Complex division, real part

Percentage Accurate: 61.6% → 84.1%

Time: 7.0s

Alternatives: 10

Speedup: 2.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.6% 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: 84.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 10^{+231}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) 1e+231)
   (* (/ 1.0 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
   (+ (/ b d) (* (/ c d) (/ a d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((a * c) + (b * d)) / ((c * c) + (d * d))) <= 1e+231) {
		tmp = (1.0 / hypot(c, d)) * (fma(a, c, (b * d)) / hypot(c, d));
	} else {
		tmp = (b / d) + ((c / d) * (a / d));
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d))) <= 1e+231)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(fma(a, c, Float64(b * d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(b / d) + Float64(Float64(c / d) * Float64(a / d)));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+231], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / d), $MachinePrecision] + N[(N[(c / d), $MachinePrecision] * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d))) < 1.0000000000000001e231

   1. Initial program 82.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 82.7%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(a \cdot c + b \cdot d\right)}}{c \cdot c + d \cdot d} \]

      2. add-sqr-sqrt 82.7%

         \[\leadsto \frac{1 \cdot \left(a \cdot c + b \cdot d\right)}{\color{blue}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}} \]

      3. times-frac 82.7%

         \[\leadsto \color{blue}{\frac{1}{\sqrt{c \cdot c + d \cdot d}} \cdot \frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}}} \]

      4. hypot-def 82.7%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{hypot}\left(c, d\right)}} \cdot \frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}} \]

      5. fma-def 82.7%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\color{blue}{\mathsf{fma}\left(a, c, b \cdot d\right)}}{\sqrt{c \cdot c + d \cdot d}} \]

      6. hypot-def 97.0%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\color{blue}{\mathsf{hypot}\left(c, d\right)}} \]

   3. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}} \]

   if 1.0000000000000001e231 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 16.4%

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

   2. Taylor expanded in c around 0 48.1%

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

      1. unpow2 48.1%

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

      2. times-frac 59.9%

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

   4. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 10^{+231}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \end{array} \]

Alternative 2: 77.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\frac{a \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d} + \frac{a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \frac{d}{\frac{c}{b}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -9e+42)
   (/ (* a (/ c (hypot c d))) (hypot c d))
   (if (<= c 1.85e-33)
     (+ (/ b d) (/ (* a (/ c d)) d))
     (* (/ 1.0 (hypot c d)) (+ a (/ d (/ c b)))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9e+42) {
		tmp = (a * (c / hypot(c, d))) / hypot(c, d);
	} else if (c <= 1.85e-33) {
		tmp = (b / d) + ((a * (c / d)) / d);
	} else {
		tmp = (1.0 / hypot(c, d)) * (a + (d / (c / b)));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9e+42) {
		tmp = (a * (c / Math.hypot(c, d))) / Math.hypot(c, d);
	} else if (c <= 1.85e-33) {
		tmp = (b / d) + ((a * (c / d)) / d);
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * (a + (d / (c / b)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -9e+42:
		tmp = (a * (c / math.hypot(c, d))) / math.hypot(c, d)
	elif c <= 1.85e-33:
		tmp = (b / d) + ((a * (c / d)) / d)
	else:
		tmp = (1.0 / math.hypot(c, d)) * (a + (d / (c / b)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -9e+42)
		tmp = Float64(Float64(a * Float64(c / hypot(c, d))) / hypot(c, d));
	elseif (c <= 1.85e-33)
		tmp = Float64(Float64(b / d) + Float64(Float64(a * Float64(c / d)) / d));
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(a + Float64(d / Float64(c / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -9e+42)
		tmp = (a * (c / hypot(c, d))) / hypot(c, d);
	elseif (c <= 1.85e-33)
		tmp = (b / d) + ((a * (c / d)) / d);
	else
		tmp = (1.0 / hypot(c, d)) * (a + (d / (c / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -9e+42], N[(N[(a * N[(c / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e-33], N[(N[(b / d), $MachinePrecision] + N[(N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a + N[(d / N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.00000000000000025e42

   1. Initial program 44.5%

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

   2. Taylor expanded in a around inf 44.6%

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

      1. associate-/l* 43.6%

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

      2. associate-/r/ 50.0%

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

      3. unpow2 50.0%

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

      4. unpow2 50.0%

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

      5. +-commutative 50.0%

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

      6. fma-def 50.0%

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

   4. Simplified 50.0%

      \[\leadsto \color{blue}{\frac{c}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot a} \]
   5. Step-by-step derivation

      1. *-un-lft-identity 50.0%

         \[\leadsto \frac{\color{blue}{1 \cdot c}}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot a \]

      2. fma-def 50.0%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{c \cdot c + d \cdot d}} \cdot a \]

      3. add-sqr-sqrt 50.0%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}} \cdot a \]

      4. hypot-udef 50.0%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{\mathsf{hypot}\left(c, d\right)} \cdot \sqrt{c \cdot c + d \cdot d}} \cdot a \]

      5. hypot-udef 50.0%

         \[\leadsto \frac{1 \cdot c}{\mathsf{hypot}\left(c, d\right) \cdot \color{blue}{\mathsf{hypot}\left(c, d\right)}} \cdot a \]

      6. times-frac 86.5%

         \[\leadsto \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}\right)} \cdot a \]

   6. Applied egg-rr 86.5%

      \[\leadsto \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}\right)} \cdot a \]
   7. Step-by-step derivation

      1. associate-*l* 93.0%

         \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(\frac{c}{\mathsf{hypot}\left(c, d\right)} \cdot a\right)} \]

      2. associate-*l/ 93.3%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{c}{\mathsf{hypot}\left(c, d\right)} \cdot a\right)}{\mathsf{hypot}\left(c, d\right)}} \]

      3. *-un-lft-identity 93.3%

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

   8. Applied egg-rr 93.3%

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

   if -9.00000000000000025e42 < c < 1.85000000000000007e-33

   1. Initial program 76.6%

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

   2. Taylor expanded in c around 0 83.1%

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

      1. unpow2 83.1%

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

      2. times-frac 83.2%

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

   4. Simplified 83.2%

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

      1. associate-*r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

   if 1.85000000000000007e-33 < c

   1. Initial program 56.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 56.7%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(a \cdot c + b \cdot d\right)}}{c \cdot c + d \cdot d} \]

      2. add-sqr-sqrt 56.7%

         \[\leadsto \frac{1 \cdot \left(a \cdot c + b \cdot d\right)}{\color{blue}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}} \]

      3. times-frac 56.7%

         \[\leadsto \color{blue}{\frac{1}{\sqrt{c \cdot c + d \cdot d}} \cdot \frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}}} \]

      4. hypot-def 56.7%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{hypot}\left(c, d\right)}} \cdot \frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}} \]

      5. fma-def 56.7%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\color{blue}{\mathsf{fma}\left(a, c, b \cdot d\right)}}{\sqrt{c \cdot c + d \cdot d}} \]

      6. hypot-def 66.3%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\color{blue}{\mathsf{hypot}\left(c, d\right)}} \]

   3. Applied egg-rr 66.3%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}} \]

   4. Taylor expanded in c around inf 78.2%

      \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \color{blue}{\left(a + \frac{d \cdot b}{c}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 81.8%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \color{blue}{\frac{d}{\frac{c}{b}}}\right) \]

   6. Simplified 81.8%

      \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \color{blue}{\left(a + \frac{d}{\frac{c}{b}}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\frac{a \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d} + \frac{a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \frac{d}{\frac{c}{b}}\right)\\ \end{array} \]

Alternative 3: 77.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d} + \frac{a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \frac{d}{\frac{c}{b}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -1e+43)
   (+ (/ a c) (* (/ d c) (/ b c)))
   (if (<= c 2.35e-33)
     (+ (/ b d) (/ (* a (/ c d)) d))
     (* (/ 1.0 (hypot c d)) (+ a (/ d (/ c b)))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1e+43) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else if (c <= 2.35e-33) {
		tmp = (b / d) + ((a * (c / d)) / d);
	} else {
		tmp = (1.0 / hypot(c, d)) * (a + (d / (c / b)));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1e+43) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else if (c <= 2.35e-33) {
		tmp = (b / d) + ((a * (c / d)) / d);
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * (a + (d / (c / b)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -1e+43:
		tmp = (a / c) + ((d / c) * (b / c))
	elif c <= 2.35e-33:
		tmp = (b / d) + ((a * (c / d)) / d)
	else:
		tmp = (1.0 / math.hypot(c, d)) * (a + (d / (c / b)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -1e+43)
		tmp = Float64(Float64(a / c) + Float64(Float64(d / c) * Float64(b / c)));
	elseif (c <= 2.35e-33)
		tmp = Float64(Float64(b / d) + Float64(Float64(a * Float64(c / d)) / d));
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(a + Float64(d / Float64(c / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -1e+43)
		tmp = (a / c) + ((d / c) * (b / c));
	elseif (c <= 2.35e-33)
		tmp = (b / d) + ((a * (c / d)) / d);
	else
		tmp = (1.0 / hypot(c, d)) * (a + (d / (c / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -1e+43], N[(N[(a / c), $MachinePrecision] + N[(N[(d / c), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.35e-33], N[(N[(b / d), $MachinePrecision] + N[(N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a + N[(d / N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.00000000000000001e43

   1. Initial program 44.5%

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

   2. Taylor expanded in c around inf 79.4%

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

      1. unpow2 79.4%

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

      2. times-frac 86.5%

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

   4. Simplified 86.5%

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

   if -1.00000000000000001e43 < c < 2.3500000000000001e-33

   1. Initial program 76.6%

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

   2. Taylor expanded in c around 0 83.1%

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

      1. unpow2 83.1%

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

      2. times-frac 83.2%

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

   4. Simplified 83.2%

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

      1. associate-*r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

   if 2.3500000000000001e-33 < c

   1. Initial program 56.7%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 56.7%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(a \cdot c + b \cdot d\right)}}{c \cdot c + d \cdot d} \]

      2. add-sqr-sqrt 56.7%

         \[\leadsto \frac{1 \cdot \left(a \cdot c + b \cdot d\right)}{\color{blue}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}} \]

      3. times-frac 56.7%

         \[\leadsto \color{blue}{\frac{1}{\sqrt{c \cdot c + d \cdot d}} \cdot \frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}}} \]

      4. hypot-def 56.7%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{hypot}\left(c, d\right)}} \cdot \frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}} \]

      5. fma-def 56.7%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\color{blue}{\mathsf{fma}\left(a, c, b \cdot d\right)}}{\sqrt{c \cdot c + d \cdot d}} \]

      6. hypot-def 66.3%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\color{blue}{\mathsf{hypot}\left(c, d\right)}} \]

   3. Applied egg-rr 66.3%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}} \]

   4. Taylor expanded in c around inf 78.2%

      \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \color{blue}{\left(a + \frac{d \cdot b}{c}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 81.8%

         \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \color{blue}{\frac{d}{\frac{c}{b}}}\right) \]

   6. Simplified 81.8%

      \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \color{blue}{\left(a + \frac{d}{\frac{c}{b}}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d} + \frac{a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \frac{d}{\frac{c}{b}}\right)\\ \end{array} \]

Alternative 4: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+43} \lor \neg \left(c \leq 1.7 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.5e+43) (not (<= c 1.7e-33)))
   (+ (/ a c) (* (/ d c) (/ b c)))
   (+ (/ b d) (* (/ c d) (/ a d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.5e+43) || !(c <= 1.7e-33)) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else {
		tmp = (b / d) + ((c / d) * (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 ((c <= (-2.5d+43)) .or. (.not. (c <= 1.7d-33))) then
        tmp = (a / c) + ((d / c) * (b / c))
    else
        tmp = (b / d) + ((c / d) * (a / d))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.5e+43) || !(c <= 1.7e-33)) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else {
		tmp = (b / d) + ((c / d) * (a / d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.5e+43) or not (c <= 1.7e-33):
		tmp = (a / c) + ((d / c) * (b / c))
	else:
		tmp = (b / d) + ((c / d) * (a / d))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.5e+43) || !(c <= 1.7e-33))
		tmp = Float64(Float64(a / c) + Float64(Float64(d / c) * Float64(b / c)));
	else
		tmp = Float64(Float64(b / d) + Float64(Float64(c / d) * Float64(a / d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.5e+43) || ~((c <= 1.7e-33)))
		tmp = (a / c) + ((d / c) * (b / c));
	else
		tmp = (b / d) + ((c / d) * (a / d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.5e+43], N[Not[LessEqual[c, 1.7e-33]], $MachinePrecision]], N[(N[(a / c), $MachinePrecision] + N[(N[(d / c), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / d), $MachinePrecision] + N[(N[(c / d), $MachinePrecision] * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.5000000000000002e43 or 1.7e-33 < c

   1. Initial program 52.7%

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

   2. Taylor expanded in c around inf 78.4%

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

      1. unpow2 78.4%

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

      2. times-frac 83.2%

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

   4. Simplified 83.2%

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

   if -2.5000000000000002e43 < c < 1.7e-33

   1. Initial program 76.6%

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

   2. Taylor expanded in c around 0 83.1%

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

      1. unpow2 83.1%

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

      2. times-frac 83.2%

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

   4. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+43} \lor \neg \left(c \leq 1.7 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \end{array} \]

Alternative 5: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42} \lor \neg \left(c \leq 1.9 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{a \cdot \frac{c}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -9e+42) (not (<= c 1.9e-33)))
   (+ (/ a c) (* (/ d c) (/ b c)))
   (+ (/ b d) (/ (* a (/ c d)) d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -9e+42) || !(c <= 1.9e-33)) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else {
		tmp = (b / d) + ((a * (c / d)) / 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+42)) .or. (.not. (c <= 1.9d-33))) then
        tmp = (a / c) + ((d / c) * (b / c))
    else
        tmp = (b / d) + ((a * (c / d)) / 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+42) || !(c <= 1.9e-33)) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else {
		tmp = (b / d) + ((a * (c / d)) / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -9e+42) or not (c <= 1.9e-33):
		tmp = (a / c) + ((d / c) * (b / c))
	else:
		tmp = (b / d) + ((a * (c / d)) / d)
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -9e+42) || !(c <= 1.9e-33))
		tmp = Float64(Float64(a / c) + Float64(Float64(d / c) * Float64(b / c)));
	else
		tmp = Float64(Float64(b / d) + Float64(Float64(a * Float64(c / d)) / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -9e+42) || ~((c <= 1.9e-33)))
		tmp = (a / c) + ((d / c) * (b / c));
	else
		tmp = (b / d) + ((a * (c / d)) / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -9e+42], N[Not[LessEqual[c, 1.9e-33]], $MachinePrecision]], N[(N[(a / c), $MachinePrecision] + N[(N[(d / c), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / d), $MachinePrecision] + N[(N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9.00000000000000025e42 or 1.89999999999999997e-33 < c

   1. Initial program 52.7%

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

   2. Taylor expanded in c around inf 78.4%

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

      1. unpow2 78.4%

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

      2. times-frac 83.2%

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

   4. Simplified 83.2%

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

   if -9.00000000000000025e42 < c < 1.89999999999999997e-33

   1. Initial program 76.6%

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

   2. Taylor expanded in c around 0 83.1%

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

      1. unpow2 83.1%

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

      2. times-frac 83.2%

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

   4. Simplified 83.2%

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

      1. associate-*r/ 85.4%

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

   6. Applied egg-rr 85.4%

      \[\leadsto \frac{b}{d} + \color{blue}{\frac{\frac{c}{d} \cdot a}{d}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42} \lor \neg \left(c \leq 1.9 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{a \cdot \frac{c}{d}}{d}\\ \end{array} \]

Alternative 6: 70.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.7 \cdot 10^{+91}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 8.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.7e+91)
   (/ b d)
   (if (<= d 8.2e+22) (+ (/ a c) (* (/ d c) (/ b c))) (/ b d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.7e+91) {
		tmp = b / d;
	} else if (d <= 8.2e+22) {
		tmp = (a / c) + ((d / c) * (b / 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 <= (-1.7d+91)) then
        tmp = b / d
    else if (d <= 8.2d+22) then
        tmp = (a / c) + ((d / c) * (b / 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 <= -1.7e+91) {
		tmp = b / d;
	} else if (d <= 8.2e+22) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.7e+91:
		tmp = b / d
	elif d <= 8.2e+22:
		tmp = (a / c) + ((d / c) * (b / c))
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.7e+91)
		tmp = Float64(b / d);
	elseif (d <= 8.2e+22)
		tmp = Float64(Float64(a / c) + Float64(Float64(d / c) * Float64(b / c)));
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.7e+91)
		tmp = b / d;
	elseif (d <= 8.2e+22)
		tmp = (a / c) + ((d / c) * (b / c));
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.7e+91], N[(b / d), $MachinePrecision], If[LessEqual[d, 8.2e+22], N[(N[(a / c), $MachinePrecision] + N[(N[(d / c), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / d), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if d < -1.7e91 or 8.19999999999999958e22 < d

   1. Initial program 48.8%

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

   2. Taylor expanded in c around 0 66.6%

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

   if -1.7e91 < d < 8.19999999999999958e22

   1. Initial program 75.5%

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

   2. Taylor expanded in c around inf 74.2%

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

      1. unpow2 74.2%

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

      2. times-frac 77.6%

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

   4. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.7 \cdot 10^{+91}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 8.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]

Alternative 7: 62.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-136}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-76}:\\ \;\;\;\;\frac{c}{d} \cdot \frac{a}{d}\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -1.9e+43)
   (/ a c)
   (if (<= c 1.05e-136)
     (/ b d)
     (if (<= c 8e-76)
       (* (/ c d) (/ a d))
       (if (<= c 2.05e-33) (/ b d) (/ a c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1.9e+43) {
		tmp = a / c;
	} else if (c <= 1.05e-136) {
		tmp = b / d;
	} else if (c <= 8e-76) {
		tmp = (c / d) * (a / d);
	} else if (c <= 2.05e-33) {
		tmp = b / d;
	} else {
		tmp = a / 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 <= (-1.9d+43)) then
        tmp = a / c
    else if (c <= 1.05d-136) then
        tmp = b / d
    else if (c <= 8d-76) then
        tmp = (c / d) * (a / d)
    else if (c <= 2.05d-33) then
        tmp = b / d
    else
        tmp = a / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -1.9e+43) {
		tmp = a / c;
	} else if (c <= 1.05e-136) {
		tmp = b / d;
	} else if (c <= 8e-76) {
		tmp = (c / d) * (a / d);
	} else if (c <= 2.05e-33) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -1.9e+43:
		tmp = a / c
	elif c <= 1.05e-136:
		tmp = b / d
	elif c <= 8e-76:
		tmp = (c / d) * (a / d)
	elif c <= 2.05e-33:
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -1.9e+43)
		tmp = Float64(a / c);
	elseif (c <= 1.05e-136)
		tmp = Float64(b / d);
	elseif (c <= 8e-76)
		tmp = Float64(Float64(c / d) * Float64(a / d));
	elseif (c <= 2.05e-33)
		tmp = Float64(b / d);
	else
		tmp = Float64(a / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -1.9e+43)
		tmp = a / c;
	elseif (c <= 1.05e-136)
		tmp = b / d;
	elseif (c <= 8e-76)
		tmp = (c / d) * (a / d);
	elseif (c <= 2.05e-33)
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -1.9e+43], N[(a / c), $MachinePrecision], If[LessEqual[c, 1.05e-136], N[(b / d), $MachinePrecision], If[LessEqual[c, 8e-76], N[(N[(c / d), $MachinePrecision] * N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.05e-33], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.90000000000000004e43 or 2.05e-33 < c

   1. Initial program 52.7%

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

   2. Taylor expanded in c around inf 74.4%

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

   if -1.90000000000000004e43 < c < 1.0499999999999999e-136 or 7.99999999999999942e-76 < c < 2.05e-33

   1. Initial program 75.2%

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

   2. Taylor expanded in c around 0 66.9%

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

   if 1.0499999999999999e-136 < c < 7.99999999999999942e-76

   1. Initial program 90.8%

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

   2. Taylor expanded in a around inf 82.3%

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

      1. associate-/l* 82.5%

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

      2. associate-/r/ 82.3%

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

      3. unpow2 82.3%

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

      4. unpow2 82.3%

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

      5. +-commutative 82.3%

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

      6. fma-def 82.3%

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

   4. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{c}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot a} \]
   5. Step-by-step derivation

      1. *-un-lft-identity 82.3%

         \[\leadsto \frac{\color{blue}{1 \cdot c}}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot a \]

      2. fma-def 82.3%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{c \cdot c + d \cdot d}} \cdot a \]

      3. add-sqr-sqrt 82.3%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}} \cdot a \]

      4. hypot-udef 82.3%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{\mathsf{hypot}\left(c, d\right)} \cdot \sqrt{c \cdot c + d \cdot d}} \cdot a \]

      5. hypot-udef 82.3%

         \[\leadsto \frac{1 \cdot c}{\mathsf{hypot}\left(c, d\right) \cdot \color{blue}{\mathsf{hypot}\left(c, d\right)}} \cdot a \]

      6. times-frac 82.3%

         \[\leadsto \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}\right)} \cdot a \]

   6. Applied egg-rr 82.3%

      \[\leadsto \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}\right)} \cdot a \]

   7. Taylor expanded in c around 0 82.3%

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

      1. unpow2 82.3%

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

      2. times-frac 89.4%

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

   9. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{c}{d} \cdot \frac{a}{d}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-136}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-76}:\\ \;\;\;\;\frac{c}{d} \cdot \frac{a}{d}\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]

Alternative 8: 62.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \frac{\frac{a}{d}}{d}\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -9e+42)
   (/ a c)
   (if (<= c 1.2e-136)
     (/ b d)
     (if (<= c 9.2e-76)
       (* c (/ (/ a d) d))
       (if (<= c 1.6e-33) (/ b d) (/ a c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9e+42) {
		tmp = a / c;
	} else if (c <= 1.2e-136) {
		tmp = b / d;
	} else if (c <= 9.2e-76) {
		tmp = c * ((a / d) / d);
	} else if (c <= 1.6e-33) {
		tmp = b / d;
	} else {
		tmp = a / 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 <= (-9d+42)) then
        tmp = a / c
    else if (c <= 1.2d-136) then
        tmp = b / d
    else if (c <= 9.2d-76) then
        tmp = c * ((a / d) / d)
    else if (c <= 1.6d-33) then
        tmp = b / d
    else
        tmp = a / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9e+42) {
		tmp = a / c;
	} else if (c <= 1.2e-136) {
		tmp = b / d;
	} else if (c <= 9.2e-76) {
		tmp = c * ((a / d) / d);
	} else if (c <= 1.6e-33) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -9e+42:
		tmp = a / c
	elif c <= 1.2e-136:
		tmp = b / d
	elif c <= 9.2e-76:
		tmp = c * ((a / d) / d)
	elif c <= 1.6e-33:
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -9e+42)
		tmp = Float64(a / c);
	elseif (c <= 1.2e-136)
		tmp = Float64(b / d);
	elseif (c <= 9.2e-76)
		tmp = Float64(c * Float64(Float64(a / d) / d));
	elseif (c <= 1.6e-33)
		tmp = Float64(b / d);
	else
		tmp = Float64(a / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -9e+42)
		tmp = a / c;
	elseif (c <= 1.2e-136)
		tmp = b / d;
	elseif (c <= 9.2e-76)
		tmp = c * ((a / d) / d);
	elseif (c <= 1.6e-33)
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -9e+42], N[(a / c), $MachinePrecision], If[LessEqual[c, 1.2e-136], N[(b / d), $MachinePrecision], If[LessEqual[c, 9.2e-76], N[(c * N[(N[(a / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e-33], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.00000000000000025e42 or 1.59999999999999988e-33 < c

   1. Initial program 52.7%

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

   2. Taylor expanded in c around inf 74.4%

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

   if -9.00000000000000025e42 < c < 1.1999999999999999e-136 or 9.20000000000000025e-76 < c < 1.59999999999999988e-33

   1. Initial program 75.2%

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

   2. Taylor expanded in c around 0 66.9%

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

   if 1.1999999999999999e-136 < c < 9.20000000000000025e-76

   1. Initial program 90.8%

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

   2. Taylor expanded in a around inf 82.3%

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

      1. associate-/l* 82.5%

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

      2. associate-/r/ 82.3%

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

      3. unpow2 82.3%

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

      4. unpow2 82.3%

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

      5. +-commutative 82.3%

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

      6. fma-def 82.3%

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

   4. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{c}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot a} \]
   5. Step-by-step derivation

      1. *-un-lft-identity 82.3%

         \[\leadsto \frac{\color{blue}{1 \cdot c}}{\mathsf{fma}\left(c, c, d \cdot d\right)} \cdot a \]

      2. fma-def 82.3%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{c \cdot c + d \cdot d}} \cdot a \]

      3. add-sqr-sqrt 82.3%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}} \cdot a \]

      4. hypot-udef 82.3%

         \[\leadsto \frac{1 \cdot c}{\color{blue}{\mathsf{hypot}\left(c, d\right)} \cdot \sqrt{c \cdot c + d \cdot d}} \cdot a \]

      5. hypot-udef 82.3%

         \[\leadsto \frac{1 \cdot c}{\mathsf{hypot}\left(c, d\right) \cdot \color{blue}{\mathsf{hypot}\left(c, d\right)}} \cdot a \]

      6. times-frac 82.3%

         \[\leadsto \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}\right)} \cdot a \]

   6. Applied egg-rr 82.3%

      \[\leadsto \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{c}{\mathsf{hypot}\left(c, d\right)}\right)} \cdot a \]

   7. Taylor expanded in c around 0 82.3%

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

      1. unpow2 82.3%

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

      2. times-frac 89.4%

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

   9. Simplified 89.4%

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

   10. Taylor expanded in c around 0 82.3%

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

       1. *-commutative 82.3%

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

       2. unpow2 82.3%

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

       3. times-frac 89.4%

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

       4. associate-*r/ 91.1%

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

       5. associate-*l/ 91.0%

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

   12. Simplified 91.0%

       \[\leadsto \color{blue}{\frac{\frac{a}{d}}{d} \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \frac{\frac{a}{d}}{d}\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]

Alternative 9: 63.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -9e+42) (/ a c) (if (<= c 1.8e-33) (/ b d) (/ a c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9e+42) {
		tmp = a / c;
	} else if (c <= 1.8e-33) {
		tmp = b / d;
	} else {
		tmp = a / 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 <= (-9d+42)) then
        tmp = a / c
    else if (c <= 1.8d-33) then
        tmp = b / d
    else
        tmp = a / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9e+42) {
		tmp = a / c;
	} else if (c <= 1.8e-33) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -9e+42:
		tmp = a / c
	elif c <= 1.8e-33:
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -9e+42)
		tmp = Float64(a / c);
	elseif (c <= 1.8e-33)
		tmp = Float64(b / d);
	else
		tmp = Float64(a / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -9e+42)
		tmp = a / c;
	elseif (c <= 1.8e-33)
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -9e+42], N[(a / c), $MachinePrecision], If[LessEqual[c, 1.8e-33], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -9.00000000000000025e42 or 1.80000000000000017e-33 < c

   1. Initial program 52.7%

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

   2. Taylor expanded in c around inf 74.4%

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

   if -9.00000000000000025e42 < c < 1.80000000000000017e-33

   1. Initial program 76.6%

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

   2. Taylor expanded in c around 0 64.4%

      \[\leadsto \color{blue}{\frac{b}{d}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]

Alternative 10: 42.1% 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

1. Initial program 64.6%

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

2. Taylor expanded in c around inf 46.5%

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

3. Final simplification 46.5%

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

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 2023224 
(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))))