	tmp = 0.0;
	if (c <= -2.3e+89)
		tmp = t_1;
	elseif (c <= -7.5e-135)
		tmp = t_0;
	elseif (c <= 6.8e-163)
		tmp = (1.0 / d) * (b + ((a * c) / d));
	elseif (c <= 2.25e+101)
		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[(a / c), $MachinePrecision] + N[(d * N[(N[(b / c), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.3e+89], t$95$1, If[LessEqual[c, -7.5e-135], t$95$0, If[LessEqual[c, 6.8e-163], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.25e+101], t$95$0, t$95$1]]]]]]

Derivation

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

Alternative 7: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+23} \lor \neg \left(c \leq 1.6 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -1.8e+23) (not (<= c 1.6e-33)))
   (/ a c)
   (* (/ 1.0 d) (+ b (/ (* a c) d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.8e+23) || !(c <= 1.6e-33)) {
		tmp = a / c;
	} else {
		tmp = (1.0 / d) * (b + ((a * 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 ((c <= (-1.8d+23)) .or. (.not. (c <= 1.6d-33))) then
        tmp = a / c
    else
        tmp = (1.0d0 / d) * (b + ((a * c) / d))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.8e+23) || !(c <= 1.6e-33)) {
		tmp = a / c;
	} else {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -1.8e+23) or not (c <= 1.6e-33):
		tmp = a / c
	else:
		tmp = (1.0 / d) * (b + ((a * c) / d))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -1.8e+23) || !(c <= 1.6e-33))
		tmp = Float64(a / c);
	else
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -1.8e+23) || ~((c <= 1.6e-33)))
		tmp = a / c;
	else
		tmp = (1.0 / d) * (b + ((a * c) / d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -1.8e+23], N[Not[LessEqual[c, 1.6e-33]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{-5} \lor \neg \left(c \leq 1.6 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{a}{c} + d \cdot \frac{\frac{b}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -1.6e-5) (not (<= c 1.6e-33)))
   (+ (/ a c) (* d (/ (/ b c) c)))
   (* (/ 1.0 d) (+ b (/ (* a c) d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.6e-5) || !(c <= 1.6e-33)) {
		tmp = (a / c) + (d * ((b / c) / c));
	} else {
		tmp = (1.0 / d) * (b + ((a * 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 ((c <= (-1.6d-5)) .or. (.not. (c <= 1.6d-33))) then
        tmp = (a / c) + (d * ((b / c) / c))
    else
        tmp = (1.0d0 / d) * (b + ((a * c) / d))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.6e-5) || !(c <= 1.6e-33)) {
		tmp = (a / c) + (d * ((b / c) / c));
	} else {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -1.6e-5) or not (c <= 1.6e-33):
		tmp = (a / c) + (d * ((b / c) / c))
	else:
		tmp = (1.0 / d) * (b + ((a * c) / d))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -1.6e-5) || !(c <= 1.6e-33))
		tmp = Float64(Float64(a / c) + Float64(d * Float64(Float64(b / c) / c)));
	else
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -1.6e-5) || ~((c <= 1.6e-33)))
		tmp = (a / c) + (d * ((b / c) / c));
	else
		tmp = (1.0 / d) * (b + ((a * c) / d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -1.6e-5], N[Not[LessEqual[c, 1.6e-33]], $MachinePrecision]], N[(N[(a / c), $MachinePrecision] + N[(d * N[(N[(b / c), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{-5}:\\ \;\;\;\;\frac{a}{c} + d \cdot \frac{\frac{b}{c}}{c}\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a \cdot c}{d}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} + \frac{\frac{b \cdot d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -7e-5)
   (+ (/ a c) (* d (/ (/ b c) c)))
   (if (<= c 9.2e-88)
     (* (/ 1.0 d) (+ b (/ (* a c) d)))
     (+ (/ a c) (/ (/ (* b d) c) c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -7e-5) {
		tmp = (a / c) + (d * ((b / c) / c));
	} else if (c <= 9.2e-88) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else {
		tmp = (a / c) + (((b * d) / c) / c);
	}
	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 <= (-7d-5)) then
        tmp = (a / c) + (d * ((b / c) / c))
    else if (c <= 9.2d-88) then
        tmp = (1.0d0 / d) * (b + ((a * c) / d))
    else
        tmp = (a / c) + (((b * d) / c) / c)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -7e-5) {
		tmp = (a / c) + (d * ((b / c) / c));
	} else if (c <= 9.2e-88) {
		tmp = (1.0 / d) * (b + ((a * c) / d));
	} else {
		tmp = (a / c) + (((b * d) / c) / c);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -7e-5:
		tmp = (a / c) + (d * ((b / c) / c))
	elif c <= 9.2e-88:
		tmp = (1.0 / d) * (b + ((a * c) / d))
	else:
		tmp = (a / c) + (((b * d) / c) / c)
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -7e-5)
		tmp = Float64(Float64(a / c) + Float64(d * Float64(Float64(b / c) / c)));
	elseif (c <= 9.2e-88)
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(Float64(a * c) / d)));
	else
		tmp = Float64(Float64(a / c) + Float64(Float64(Float64(b * d) / c) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -7e-5)
		tmp = (a / c) + (d * ((b / c) / c));
	elseif (c <= 9.2e-88)
		tmp = (1.0 / d) * (b + ((a * c) / d));
	else
		tmp = (a / c) + (((b * d) / c) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -7e-5], N[(N[(a / c), $MachinePrecision] + N[(d * N[(N[(b / c), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e-88], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] + N[(N[(N[(b * d), $MachinePrecision] / c), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 10: 63.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{-15} \lor \neg \left(c \leq 5.2 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.8e-15) (not (<= c 5.2e-34))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.8e-15) || !(c <= 5.2e-34)) {
		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 <= (-2.8d-15)) .or. (.not. (c <= 5.2d-34))) 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 <= -2.8e-15) || !(c <= 5.2e-34)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.8e-15) or not (c <= 5.2e-34):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.8e-15) || !(c <= 5.2e-34))
		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 <= -2.8e-15) || ~((c <= 5.2e-34)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.8e-15], N[Not[LessEqual[c, 5.2e-34]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

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

Alternative 11: 43.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq 3 \cdot 10^{+160}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (if (<= d 3e+160) (/ a c) (/ a d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= 3e+160) {
		tmp = a / c;
	} else {
		tmp = a / 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 (d <= 3d+160) then
        tmp = a / c
    else
        tmp = a / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= 3e+160) {
		tmp = a / c;
	} else {
		tmp = a / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= 3e+160:
		tmp = a / c
	else:
		tmp = a / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= 3e+160)
		tmp = Float64(a / c);
	else
		tmp = Float64(a / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= 3e+160)
		tmp = a / c;
	else
		tmp = a / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, 3e+160], N[(a / c), $MachinePrecision], N[(a / d), $MachinePrecision]]

Derivation

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

Alternative 12: 43.2% 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: 99.3% 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 2024006 
(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))))