Complex division, real part

Percentage Accurate: 62.3% → 85.4%

Time: 10.5s

Alternatives: 11

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: 62.3% 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: 85.4% accurate, 0.0× speedup

Math

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

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))
   (* (/ 1.0 d) (+ b (/ a (/ d c))))))

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 = (1.0 / d) * (b + (a / (d / c)));
	}
	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(1.0 / d) * Float64(b + Float64(a / Float64(d / c))));
	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[(1.0 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 82.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{c}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-128}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-105}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(a, c, b \cdot d\right) \cdot {\left(\frac{1}{\mathsf{hypot}\left(c, d\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -7.2e+109)
   (* (/ c (hypot c d)) (/ a (hypot c d)))
   (if (<= c -6.8e-128)
     (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
     (if (<= c 2.6e-105)
       (+ (/ b d) (/ (/ (* a c) d) d))
       (if (<= c 5.8e+91)
         (* (fma a c (* b d)) (pow (/ 1.0 (hypot c d)) 2.0))
         (/ (+ a (/ b (/ c d))) (hypot c d)))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -7.2e+109) {
		tmp = (c / hypot(c, d)) * (a / hypot(c, d));
	} else if (c <= -6.8e-128) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 2.6e-105) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else if (c <= 5.8e+91) {
		tmp = fma(a, c, (b * d)) * pow((1.0 / hypot(c, d)), 2.0);
	} else {
		tmp = (a + (b / (c / d))) / hypot(c, d);
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -7.2e+109)
		tmp = Float64(Float64(c / hypot(c, d)) * Float64(a / hypot(c, d)));
	elseif (c <= -6.8e-128)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 2.6e-105)
		tmp = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d));
	elseif (c <= 5.8e+91)
		tmp = Float64(fma(a, c, Float64(b * d)) * (Float64(1.0 / hypot(c, d)) ^ 2.0));
	else
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / hypot(c, d));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -7.2e+109], N[(N[(c / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.8e-128], 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, 2.6e-105], N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+91], N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] * N[Power[N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], 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 3: 81.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{+109}:\\ \;\;\;\;\frac{c}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 2.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -1.9e+109)
     (* (/ c (hypot c d)) (/ a (hypot c d)))
     (if (<= c -1.5e-127)
       t_0
       (if (<= c 2.75e-100)
         (+ (/ b d) (/ (/ (* a c) d) d))
         (if (<= c 1.05e+92) 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 <= -1.9e+109) {
		tmp = (c / hypot(c, d)) * (a / hypot(c, d));
	} else if (c <= -1.5e-127) {
		tmp = t_0;
	} else if (c <= 2.75e-100) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else if (c <= 1.05e+92) {
		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 <= -1.9e+109) {
		tmp = (c / Math.hypot(c, d)) * (a / Math.hypot(c, d));
	} else if (c <= -1.5e-127) {
		tmp = t_0;
	} else if (c <= 2.75e-100) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else if (c <= 1.05e+92) {
		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 <= -1.9e+109:
		tmp = (c / math.hypot(c, d)) * (a / math.hypot(c, d))
	elif c <= -1.5e-127:
		tmp = t_0
	elif c <= 2.75e-100:
		tmp = (b / d) + (((a * c) / d) / d)
	elif c <= 1.05e+92:
		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 <= -1.9e+109)
		tmp = Float64(Float64(c / hypot(c, d)) * Float64(a / hypot(c, d)));
	elseif (c <= -1.5e-127)
		tmp = t_0;
	elseif (c <= 2.75e-100)
		tmp = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d));
	elseif (c <= 1.05e+92)
		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 <= -1.9e+109)
		tmp = (c / hypot(c, d)) * (a / hypot(c, d));
	elseif (c <= -1.5e-127)
		tmp = t_0;
	elseif (c <= 2.75e-100)
		tmp = (b / d) + (((a * c) / d) / d);
	elseif (c <= 1.05e+92)
		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, -1.9e+109], N[(N[(c / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.5e-127], t$95$0, If[LessEqual[c, 2.75e-100], N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e+92], 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 4: 81.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -1.25 \cdot 10^{+99}:\\ \;\;\;\;\frac{a}{c} + d \cdot \frac{b}{{c}^{2}}\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-128}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{-102}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -1.25e+99)
     (+ (/ a c) (* d (/ b (pow c 2.0))))
     (if (<= c -2.5e-128)
       t_0
       (if (<= c 8.6e-102)
         (+ (/ b d) (/ (/ (* a c) d) d))
         (if (<= c 2.5e+85) 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 <= -1.25e+99) {
		tmp = (a / c) + (d * (b / pow(c, 2.0)));
	} else if (c <= -2.5e-128) {
		tmp = t_0;
	} else if (c <= 8.6e-102) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else if (c <= 2.5e+85) {
		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 <= -1.25e+99) {
		tmp = (a / c) + (d * (b / Math.pow(c, 2.0)));
	} else if (c <= -2.5e-128) {
		tmp = t_0;
	} else if (c <= 8.6e-102) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else if (c <= 2.5e+85) {
		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 <= -1.25e+99:
		tmp = (a / c) + (d * (b / math.pow(c, 2.0)))
	elif c <= -2.5e-128:
		tmp = t_0
	elif c <= 8.6e-102:
		tmp = (b / d) + (((a * c) / d) / d)
	elif c <= 2.5e+85:
		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 <= -1.25e+99)
		tmp = Float64(Float64(a / c) + Float64(d * Float64(b / (c ^ 2.0))));
	elseif (c <= -2.5e-128)
		tmp = t_0;
	elseif (c <= 8.6e-102)
		tmp = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d));
	elseif (c <= 2.5e+85)
		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 <= -1.25e+99)
		tmp = (a / c) + (d * (b / (c ^ 2.0)));
	elseif (c <= -2.5e-128)
		tmp = t_0;
	elseif (c <= 8.6e-102)
		tmp = (b / d) + (((a * c) / d) / d);
	elseif (c <= 2.5e+85)
		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, -1.25e+99], N[(N[(a / c), $MachinePrecision] + N[(d * N[(b / N[Power[c, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.5e-128], t$95$0, If[LessEqual[c, 8.6e-102], N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+85], 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: 83.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{b}{\frac{c}{d}}\\ \mathbf{if}\;c \leq -1.36 \cdot 10^{+109}:\\ \;\;\;\;\frac{\left(-a\right) - t_1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{-129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-101}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a + t_1}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))) (t_1 (/ b (/ c d))))
   (if (<= c -1.36e+109)
     (/ (- (- a) t_1) (hypot c d))
     (if (<= c -5.1e-129)
       t_0
       (if (<= c 2e-101)
         (+ (/ b d) (/ (/ (* a c) d) d))
         (if (<= c 4.2e+91) t_0 (/ (+ a t_1) (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 t_1 = b / (c / d);
	double tmp;
	if (c <= -1.36e+109) {
		tmp = (-a - t_1) / hypot(c, d);
	} else if (c <= -5.1e-129) {
		tmp = t_0;
	} else if (c <= 2e-101) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else if (c <= 4.2e+91) {
		tmp = t_0;
	} else {
		tmp = (a + t_1) / 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 t_1 = b / (c / d);
	double tmp;
	if (c <= -1.36e+109) {
		tmp = (-a - t_1) / Math.hypot(c, d);
	} else if (c <= -5.1e-129) {
		tmp = t_0;
	} else if (c <= 2e-101) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else if (c <= 4.2e+91) {
		tmp = t_0;
	} else {
		tmp = (a + t_1) / Math.hypot(c, d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	t_1 = b / (c / d)
	tmp = 0
	if c <= -1.36e+109:
		tmp = (-a - t_1) / math.hypot(c, d)
	elif c <= -5.1e-129:
		tmp = t_0
	elif c <= 2e-101:
		tmp = (b / d) + (((a * c) / d) / d)
	elif c <= 4.2e+91:
		tmp = t_0
	else:
		tmp = (a + t_1) / 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)))
	t_1 = Float64(b / Float64(c / d))
	tmp = 0.0
	if (c <= -1.36e+109)
		tmp = Float64(Float64(Float64(-a) - t_1) / hypot(c, d));
	elseif (c <= -5.1e-129)
		tmp = t_0;
	elseif (c <= 2e-101)
		tmp = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d));
	elseif (c <= 4.2e+91)
		tmp = t_0;
	else
		tmp = Float64(Float64(a + t_1) / 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));
	t_1 = b / (c / d);
	tmp = 0.0;
	if (c <= -1.36e+109)
		tmp = (-a - t_1) / hypot(c, d);
	elseif (c <= -5.1e-129)
		tmp = t_0;
	elseif (c <= 2e-101)
		tmp = (b / d) + (((a * c) / d) / d);
	elseif (c <= 4.2e+91)
		tmp = t_0;
	else
		tmp = (a + t_1) / 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]}, Block[{t$95$1 = N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.36e+109], N[(N[((-a) - t$95$1), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.1e-129], t$95$0, If[LessEqual[c, 2e-101], N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e+91], t$95$0, N[(N[(a + t$95$1), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 6: 78.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \mathbf{if}\;d \leq -1.25 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -1.28 \cdot 10^{-202}:\\ \;\;\;\;\frac{a}{c} + d \cdot \frac{b}{{c}^{2}}\\ \mathbf{elif}\;d \leq -6.5 \cdot 10^{-225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 8 \cdot 10^{-136}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq 2.8 \cdot 10^{+96}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (* (/ 1.0 d) (+ b (/ a (/ d c))))))
   (if (<= d -1.25e+153)
     t_1
     (if (<= d -6.2e-147)
       t_0
       (if (<= d -1.28e-202)
         (+ (/ a c) (* d (/ b (pow c 2.0))))
         (if (<= d -6.5e-225)
           t_0
           (if (<= d 8e-136) (/ a c) (if (<= d 2.8e+96) 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 / d) * (b + (a / (d / c)));
	double tmp;
	if (d <= -1.25e+153) {
		tmp = t_1;
	} else if (d <= -6.2e-147) {
		tmp = t_0;
	} else if (d <= -1.28e-202) {
		tmp = (a / c) + (d * (b / pow(c, 2.0)));
	} else if (d <= -6.5e-225) {
		tmp = t_0;
	} else if (d <= 8e-136) {
		tmp = a / c;
	} else if (d <= 2.8e+96) {
		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 / d) * (b + (a / (d / c)))
    if (d <= (-1.25d+153)) then
        tmp = t_1
    else if (d <= (-6.2d-147)) then
        tmp = t_0
    else if (d <= (-1.28d-202)) then
        tmp = (a / c) + (d * (b / (c ** 2.0d0)))
    else if (d <= (-6.5d-225)) then
        tmp = t_0
    else if (d <= 8d-136) then
        tmp = a / c
    else if (d <= 2.8d+96) 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 / d) * (b + (a / (d / c)));
	double tmp;
	if (d <= -1.25e+153) {
		tmp = t_1;
	} else if (d <= -6.2e-147) {
		tmp = t_0;
	} else if (d <= -1.28e-202) {
		tmp = (a / c) + (d * (b / Math.pow(c, 2.0)));
	} else if (d <= -6.5e-225) {
		tmp = t_0;
	} else if (d <= 8e-136) {
		tmp = a / c;
	} else if (d <= 2.8e+96) {
		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 / d) * (b + (a / (d / c)))
	tmp = 0
	if d <= -1.25e+153:
		tmp = t_1
	elif d <= -6.2e-147:
		tmp = t_0
	elif d <= -1.28e-202:
		tmp = (a / c) + (d * (b / math.pow(c, 2.0)))
	elif d <= -6.5e-225:
		tmp = t_0
	elif d <= 8e-136:
		tmp = a / c
	elif d <= 2.8e+96:
		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 / d) * Float64(b + Float64(a / Float64(d / c))))
	tmp = 0.0
	if (d <= -1.25e+153)
		tmp = t_1;
	elseif (d <= -6.2e-147)
		tmp = t_0;
	elseif (d <= -1.28e-202)
		tmp = Float64(Float64(a / c) + Float64(d * Float64(b / (c ^ 2.0))));
	elseif (d <= -6.5e-225)
		tmp = t_0;
	elseif (d <= 8e-136)
		tmp = Float64(a / c);
	elseif (d <= 2.8e+96)
		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 / d) * (b + (a / (d / c)));
	tmp = 0.0;
	if (d <= -1.25e+153)
		tmp = t_1;
	elseif (d <= -6.2e-147)
		tmp = t_0;
	elseif (d <= -1.28e-202)
		tmp = (a / c) + (d * (b / (c ^ 2.0)));
	elseif (d <= -6.5e-225)
		tmp = t_0;
	elseif (d <= 8e-136)
		tmp = a / c;
	elseif (d <= 2.8e+96)
		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 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.25e+153], t$95$1, If[LessEqual[d, -6.2e-147], t$95$0, If[LessEqual[d, -1.28e-202], N[(N[(a / c), $MachinePrecision] + N[(d * N[(b / N[Power[c, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -6.5e-225], t$95$0, If[LessEqual[d, 8e-136], N[(a / c), $MachinePrecision], If[LessEqual[d, 2.8e+96], t$95$0, t$95$1]]]]]]]]

Derivation

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

Alternative 7: 79.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \mathbf{if}\;d \leq -1.25 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -5.5 \cdot 10^{-159}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 2.15 \cdot 10^{-222}:\\ \;\;\;\;\frac{a}{c} + \frac{b}{\frac{{c}^{2}}{d}}\\ \mathbf{elif}\;d \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (* (/ 1.0 d) (+ b (/ a (/ d c))))))
   (if (<= d -1.25e+153)
     t_1
     (if (<= d -5.5e-159)
       t_0
       (if (<= d 2.15e-222)
         (+ (/ a c) (/ b (/ (pow c 2.0) d)))
         (if (<= d 1.55e+100) 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 / d) * (b + (a / (d / c)));
	double tmp;
	if (d <= -1.25e+153) {
		tmp = t_1;
	} else if (d <= -5.5e-159) {
		tmp = t_0;
	} else if (d <= 2.15e-222) {
		tmp = (a / c) + (b / (pow(c, 2.0) / d));
	} else if (d <= 1.55e+100) {
		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 / d) * (b + (a / (d / c)))
    if (d <= (-1.25d+153)) then
        tmp = t_1
    else if (d <= (-5.5d-159)) then
        tmp = t_0
    else if (d <= 2.15d-222) then
        tmp = (a / c) + (b / ((c ** 2.0d0) / d))
    else if (d <= 1.55d+100) 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 / d) * (b + (a / (d / c)));
	double tmp;
	if (d <= -1.25e+153) {
		tmp = t_1;
	} else if (d <= -5.5e-159) {
		tmp = t_0;
	} else if (d <= 2.15e-222) {
		tmp = (a / c) + (b / (Math.pow(c, 2.0) / d));
	} else if (d <= 1.55e+100) {
		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 / d) * (b + (a / (d / c)))
	tmp = 0
	if d <= -1.25e+153:
		tmp = t_1
	elif d <= -5.5e-159:
		tmp = t_0
	elif d <= 2.15e-222:
		tmp = (a / c) + (b / (math.pow(c, 2.0) / d))
	elif d <= 1.55e+100:
		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 / d) * Float64(b + Float64(a / Float64(d / c))))
	tmp = 0.0
	if (d <= -1.25e+153)
		tmp = t_1;
	elseif (d <= -5.5e-159)
		tmp = t_0;
	elseif (d <= 2.15e-222)
		tmp = Float64(Float64(a / c) + Float64(b / Float64((c ^ 2.0) / d)));
	elseif (d <= 1.55e+100)
		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 / d) * (b + (a / (d / c)));
	tmp = 0.0;
	if (d <= -1.25e+153)
		tmp = t_1;
	elseif (d <= -5.5e-159)
		tmp = t_0;
	elseif (d <= 2.15e-222)
		tmp = (a / c) + (b / ((c ^ 2.0) / d));
	elseif (d <= 1.55e+100)
		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 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.25e+153], t$95$1, If[LessEqual[d, -5.5e-159], t$95$0, If[LessEqual[d, 2.15e-222], N[(N[(a / c), $MachinePrecision] + N[(b / N[(N[Power[c, 2.0], $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 1.55e+100], t$95$0, t$95$1]]]]]]

Derivation

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

Alternative 8: 78.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \mathbf{if}\;d \leq -1.25 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -9.5 \cdot 10^{-161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-136}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq 1.8 \cdot 10^{+103}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (* (/ 1.0 d) (+ b (/ a (/ d c))))))
   (if (<= d -1.25e+153)
     t_1
     (if (<= d -9.5e-161)
       t_0
       (if (<= d 6e-136) (/ a c) (if (<= d 1.8e+103) 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 / d) * (b + (a / (d / c)));
	double tmp;
	if (d <= -1.25e+153) {
		tmp = t_1;
	} else if (d <= -9.5e-161) {
		tmp = t_0;
	} else if (d <= 6e-136) {
		tmp = a / c;
	} else if (d <= 1.8e+103) {
		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 / d) * (b + (a / (d / c)))
    if (d <= (-1.25d+153)) then
        tmp = t_1
    else if (d <= (-9.5d-161)) then
        tmp = t_0
    else if (d <= 6d-136) then
        tmp = a / c
    else if (d <= 1.8d+103) 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 / d) * (b + (a / (d / c)));
	double tmp;
	if (d <= -1.25e+153) {
		tmp = t_1;
	} else if (d <= -9.5e-161) {
		tmp = t_0;
	} else if (d <= 6e-136) {
		tmp = a / c;
	} else if (d <= 1.8e+103) {
		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 / d) * (b + (a / (d / c)))
	tmp = 0
	if d <= -1.25e+153:
		tmp = t_1
	elif d <= -9.5e-161:
		tmp = t_0
	elif d <= 6e-136:
		tmp = a / c
	elif d <= 1.8e+103:
		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 / d) * Float64(b + Float64(a / Float64(d / c))))
	tmp = 0.0
	if (d <= -1.25e+153)
		tmp = t_1;
	elseif (d <= -9.5e-161)
		tmp = t_0;
	elseif (d <= 6e-136)
		tmp = Float64(a / c);
	elseif (d <= 1.8e+103)
		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 / d) * (b + (a / (d / c)));
	tmp = 0.0;
	if (d <= -1.25e+153)
		tmp = t_1;
	elseif (d <= -9.5e-161)
		tmp = t_0;
	elseif (d <= 6e-136)
		tmp = a / c;
	elseif (d <= 1.8e+103)
		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 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.25e+153], t$95$1, If[LessEqual[d, -9.5e-161], t$95$0, If[LessEqual[d, 6e-136], N[(a / c), $MachinePrecision], If[LessEqual[d, 1.8e+103], t$95$0, t$95$1]]]]]]

Derivation

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

Alternative 9: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+46} \lor \neg \left(c \leq 1.9 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -4e+46) (not (<= c 1.9e+93)))
   (/ a c)
   (* (/ 1.0 d) (+ b (/ a (/ d c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4e+46) || !(c <= 1.9e+93)) {
		tmp = a / c;
	} else {
		tmp = (1.0 / d) * (b + (a / (d / 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 <= (-4d+46)) .or. (.not. (c <= 1.9d+93))) then
        tmp = a / c
    else
        tmp = (1.0d0 / d) * (b + (a / (d / c)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4e+46) || !(c <= 1.9e+93)) {
		tmp = a / c;
	} else {
		tmp = (1.0 / d) * (b + (a / (d / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -4e+46) or not (c <= 1.9e+93):
		tmp = a / c
	else:
		tmp = (1.0 / d) * (b + (a / (d / c)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -4e+46) || !(c <= 1.9e+93))
		tmp = Float64(a / c);
	else
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(a / Float64(d / c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -4e+46) || ~((c <= 1.9e+93)))
		tmp = a / c;
	else
		tmp = (1.0 / d) * (b + (a / (d / c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -4e+46], N[Not[LessEqual[c, 1.9e+93]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 63.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+46} \lor \neg \left(c \leq 2.3 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.15e+46) (not (<= c 2.3e+85))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.15e+46) || !(c <= 2.3e+85)) {
		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 <= (-2.15d+46)) .or. (.not. (c <= 2.3d+85))) 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 <= -2.15e+46) || !(c <= 2.3e+85)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.15e+46) or not (c <= 2.3e+85):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.15e+46) || !(c <= 2.3e+85))
		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 <= -2.15e+46) || ~((c <= 2.3e+85)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.15e+46], N[Not[LessEqual[c, 2.3e+85]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

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

Alternative 11: 42.5% 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 2024008 
(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))))