Complex division, real part

Percentage Accurate: 61.2% → 84.5%

Time: 13.4s

Alternatives: 12

Speedup: 1.1×

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

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

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) INFINITY)
   (/ (/ (fma b d (* a c)) (hypot c d)) (hypot c d))
   (* (/ c (hypot d c)) (/ a (hypot 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(b, d, (a * c)) / hypot(c, d)) / hypot(c, d);
	} else {
		tmp = (c / hypot(d, c)) * (a / hypot(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(b, d, Float64(a * c)) / hypot(c, d)) / hypot(c, d));
	else
		tmp = Float64(Float64(c / hypot(d, c)) * Float64(a / hypot(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[(b * d + N[(a * c), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], N[(N[(c / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 84.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot c + b \cdot d\\ \mathbf{if}\;\frac{t_0}{c \cdot c + d \cdot d} \leq \infty:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{t_0}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (+ (* a c) (* b d))))
   (if (<= (/ t_0 (+ (* c c) (* d d))) INFINITY)
     (* (/ 1.0 (hypot c d)) (/ t_0 (hypot c d)))
     (* (/ c (hypot d c)) (/ a (hypot d c))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a * c) + (b * d);
	double tmp;
	if ((t_0 / ((c * c) + (d * d))) <= ((double) INFINITY)) {
		tmp = (1.0 / hypot(c, d)) * (t_0 / hypot(c, d));
	} else {
		tmp = (c / hypot(d, c)) * (a / hypot(d, c));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (a * c) + (b * d);
	double tmp;
	if ((t_0 / ((c * c) + (d * d))) <= Double.POSITIVE_INFINITY) {
		tmp = (1.0 / Math.hypot(c, d)) * (t_0 / Math.hypot(c, d));
	} else {
		tmp = (c / Math.hypot(d, c)) * (a / Math.hypot(d, c));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a * c) + (b * d)
	tmp = 0
	if (t_0 / ((c * c) + (d * d))) <= math.inf:
		tmp = (1.0 / math.hypot(c, d)) * (t_0 / math.hypot(c, d))
	else:
		tmp = (c / math.hypot(d, c)) * (a / math.hypot(d, c))
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a * c) + Float64(b * d))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(c * c) + Float64(d * d))) <= Inf)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(t_0 / hypot(c, d)));
	else
		tmp = Float64(Float64(c / hypot(d, c)) * Float64(a / hypot(d, c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a * c) + (b * d);
	tmp = 0.0;
	if ((t_0 / ((c * c) + (d * d))) <= Inf)
		tmp = (1.0 / hypot(c, d)) * (t_0 / hypot(c, d));
	else
		tmp = (c / hypot(d, c)) * (a / hypot(d, c));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 3: 80.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{+88}:\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{b}{d} + \frac{a}{d \cdot \frac{d}{c}}\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -4.5e+88)
     (* (+ a (/ b (/ c d))) (/ -1.0 (hypot c d)))
     (if (<= c -3.6e-217)
       t_0
       (if (<= c 1.5e-193)
         (+ (/ b d) (/ a (* d (/ d c))))
         (if (<= c 2.7e+68) t_0 (* (/ c (hypot d c)) (/ a (hypot 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 <= -4.5e+88) {
		tmp = (a + (b / (c / d))) * (-1.0 / hypot(c, d));
	} else if (c <= -3.6e-217) {
		tmp = t_0;
	} else if (c <= 1.5e-193) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 2.7e+68) {
		tmp = t_0;
	} else {
		tmp = (c / hypot(d, c)) * (a / hypot(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 <= -4.5e+88) {
		tmp = (a + (b / (c / d))) * (-1.0 / Math.hypot(c, d));
	} else if (c <= -3.6e-217) {
		tmp = t_0;
	} else if (c <= 1.5e-193) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 2.7e+68) {
		tmp = t_0;
	} else {
		tmp = (c / Math.hypot(d, c)) * (a / Math.hypot(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 <= -4.5e+88:
		tmp = (a + (b / (c / d))) * (-1.0 / math.hypot(c, d))
	elif c <= -3.6e-217:
		tmp = t_0
	elif c <= 1.5e-193:
		tmp = (b / d) + (a / (d * (d / c)))
	elif c <= 2.7e+68:
		tmp = t_0
	else:
		tmp = (c / math.hypot(d, c)) * (a / math.hypot(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 <= -4.5e+88)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) * Float64(-1.0 / hypot(c, d)));
	elseif (c <= -3.6e-217)
		tmp = t_0;
	elseif (c <= 1.5e-193)
		tmp = Float64(Float64(b / d) + Float64(a / Float64(d * Float64(d / c))));
	elseif (c <= 2.7e+68)
		tmp = t_0;
	else
		tmp = Float64(Float64(c / hypot(d, c)) * Float64(a / hypot(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 <= -4.5e+88)
		tmp = (a + (b / (c / d))) * (-1.0 / hypot(c, d));
	elseif (c <= -3.6e-217)
		tmp = t_0;
	elseif (c <= 1.5e-193)
		tmp = (b / d) + (a / (d * (d / c)));
	elseif (c <= 2.7e+68)
		tmp = t_0;
	else
		tmp = (c / hypot(d, c)) * (a / hypot(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, -4.5e+88], 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, -3.6e-217], t$95$0, If[LessEqual[c, 1.5e-193], N[(N[(b / d), $MachinePrecision] + N[(a / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e+68], t$95$0, N[(N[(c / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 80.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{+88}:\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{--1}{c}\\ \mathbf{elif}\;c \leq -2.65 \cdot 10^{-216}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-193}:\\ \;\;\;\;\frac{b}{d} + \frac{a}{d \cdot \frac{d}{c}}\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + d \cdot \frac{b}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -2.2e+88)
     (* (+ a (/ b (/ c d))) (/ (- -1.0) c))
     (if (<= c -2.65e-216)
       t_0
       (if (<= c 2.9e-193)
         (+ (/ b d) (/ a (* d (/ d c))))
         (if (<= c 2.7e+102)
           t_0
           (* (/ 1.0 (hypot c d)) (+ a (* d (/ b 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 <= -2.2e+88) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else if (c <= -2.65e-216) {
		tmp = t_0;
	} else if (c <= 2.9e-193) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 2.7e+102) {
		tmp = t_0;
	} else {
		tmp = (1.0 / hypot(c, d)) * (a + (d * (b / 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 <= -2.2e+88) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else if (c <= -2.65e-216) {
		tmp = t_0;
	} else if (c <= 2.9e-193) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 2.7e+102) {
		tmp = t_0;
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * (a + (d * (b / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -2.2e+88:
		tmp = (a + (b / (c / d))) * (-(-1.0) / c)
	elif c <= -2.65e-216:
		tmp = t_0
	elif c <= 2.9e-193:
		tmp = (b / d) + (a / (d * (d / c)))
	elif c <= 2.7e+102:
		tmp = t_0
	else:
		tmp = (1.0 / math.hypot(c, d)) * (a + (d * (b / 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 <= -2.2e+88)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) * Float64(Float64(-(-1.0)) / c));
	elseif (c <= -2.65e-216)
		tmp = t_0;
	elseif (c <= 2.9e-193)
		tmp = Float64(Float64(b / d) + Float64(a / Float64(d * Float64(d / c))));
	elseif (c <= 2.7e+102)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(a + Float64(d * Float64(b / 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 <= -2.2e+88)
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	elseif (c <= -2.65e-216)
		tmp = t_0;
	elseif (c <= 2.9e-193)
		tmp = (b / d) + (a / (d * (d / c)));
	elseif (c <= 2.7e+102)
		tmp = t_0;
	else
		tmp = (1.0 / hypot(c, d)) * (a + (d * (b / 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, -2.2e+88], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[((--1.0) / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.65e-216], t$95$0, If[LessEqual[c, 2.9e-193], N[(N[(b / d), $MachinePrecision] + N[(a / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e+102], t$95$0, N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 81.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := a + d \cdot \frac{b}{c}\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+87}:\\ \;\;\;\;t_1 \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-214}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{b}{d} + \frac{a}{d \cdot \frac{d}{c}}\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (+ a (* d (/ b c)))))
   (if (<= c -1.3e+87)
     (* t_1 (/ -1.0 (hypot c d)))
     (if (<= c -2.6e-214)
       t_0
       (if (<= c 3.2e-194)
         (+ (/ b d) (/ a (* d (/ d c))))
         (if (<= c 4.9e+101) 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 + (d * (b / c));
	double tmp;
	if (c <= -1.3e+87) {
		tmp = t_1 * (-1.0 / hypot(c, d));
	} else if (c <= -2.6e-214) {
		tmp = t_0;
	} else if (c <= 3.2e-194) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 4.9e+101) {
		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 + (d * (b / c));
	double tmp;
	if (c <= -1.3e+87) {
		tmp = t_1 * (-1.0 / Math.hypot(c, d));
	} else if (c <= -2.6e-214) {
		tmp = t_0;
	} else if (c <= 3.2e-194) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 4.9e+101) {
		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 + (d * (b / c))
	tmp = 0
	if c <= -1.3e+87:
		tmp = t_1 * (-1.0 / math.hypot(c, d))
	elif c <= -2.6e-214:
		tmp = t_0
	elif c <= 3.2e-194:
		tmp = (b / d) + (a / (d * (d / c)))
	elif c <= 4.9e+101:
		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(d * Float64(b / c)))
	tmp = 0.0
	if (c <= -1.3e+87)
		tmp = Float64(t_1 * Float64(-1.0 / hypot(c, d)));
	elseif (c <= -2.6e-214)
		tmp = t_0;
	elseif (c <= 3.2e-194)
		tmp = Float64(Float64(b / d) + Float64(a / Float64(d * Float64(d / c))));
	elseif (c <= 4.9e+101)
		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 + (d * (b / c));
	tmp = 0.0;
	if (c <= -1.3e+87)
		tmp = t_1 * (-1.0 / hypot(c, d));
	elseif (c <= -2.6e-214)
		tmp = t_0;
	elseif (c <= 3.2e-194)
		tmp = (b / d) + (a / (d * (d / c)));
	elseif (c <= 4.9e+101)
		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[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e+87], N[(t$95$1 * N[(-1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.6e-214], t$95$0, If[LessEqual[c, 3.2e-194], N[(N[(b / d), $MachinePrecision] + N[(a / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.9e+101], 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 6: 81.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -2.4 \cdot 10^{+88}:\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-214}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{b}{d} + \frac{a}{d \cdot \frac{d}{c}}\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + d \cdot \frac{b}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -2.4e+88)
     (* (+ a (/ b (/ c d))) (/ -1.0 (hypot c d)))
     (if (<= c -1.5e-214)
       t_0
       (if (<= c 2.4e-193)
         (+ (/ b d) (/ a (* d (/ d c))))
         (if (<= c 5e+101)
           t_0
           (* (/ 1.0 (hypot c d)) (+ a (* d (/ b 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 <= -2.4e+88) {
		tmp = (a + (b / (c / d))) * (-1.0 / hypot(c, d));
	} else if (c <= -1.5e-214) {
		tmp = t_0;
	} else if (c <= 2.4e-193) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 5e+101) {
		tmp = t_0;
	} else {
		tmp = (1.0 / hypot(c, d)) * (a + (d * (b / 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 <= -2.4e+88) {
		tmp = (a + (b / (c / d))) * (-1.0 / Math.hypot(c, d));
	} else if (c <= -1.5e-214) {
		tmp = t_0;
	} else if (c <= 2.4e-193) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 5e+101) {
		tmp = t_0;
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * (a + (d * (b / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -2.4e+88:
		tmp = (a + (b / (c / d))) * (-1.0 / math.hypot(c, d))
	elif c <= -1.5e-214:
		tmp = t_0
	elif c <= 2.4e-193:
		tmp = (b / d) + (a / (d * (d / c)))
	elif c <= 5e+101:
		tmp = t_0
	else:
		tmp = (1.0 / math.hypot(c, d)) * (a + (d * (b / 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 <= -2.4e+88)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) * Float64(-1.0 / hypot(c, d)));
	elseif (c <= -1.5e-214)
		tmp = t_0;
	elseif (c <= 2.4e-193)
		tmp = Float64(Float64(b / d) + Float64(a / Float64(d * Float64(d / c))));
	elseif (c <= 5e+101)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(a + Float64(d * Float64(b / 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 <= -2.4e+88)
		tmp = (a + (b / (c / d))) * (-1.0 / hypot(c, d));
	elseif (c <= -1.5e-214)
		tmp = t_0;
	elseif (c <= 2.4e-193)
		tmp = (b / d) + (a / (d * (d / c)));
	elseif (c <= 5e+101)
		tmp = t_0;
	else
		tmp = (1.0 / hypot(c, d)) * (a + (d * (b / 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, -2.4e+88], 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, -1.5e-214], t$95$0, If[LessEqual[c, 2.4e-193], N[(N[(b / d), $MachinePrecision] + N[(a / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e+101], t$95$0, N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 7: 80.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{--1}{c}\\ \mathbf{if}\;c \leq -4.9 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-215}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-195}:\\ \;\;\;\;\frac{b}{d} + \frac{a}{d \cdot \frac{d}{c}}\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+103}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (* (+ a (/ b (/ c d))) (/ (- -1.0) c))))
   (if (<= c -4.9e+86)
     t_1
     (if (<= c -3.2e-215)
       t_0
       (if (<= c 3.2e-195)
         (+ (/ b d) (/ a (* d (/ d c))))
         (if (<= c 6.2e+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 = (a + (b / (c / d))) * (-(-1.0) / c);
	double tmp;
	if (c <= -4.9e+86) {
		tmp = t_1;
	} else if (c <= -3.2e-215) {
		tmp = t_0;
	} else if (c <= 3.2e-195) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 6.2e+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 = (a + (b / (c / d))) * (-(-1.0d0) / c)
    if (c <= (-4.9d+86)) then
        tmp = t_1
    else if (c <= (-3.2d-215)) then
        tmp = t_0
    else if (c <= 3.2d-195) then
        tmp = (b / d) + (a / (d * (d / c)))
    else if (c <= 6.2d+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 = (a + (b / (c / d))) * (-(-1.0) / c);
	double tmp;
	if (c <= -4.9e+86) {
		tmp = t_1;
	} else if (c <= -3.2e-215) {
		tmp = t_0;
	} else if (c <= 3.2e-195) {
		tmp = (b / d) + (a / (d * (d / c)));
	} else if (c <= 6.2e+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 = (a + (b / (c / d))) * (-(-1.0) / c)
	tmp = 0
	if c <= -4.9e+86:
		tmp = t_1
	elif c <= -3.2e-215:
		tmp = t_0
	elif c <= 3.2e-195:
		tmp = (b / d) + (a / (d * (d / c)))
	elif c <= 6.2e+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(a + Float64(b / Float64(c / d))) * Float64(Float64(-(-1.0)) / c))
	tmp = 0.0
	if (c <= -4.9e+86)
		tmp = t_1;
	elseif (c <= -3.2e-215)
		tmp = t_0;
	elseif (c <= 3.2e-195)
		tmp = Float64(Float64(b / d) + Float64(a / Float64(d * Float64(d / c))));
	elseif (c <= 6.2e+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 = (a + (b / (c / d))) * (-(-1.0) / c);
	tmp = 0.0;
	if (c <= -4.9e+86)
		tmp = t_1;
	elseif (c <= -3.2e-215)
		tmp = t_0;
	elseif (c <= 3.2e-195)
		tmp = (b / d) + (a / (d * (d / c)));
	elseif (c <= 6.2e+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[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[((--1.0) / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.9e+86], t$95$1, If[LessEqual[c, -3.2e-215], t$95$0, If[LessEqual[c, 3.2e-195], N[(N[(b / d), $MachinePrecision] + N[(a / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.2e+103], t$95$0, t$95$1]]]]]]

Derivation

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

Alternative 8: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{+23} \lor \neg \left(c \leq 8 \cdot 10^{-89}\right):\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{--1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{a}{d \cdot \frac{d}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.7e+23) (not (<= c 8e-89)))
   (* (+ a (/ b (/ c d))) (/ (- -1.0) c))
   (+ (/ b d) (/ a (* d (/ d c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.7e+23) || !(c <= 8e-89)) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else {
		tmp = (b / d) + (a / (d * (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 <= (-2.7d+23)) .or. (.not. (c <= 8d-89))) then
        tmp = (a + (b / (c / d))) * (-(-1.0d0) / c)
    else
        tmp = (b / d) + (a / (d * (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 <= -2.7e+23) || !(c <= 8e-89)) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else {
		tmp = (b / d) + (a / (d * (d / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.7e+23) or not (c <= 8e-89):
		tmp = (a + (b / (c / d))) * (-(-1.0) / c)
	else:
		tmp = (b / d) + (a / (d * (d / c)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.7e+23) || !(c <= 8e-89))
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) * Float64(Float64(-(-1.0)) / c));
	else
		tmp = Float64(Float64(b / d) + Float64(a / Float64(d * Float64(d / c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.7e+23) || ~((c <= 8e-89)))
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	else
		tmp = (b / d) + (a / (d * (d / c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.7e+23], N[Not[LessEqual[c, 8e-89]], $MachinePrecision]], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[((--1.0) / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / d), $MachinePrecision] + N[(a / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+23} \lor \neg \left(c \leq 1.45 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{a}{d \cdot \frac{d}{c}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.5e+23) (not (<= c 1.45e-33)))
   (/ a c)
   (+ (/ b d) (/ a (* d (/ d c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.5e+23) || !(c <= 1.45e-33)) {
		tmp = a / c;
	} else {
		tmp = (b / d) + (a / (d * (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 <= (-2.5d+23)) .or. (.not. (c <= 1.45d-33))) then
        tmp = a / c
    else
        tmp = (b / d) + (a / (d * (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 <= -2.5e+23) || !(c <= 1.45e-33)) {
		tmp = a / c;
	} else {
		tmp = (b / d) + (a / (d * (d / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.5e+23) or not (c <= 1.45e-33):
		tmp = a / c
	else:
		tmp = (b / d) + (a / (d * (d / c)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.5e+23) || !(c <= 1.45e-33))
		tmp = Float64(a / c);
	else
		tmp = Float64(Float64(b / d) + Float64(a / Float64(d * Float64(d / c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.5e+23) || ~((c <= 1.45e-33)))
		tmp = a / c;
	else
		tmp = (b / d) + (a / (d * (d / c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.5e+23], N[Not[LessEqual[c, 1.45e-33]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(N[(b / d), $MachinePrecision] + N[(a / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 63.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{-15} \lor \neg \left(c \leq 2.1 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -9e-15) (not (<= c 2.1e-34))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -9e-15) || !(c <= 2.1e-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 <= (-9d-15)) .or. (.not. (c <= 2.1d-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 <= -9e-15) || !(c <= 2.1e-34)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -9e-15) or not (c <= 2.1e-34):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -9e-15) || !(c <= 2.1e-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 <= -9e-15) || ~((c <= 2.1e-34)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -9e-15], N[Not[LessEqual[c, 2.1e-34]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

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

Alternative 11: 43.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq 1.35 \cdot 10^{+160}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (if (<= d 1.35e+160) (/ a c) (/ a d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= 1.35e+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 <= 1.35d+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 <= 1.35e+160) {
		tmp = a / c;
	} else {
		tmp = a / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= 1.35e+160:
		tmp = a / c
	else:
		tmp = a / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= 1.35e+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 <= 1.35e+160)
		tmp = a / c;
	else
		tmp = a / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, 1.35e+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))))