Complex division, real part

Percentage Accurate: 62.1% → 82.3%

Time: 6.9s

Alternatives: 8

Speedup: 1.6×

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: 62.1% 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: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b \cdot d + c \cdot a}{d \cdot d + c \cdot c}\\ \mathbf{if}\;d \leq -4.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{c}{d}, a, b\right)}{d}\\ \mathbf{elif}\;d \leq -2.95 \cdot 10^{-161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}{c}\\ \mathbf{elif}\;d \leq 4.1 \cdot 10^{+99}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* b d) (* c a)) (+ (* d d) (* c c)))))
   (if (<= d -4.5e+91)
     (/ (fma (/ c d) a b) d)
     (if (<= d -2.95e-161)
       t_0
       (if (<= d 1.1e-129)
         (/ (fma (/ b c) d a) c)
         (if (<= d 4.1e+99) t_0 (/ (fma (/ a d) c b) d)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((b * d) + (c * a)) / ((d * d) + (c * c));
	double tmp;
	if (d <= -4.5e+91) {
		tmp = fma((c / d), a, b) / d;
	} else if (d <= -2.95e-161) {
		tmp = t_0;
	} else if (d <= 1.1e-129) {
		tmp = fma((b / c), d, a) / c;
	} else if (d <= 4.1e+99) {
		tmp = t_0;
	} else {
		tmp = fma((a / d), c, b) / d;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(b * d) + Float64(c * a)) / Float64(Float64(d * d) + Float64(c * c)))
	tmp = 0.0
	if (d <= -4.5e+91)
		tmp = Float64(fma(Float64(c / d), a, b) / d);
	elseif (d <= -2.95e-161)
		tmp = t_0;
	elseif (d <= 1.1e-129)
		tmp = Float64(fma(Float64(b / c), d, a) / c);
	elseif (d <= 4.1e+99)
		tmp = t_0;
	else
		tmp = Float64(fma(Float64(a / d), c, b) / d);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b * d), $MachinePrecision] + N[(c * a), $MachinePrecision]), $MachinePrecision] / N[(N[(d * d), $MachinePrecision] + N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -4.5e+91], N[(N[(N[(c / d), $MachinePrecision] * a + b), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, -2.95e-161], t$95$0, If[LessEqual[d, 1.1e-129], N[(N[(N[(b / c), $MachinePrecision] * d + a), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 4.1e+99], t$95$0, N[(N[(N[(a / d), $MachinePrecision] * c + b), $MachinePrecision] / d), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -4.5e91

   1. Initial program 19.9%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 16.6

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 16.6%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   6. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{d} + b}{d} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{\color{blue}{\frac{c}{d} \cdot a} + b}{d} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{c}{d}, a, b\right)}}{d} \]

      6. lower-/.f64 85.9

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{c}{d}}, a, b\right)}{d} \]

   8. Applied rewrites 85.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{c}{d}, a, b\right)}{d}} \]

   if -4.5e91 < d < -2.9500000000000001e-161 or 1.10000000000000001e-129 < d < 4.09999999999999979e99

   1. Initial program 81.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   if -2.9500000000000001e-161 < d < 1.10000000000000001e-129

   1. Initial program 73.8%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b \cdot d}{c} + a}}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{d \cdot b}}{c} + a}{c} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{d \cdot \frac{b}{c}} + a}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b}{c} \cdot d} + a}{c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}}{c} \]

      7. lower-/.f64 90.5

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{b}{c}}, d, a\right)}{c} \]

   5. Applied rewrites 90.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}{c}} \]

   if 4.09999999999999979e99 < d

   1. Initial program 35.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{d} + b}{d} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{c \cdot \frac{a}{d}} + b}{d} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a}{d} \cdot c} + b}{d} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}}{d} \]

      7. lower-/.f64 92.6

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{a}{d}}, c, b\right)}{d} \]

   5. Applied rewrites 92.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}{d}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -4.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{c}{d}, a, b\right)}{d}\\ \mathbf{elif}\;d \leq -2.95 \cdot 10^{-161}:\\ \;\;\;\;\frac{b \cdot d + c \cdot a}{d \cdot d + c \cdot c}\\ \mathbf{elif}\;d \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}{c}\\ \mathbf{elif}\;d \leq 4.1 \cdot 10^{+99}:\\ \;\;\;\;\frac{b \cdot d + c \cdot a}{d \cdot d + c \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(c, c, d \cdot d\right)\\ \mathbf{if}\;d \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{t\_0} \cdot d\\ \mathbf{elif}\;d \leq 3.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq 1.18 \cdot 10^{+93}:\\ \;\;\;\;\frac{d}{t\_0} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (fma c c (* d d))))
   (if (<= d -2.1e+137)
     (/ b d)
     (if (<= d -5.5e-20)
       (* (/ b t_0) d)
       (if (<= d 3.5e-118)
         (/ a c)
         (if (<= d 1.18e+93) (* (/ d t_0) b) (/ b d)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(c, c, (d * d));
	double tmp;
	if (d <= -2.1e+137) {
		tmp = b / d;
	} else if (d <= -5.5e-20) {
		tmp = (b / t_0) * d;
	} else if (d <= 3.5e-118) {
		tmp = a / c;
	} else if (d <= 1.18e+93) {
		tmp = (d / t_0) * b;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = fma(c, c, Float64(d * d))
	tmp = 0.0
	if (d <= -2.1e+137)
		tmp = Float64(b / d);
	elseif (d <= -5.5e-20)
		tmp = Float64(Float64(b / t_0) * d);
	elseif (d <= 3.5e-118)
		tmp = Float64(a / c);
	elseif (d <= 1.18e+93)
		tmp = Float64(Float64(d / t_0) * b);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(c * c + N[(d * d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -2.1e+137], N[(b / d), $MachinePrecision], If[LessEqual[d, -5.5e-20], N[(N[(b / t$95$0), $MachinePrecision] * d), $MachinePrecision], If[LessEqual[d, 3.5e-118], N[(a / c), $MachinePrecision], If[LessEqual[d, 1.18e+93], N[(N[(d / t$95$0), $MachinePrecision] * b), $MachinePrecision], N[(b / d), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -2.0999999999999999e137 or 1.1799999999999999e93 < d

   1. Initial program 29.0%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{b}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 83.9

         \[\leadsto \color{blue}{\frac{b}{d}} \]

   5. Applied rewrites 83.9%

      \[\leadsto \color{blue}{\frac{b}{d}} \]

   if -2.0999999999999999e137 < d < -5.4999999999999996e-20

   1. Initial program 69.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot d}{{c}^{2} + {d}^{2}}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b}}{{c}^{2} + {d}^{2}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{d \cdot \frac{b}{{c}^{2} + {d}^{2}}} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{b}{{c}^{2} + {d}^{2}} \cdot d} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{{c}^{2} + {d}^{2}} \cdot d} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{{c}^{2} + {d}^{2}}} \cdot d \]

      6. unpow2 N/A

         \[\leadsto \frac{b}{\color{blue}{c \cdot c} + {d}^{2}} \cdot d \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{\mathsf{fma}\left(c, c, {d}^{2}\right)}} \cdot d \]

      8. unpow2 N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(c, c, \color{blue}{d \cdot d}\right)} \cdot d \]

      9. lower-*.f64 63.3

         \[\leadsto \frac{b}{\mathsf{fma}\left(c, c, \color{blue}{d \cdot d}\right)} \cdot d \]

   5. Applied rewrites 63.3%

      \[\leadsto \color{blue}{\frac{b}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot d} \]

   if -5.4999999999999996e-20 < d < 3.5e-118

   1. Initial program 76.2%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 77.4

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 77.4%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   if 3.5e-118 < d < 1.1799999999999999e93

   1. Initial program 79.6%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 37.9

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 37.9%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot d}{{c}^{2} + {d}^{2}}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b}}{{c}^{2} + {d}^{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{d}{{c}^{2} + {d}^{2}} \cdot b} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{d}{{c}^{2} + {d}^{2}} \cdot b} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{d}{{c}^{2} + {d}^{2}}} \cdot b \]

      5. unpow2 N/A

         \[\leadsto \frac{d}{\color{blue}{c \cdot c} + {d}^{2}} \cdot b \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{d}{\color{blue}{\mathsf{fma}\left(c, c, {d}^{2}\right)}} \cdot b \]

      7. unpow2 N/A

         \[\leadsto \frac{d}{\mathsf{fma}\left(c, c, \color{blue}{d \cdot d}\right)} \cdot b \]

      8. lower-*.f64 56.6

         \[\leadsto \frac{d}{\mathsf{fma}\left(c, c, \color{blue}{d \cdot d}\right)} \cdot b \]

   8. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\frac{d}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot b} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}{c}\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{c}{d}, a, b\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma (/ b c) d a) c)))
   (if (<= c -1.6e+14) t_0 (if (<= c 2.05e+77) (/ (fma (/ c d) a b) d) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma((b / c), d, a) / c;
	double tmp;
	if (c <= -1.6e+14) {
		tmp = t_0;
	} else if (c <= 2.05e+77) {
		tmp = fma((c / d), a, b) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(Float64(b / c), d, a) / c)
	tmp = 0.0
	if (c <= -1.6e+14)
		tmp = t_0;
	elseif (c <= 2.05e+77)
		tmp = Float64(fma(Float64(c / d), a, b) / d);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b / c), $MachinePrecision] * d + a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -1.6e+14], t$95$0, If[LessEqual[c, 2.05e+77], N[(N[(N[(c / d), $MachinePrecision] * a + b), $MachinePrecision] / d), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.6e14 or 2.05e77 < c

   1. Initial program 49.9%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b \cdot d}{c} + a}}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{d \cdot b}}{c} + a}{c} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{d \cdot \frac{b}{c}} + a}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b}{c} \cdot d} + a}{c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}}{c} \]

      7. lower-/.f64 81.0

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{b}{c}}, d, a\right)}{c} \]

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}{c}} \]

   if -1.6e14 < c < 2.05e77

   1. Initial program 68.9%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 24.3

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 24.3%

      \[\leadsto \color{blue}{\frac{a}{c}} \]

   6. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{d} + b}{d} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{\color{blue}{\frac{c}{d} \cdot a} + b}{d} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{c}{d}, a, b\right)}}{d} \]

      6. lower-/.f64 82.3

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{c}{d}}, a, b\right)}{d} \]

   8. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{c}{d}, a, b\right)}{d}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 77.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}{c}\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma (/ b c) d a) c)))
   (if (<= c -1.6e+14) t_0 (if (<= c 2.05e+77) (/ (fma (/ a d) c b) d) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma((b / c), d, a) / c;
	double tmp;
	if (c <= -1.6e+14) {
		tmp = t_0;
	} else if (c <= 2.05e+77) {
		tmp = fma((a / d), c, b) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(Float64(b / c), d, a) / c)
	tmp = 0.0
	if (c <= -1.6e+14)
		tmp = t_0;
	elseif (c <= 2.05e+77)
		tmp = Float64(fma(Float64(a / d), c, b) / d);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b / c), $MachinePrecision] * d + a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -1.6e+14], t$95$0, If[LessEqual[c, 2.05e+77], N[(N[(N[(a / d), $MachinePrecision] * c + b), $MachinePrecision] / d), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.6e14 or 2.05e77 < c

   1. Initial program 49.9%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a + \frac{b \cdot d}{c}}{c}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b \cdot d}{c} + a}}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{d \cdot b}}{c} + a}{c} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{d \cdot \frac{b}{c}} + a}{c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{b}{c} \cdot d} + a}{c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}}{c} \]

      7. lower-/.f64 81.0

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{b}{c}}, d, a\right)}{c} \]

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{b}{c}, d, a\right)}{c}} \]

   if -1.6e14 < c < 2.05e77

   1. Initial program 68.9%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{d} + b}{d} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{c \cdot \frac{a}{d}} + b}{d} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a}{d} \cdot c} + b}{d} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}}{d} \]

      7. lower-/.f64 81.1

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{a}{d}}, c, b\right)}{d} \]

   5. Applied rewrites 81.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}{d}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 70.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}{d}\\ \mathbf{if}\;d \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 7.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma (/ a d) c b) d)))
   (if (<= d -1.35e-19) t_0 (if (<= d 7.8e-42) (/ a c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma((a / d), c, b) / d;
	double tmp;
	if (d <= -1.35e-19) {
		tmp = t_0;
	} else if (d <= 7.8e-42) {
		tmp = a / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(Float64(a / d), c, b) / d)
	tmp = 0.0
	if (d <= -1.35e-19)
		tmp = t_0;
	elseif (d <= 7.8e-42)
		tmp = Float64(a / c);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(a / d), $MachinePrecision] * c + b), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -1.35e-19], t$95$0, If[LessEqual[d, 7.8e-42], N[(a / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -1.35e-19 or 7.8000000000000003e-42 < d

   1. Initial program 47.6%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in d around inf

      \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b + \frac{a \cdot c}{d}}{d}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a \cdot c}{d} + b}}{d} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{d} + b}{d} \]

      4. associate-/l* N/A

         \[\leadsto \frac{\color{blue}{c \cdot \frac{a}{d}} + b}{d} \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{a}{d} \cdot c} + b}{d} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}}{d} \]

      7. lower-/.f64 79.3

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\frac{a}{d}}, c, b\right)}{d} \]

   5. Applied rewrites 79.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{a}{d}, c, b\right)}{d}} \]

   if -1.35e-19 < d < 7.8000000000000003e-42

   1. Initial program 77.5%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 74.2

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 74.2%

      \[\leadsto \color{blue}{\frac{a}{c}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot d\\ \mathbf{elif}\;d \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -2.1e+137)
   (/ b d)
   (if (<= d -5.5e-20)
     (* (/ b (fma c c (* d d))) d)
     (if (<= d 1.15e+23) (/ a c) (/ b d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -2.1e+137) {
		tmp = b / d;
	} else if (d <= -5.5e-20) {
		tmp = (b / fma(c, c, (d * d))) * d;
	} else if (d <= 1.15e+23) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -2.1e+137)
		tmp = Float64(b / d);
	elseif (d <= -5.5e-20)
		tmp = Float64(Float64(b / fma(c, c, Float64(d * d))) * d);
	elseif (d <= 1.15e+23)
		tmp = Float64(a / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -2.1e+137], N[(b / d), $MachinePrecision], If[LessEqual[d, -5.5e-20], N[(N[(b / N[(c * c + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision], If[LessEqual[d, 1.15e+23], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if d < -2.0999999999999999e137 or 1.15e23 < d

   1. Initial program 36.1%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{b}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 77.3

         \[\leadsto \color{blue}{\frac{b}{d}} \]

   5. Applied rewrites 77.3%

      \[\leadsto \color{blue}{\frac{b}{d}} \]

   if -2.0999999999999999e137 < d < -5.4999999999999996e-20

   1. Initial program 69.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot d}{{c}^{2} + {d}^{2}}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{d \cdot b}}{{c}^{2} + {d}^{2}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{d \cdot \frac{b}{{c}^{2} + {d}^{2}}} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{b}{{c}^{2} + {d}^{2}} \cdot d} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{{c}^{2} + {d}^{2}} \cdot d} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{{c}^{2} + {d}^{2}}} \cdot d \]

      6. unpow2 N/A

         \[\leadsto \frac{b}{\color{blue}{c \cdot c} + {d}^{2}} \cdot d \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{\mathsf{fma}\left(c, c, {d}^{2}\right)}} \cdot d \]

      8. unpow2 N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(c, c, \color{blue}{d \cdot d}\right)} \cdot d \]

      9. lower-*.f64 63.3

         \[\leadsto \frac{b}{\mathsf{fma}\left(c, c, \color{blue}{d \cdot d}\right)} \cdot d \]

   5. Applied rewrites 63.3%

      \[\leadsto \color{blue}{\frac{b}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot d} \]

   if -5.4999999999999996e-20 < d < 1.15e23

   1. Initial program 77.6%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 71.0

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 71.0%

      \[\leadsto \color{blue}{\frac{a}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.35e-19) (/ b d) (if (<= d 1.15e+23) (/ a c) (/ b d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.35e-19) {
		tmp = b / d;
	} else if (d <= 1.15e+23) {
		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 (d <= (-1.35d-19)) then
        tmp = b / d
    else if (d <= 1.15d+23) 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 (d <= -1.35e-19) {
		tmp = b / d;
	} else if (d <= 1.15e+23) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.35e-19:
		tmp = b / d
	elif d <= 1.15e+23:
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.35e-19)
		tmp = Float64(b / d);
	elseif (d <= 1.15e+23)
		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 (d <= -1.35e-19)
		tmp = b / d;
	elseif (d <= 1.15e+23)
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.35e-19], N[(b / d), $MachinePrecision], If[LessEqual[d, 1.15e+23], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if d < -1.35e-19 or 1.15e23 < d

   1. Initial program 43.9%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{b}{d}} \]
   4. Step-by-step derivation

      1. lower-/.f64 70.7

         \[\leadsto \color{blue}{\frac{b}{d}} \]

   5. Applied rewrites 70.7%

      \[\leadsto \color{blue}{\frac{b}{d}} \]

   if -1.35e-19 < d < 1.15e23

   1. Initial program 77.6%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{a}{c}} \]
   4. Step-by-step derivation

      1. lower-/.f64 71.0

         \[\leadsto \color{blue}{\frac{a}{c}} \]

   5. Applied rewrites 71.0%

      \[\leadsto \color{blue}{\frac{a}{c}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 43.3% accurate, 3.2× 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

1. Initial program 61.1%

   \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
2. Add Preprocessing

3. Taylor expanded in c around inf

   \[\leadsto \color{blue}{\frac{a}{c}} \]
4. Step-by-step derivation

   1. lower-/.f64 43.3

      \[\leadsto \color{blue}{\frac{a}{c}} \]

5. Applied rewrites 43.3%

   \[\leadsto \color{blue}{\frac{a}{c}} \]
6. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.6× 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 2024242 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :alt
  (! :herbie-platform default (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))))