Complex division, real part

Percentage Accurate: 61.6% → 82.2%

Time: 8.2s

Alternatives: 7

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: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \mathbf{if}\;d \leq -1.5 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{--1}{c}\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 2.7 \cdot 10^{+124}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_1 (+ (/ b d) (* (/ c d) (/ a d)))))
   (if (<= d -1.5e+115)
     t_1
     (if (<= d -6.2e-123)
       t_0
       (if (<= d 3.7e-10)
         (* (+ a (/ b (/ c d))) (/ (- -1.0) c))
         (if (<= d 2.5e+117) t_0 (if (<= d 2.7e+124) (/ a c) 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 = (b / d) + ((c / d) * (a / d));
	double tmp;
	if (d <= -1.5e+115) {
		tmp = t_1;
	} else if (d <= -6.2e-123) {
		tmp = t_0;
	} else if (d <= 3.7e-10) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else if (d <= 2.5e+117) {
		tmp = t_0;
	} else if (d <= 2.7e+124) {
		tmp = a / c;
	} 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 = (b / d) + ((c / d) * (a / d))
    if (d <= (-1.5d+115)) then
        tmp = t_1
    else if (d <= (-6.2d-123)) then
        tmp = t_0
    else if (d <= 3.7d-10) then
        tmp = (a + (b / (c / d))) * (-(-1.0d0) / c)
    else if (d <= 2.5d+117) then
        tmp = t_0
    else if (d <= 2.7d+124) then
        tmp = a / c
    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 = (b / d) + ((c / d) * (a / d));
	double tmp;
	if (d <= -1.5e+115) {
		tmp = t_1;
	} else if (d <= -6.2e-123) {
		tmp = t_0;
	} else if (d <= 3.7e-10) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else if (d <= 2.5e+117) {
		tmp = t_0;
	} else if (d <= 2.7e+124) {
		tmp = a / c;
	} 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 = (b / d) + ((c / d) * (a / d))
	tmp = 0
	if d <= -1.5e+115:
		tmp = t_1
	elif d <= -6.2e-123:
		tmp = t_0
	elif d <= 3.7e-10:
		tmp = (a + (b / (c / d))) * (-(-1.0) / c)
	elif d <= 2.5e+117:
		tmp = t_0
	elif d <= 2.7e+124:
		tmp = a / c
	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(b / d) + Float64(Float64(c / d) * Float64(a / d)))
	tmp = 0.0
	if (d <= -1.5e+115)
		tmp = t_1;
	elseif (d <= -6.2e-123)
		tmp = t_0;
	elseif (d <= 3.7e-10)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) * Float64(Float64(-(-1.0)) / c));
	elseif (d <= 2.5e+117)
		tmp = t_0;
	elseif (d <= 2.7e+124)
		tmp = Float64(a / c);
	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 = (b / d) + ((c / d) * (a / d));
	tmp = 0.0;
	if (d <= -1.5e+115)
		tmp = t_1;
	elseif (d <= -6.2e-123)
		tmp = t_0;
	elseif (d <= 3.7e-10)
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	elseif (d <= 2.5e+117)
		tmp = t_0;
	elseif (d <= 2.7e+124)
		tmp = a / c;
	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[(b / d), $MachinePrecision] + N[(N[(c / d), $MachinePrecision] * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.5e+115], t$95$1, If[LessEqual[d, -6.2e-123], t$95$0, If[LessEqual[d, 3.7e-10], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[((--1.0) / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2.5e+117], t$95$0, If[LessEqual[d, 2.7e+124], N[(a / c), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -1.5e115 or 2.69999999999999978e124 < d

   1. Initial program 32.3%

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

      1. *-un-lft-identity 32.3%

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

      2. add-sqr-sqrt 32.3%

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

      3. times-frac 32.4%

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

      4. hypot-def 32.4%

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

      5. fma-def 32.4%

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

      6. hypot-def 50.6%

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

   3. Applied egg-rr 50.6%

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

   4. Taylor expanded in c around 0 80.6%

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

      1. *-commutative 80.6%

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

      2. unpow2 80.6%

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

      3. times-frac 90.1%

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

   6. Applied egg-rr 90.1%

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

   if -1.5e115 < d < -6.19999999999999996e-123 or 3.70000000000000015e-10 < d < 2.49999999999999992e117

   1. Initial program 82.9%

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

   if -6.19999999999999996e-123 < d < 3.70000000000000015e-10

   1. Initial program 70.8%

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

      1. *-un-lft-identity 70.8%

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

      2. add-sqr-sqrt 70.8%

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

      3. times-frac 70.8%

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

      4. hypot-def 70.8%

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

      5. fma-def 70.8%

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

      6. hypot-def 84.3%

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

   3. Applied egg-rr 84.3%

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

   4. Taylor expanded in c around -inf 42.6%

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

      1. neg-mul-1 42.6%

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

      2. +-commutative 42.6%

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

      3. unsub-neg 42.6%

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

      4. mul-1-neg 42.6%

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

      5. associate-/l* 42.6%

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

      6. distribute-neg-frac 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in c around -inf 89.9%

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

   if 2.49999999999999992e117 < d < 2.69999999999999978e124

   1. Initial program 21.9%

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

   2. Taylor expanded in c around inf 80.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \mathbf{elif}\;d \leq -6.2 \cdot 10^{-123}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{--1}{c}\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 2.7 \cdot 10^{+124}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \end{array} \]

Alternative 2: 85.5% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) INFINITY)
   (* (/ 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))) <= ((double) INFINITY)) {
		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))) <= Inf)
		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], Infinity], 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))) < +inf.0

   1. Initial program 78.8%

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

      1. *-un-lft-identity 78.8%

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

      2. add-sqr-sqrt 78.8%

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

      3. times-frac 78.8%

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

      4. hypot-def 78.8%

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

      5. fma-def 78.8%

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

      6. hypot-def 95.3%

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

   3. Applied egg-rr 95.3%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 0.0%

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

      1. *-un-lft-identity 0.0%

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

      2. add-sqr-sqrt 0.0%

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

      3. times-frac 0.0%

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

      4. hypot-def 0.0%

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

      5. fma-def 0.0%

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

      6. hypot-def 2.6%

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

   3. Applied egg-rr 2.6%

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

   4. Taylor expanded in c around 0 43.7%

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

      1. *-commutative 43.7%

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

      2. unpow2 43.7%

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

      3. times-frac 55.6%

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

   6. Applied egg-rr 55.6%

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

4. Final simplification 87.0%

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

Alternative 3: 83.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;\left(a + b \cdot \frac{d}{c}\right) \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \frac{b}{\frac{c}{d}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -2.6e+80)
     (* (+ a (* b (/ d c))) (/ -1.0 (hypot c d)))
     (if (<= c -8.2e-80)
       t_0
       (if (<= c 4.2e-109)
         (* (/ 1.0 d) (+ b (/ a (/ d c))))
         (if (<= c 5.1e+91)
           t_0
           (* (/ 1.0 (hypot c d)) (+ a (/ b (/ c d))))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double tmp;
	if (c <= -2.6e+80) {
		tmp = (a + (b * (d / c))) * (-1.0 / hypot(c, d));
	} else if (c <= -8.2e-80) {
		tmp = t_0;
	} else if (c <= 4.2e-109) {
		tmp = (1.0 / d) * (b + (a / (d / c)));
	} else if (c <= 5.1e+91) {
		tmp = t_0;
	} else {
		tmp = (1.0 / hypot(c, d)) * (a + (b / (c / d)));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double tmp;
	if (c <= -2.6e+80) {
		tmp = (a + (b * (d / c))) * (-1.0 / Math.hypot(c, d));
	} else if (c <= -8.2e-80) {
		tmp = t_0;
	} else if (c <= 4.2e-109) {
		tmp = (1.0 / d) * (b + (a / (d / c)));
	} else if (c <= 5.1e+91) {
		tmp = t_0;
	} else {
		tmp = (1.0 / Math.hypot(c, d)) * (a + (b / (c / d)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -2.6e+80:
		tmp = (a + (b * (d / c))) * (-1.0 / math.hypot(c, d))
	elif c <= -8.2e-80:
		tmp = t_0
	elif c <= 4.2e-109:
		tmp = (1.0 / d) * (b + (a / (d / c)))
	elif c <= 5.1e+91:
		tmp = t_0
	else:
		tmp = (1.0 / math.hypot(c, d)) * (a + (b / (c / d)))
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (c <= -2.6e+80)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) * Float64(-1.0 / hypot(c, d)));
	elseif (c <= -8.2e-80)
		tmp = t_0;
	elseif (c <= 4.2e-109)
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(a / Float64(d / c))));
	elseif (c <= 5.1e+91)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(a + Float64(b / Float64(c / d))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (c <= -2.6e+80)
		tmp = (a + (b * (d / c))) * (-1.0 / hypot(c, d));
	elseif (c <= -8.2e-80)
		tmp = t_0;
	elseif (c <= 4.2e-109)
		tmp = (1.0 / d) * (b + (a / (d / c)));
	elseif (c <= 5.1e+91)
		tmp = t_0;
	else
		tmp = (1.0 / hypot(c, d)) * (a + (b / (c / d)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.6e+80], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e-80], t$95$0, If[LessEqual[c, 4.2e-109], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.1e+91], t$95$0, N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.59999999999999982e80

   1. Initial program 45.1%

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

      1. *-un-lft-identity 45.1%

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

      2. add-sqr-sqrt 45.1%

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

      3. times-frac 45.0%

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

      4. hypot-def 45.0%

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

      5. fma-def 45.0%

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

      6. hypot-def 68.0%

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

   3. Applied egg-rr 68.0%

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

   4. Taylor expanded in c around -inf 82.8%

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

      1. neg-mul-1 82.8%

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

      2. +-commutative 82.8%

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

      3. unsub-neg 82.8%

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

      4. mul-1-neg 82.8%

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

      5. associate-/l* 89.3%

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

      6. distribute-neg-frac 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in b around 0 82.8%

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

      1. associate-*r/ 89.3%

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

      2. neg-mul-1 89.3%

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

      3. distribute-rgt-neg-in 89.3%

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

   9. Simplified 89.3%

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

   if -2.59999999999999982e80 < c < -8.1999999999999999e-80 or 4.19999999999999992e-109 < c < 5.10000000000000013e91

   1. Initial program 76.9%

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

   if -8.1999999999999999e-80 < c < 4.19999999999999992e-109

   1. Initial program 69.1%

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

      1. *-un-lft-identity 69.1%

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

      2. add-sqr-sqrt 69.1%

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

      3. times-frac 69.1%

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

      4. hypot-def 69.1%

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

      5. fma-def 69.1%

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

      6. hypot-def 82.1%

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

   3. Applied egg-rr 82.1%

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

   4. Taylor expanded in c around 0 83.3%

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

      1. *-commutative 83.3%

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

      2. unpow2 83.3%

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

      3. times-frac 85.8%

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

   6. Applied egg-rr 85.8%

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

      1. +-commutative 85.8%

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

      2. frac-times 83.3%

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

      3. *-un-lft-identity 83.3%

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

      4. frac-times 87.7%

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

      5. *-commutative 87.7%

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

      6. div-inv 87.6%

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

      7. distribute-rgt-out 87.7%

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

      8. *-commutative 87.7%

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

      9. associate-/l* 89.8%

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

   8. Applied egg-rr 89.8%

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

   if 5.10000000000000013e91 < c

   1. Initial program 38.4%

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

      1. *-un-lft-identity 38.4%

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

      2. add-sqr-sqrt 38.4%

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

      3. times-frac 38.4%

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

      4. hypot-def 38.4%

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

      5. fma-def 38.4%

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

      6. hypot-def 54.6%

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

   3. Applied egg-rr 54.6%

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

   4. Taylor expanded in c around inf 73.9%

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

      1. associate-/l* 88.4%

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

   6. Simplified 88.4%

      \[\leadsto \frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \color{blue}{\left(a + \frac{b}{\frac{c}{d}}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;\left(a + b \cdot \frac{d}{c}\right) \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+91}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(a + \frac{b}{\frac{c}{d}}\right)\\ \end{array} \]

Alternative 4: 78.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+30} \lor \neg \left(c \leq 68000\right):\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{--1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.9e+30) (not (<= c 68000.0)))
   (* (+ a (/ b (/ c d))) (/ (- -1.0) c))
   (* (/ 1.0 d) (+ b (/ a (/ d c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.9e+30) || !(c <= 68000.0)) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else {
		tmp = (1.0 / d) * (b + (a / (d / c)));
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((c <= (-2.9d+30)) .or. (.not. (c <= 68000.0d0))) then
        tmp = (a + (b / (c / d))) * (-(-1.0d0) / c)
    else
        tmp = (1.0d0 / d) * (b + (a / (d / c)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.9e+30) || !(c <= 68000.0)) {
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	} else {
		tmp = (1.0 / d) * (b + (a / (d / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.9e+30) or not (c <= 68000.0):
		tmp = (a + (b / (c / d))) * (-(-1.0) / c)
	else:
		tmp = (1.0 / d) * (b + (a / (d / c)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.9e+30) || !(c <= 68000.0))
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) * Float64(Float64(-(-1.0)) / c));
	else
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(a / Float64(d / c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.9e+30) || ~((c <= 68000.0)))
		tmp = (a + (b / (c / d))) * (-(-1.0) / c);
	else
		tmp = (1.0 / d) * (b + (a / (d / c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.9e+30], N[Not[LessEqual[c, 68000.0]], $MachinePrecision]], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[((--1.0) / c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.8999999999999998e30 or 68000 < c

   1. Initial program 50.9%

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

      1. *-un-lft-identity 50.9%

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

      2. add-sqr-sqrt 50.9%

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

      3. times-frac 50.9%

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

      4. hypot-def 50.9%

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

      5. fma-def 50.9%

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

      6. hypot-def 67.0%

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

   3. Applied egg-rr 67.0%

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

   4. Taylor expanded in c around -inf 48.2%

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

      1. neg-mul-1 48.2%

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

      2. +-commutative 48.2%

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

      3. unsub-neg 48.2%

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

      4. mul-1-neg 48.2%

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

      5. associate-/l* 50.9%

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

      6. distribute-neg-frac 50.9%

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

   6. Simplified 50.9%

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

   7. Taylor expanded in c around -inf 84.6%

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

   if -2.8999999999999998e30 < c < 68000

   1. Initial program 70.3%

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

      1. *-un-lft-identity 70.3%

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

      2. add-sqr-sqrt 70.3%

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

      3. times-frac 70.3%

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

      4. hypot-def 70.3%

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

      5. fma-def 70.3%

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

      6. hypot-def 82.1%

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

   3. Applied egg-rr 82.1%

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

   4. Taylor expanded in c around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. unpow2 72.4%

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

      3. times-frac 74.6%

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

   6. Applied egg-rr 74.6%

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

      1. +-commutative 74.6%

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

      2. frac-times 72.4%

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

      3. *-un-lft-identity 72.4%

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

      4. frac-times 75.8%

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

      5. *-commutative 75.8%

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

      6. div-inv 75.6%

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

      7. distribute-rgt-out 75.7%

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

      8. *-commutative 75.7%

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

      9. associate-/l* 77.0%

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

   8. Applied egg-rr 77.0%

      \[\leadsto \color{blue}{\frac{1}{d} \cdot \left(\frac{a}{\frac{d}{c}} + b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+30} \lor \neg \left(c \leq 68000\right):\\ \;\;\;\;\left(a + \frac{b}{\frac{c}{d}}\right) \cdot \frac{--1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \end{array} \]

Alternative 5: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+44} \lor \neg \left(c \leq 72\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -3.8e+44) (not (<= c 72.0)))
   (/ a c)
   (* (/ 1.0 d) (+ b (/ a (/ d c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -3.8e+44) || !(c <= 72.0)) {
		tmp = a / c;
	} else {
		tmp = (1.0 / d) * (b + (a / (d / c)));
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((c <= (-3.8d+44)) .or. (.not. (c <= 72.0d0))) then
        tmp = a / c
    else
        tmp = (1.0d0 / d) * (b + (a / (d / c)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -3.8e+44) || !(c <= 72.0)) {
		tmp = a / c;
	} else {
		tmp = (1.0 / d) * (b + (a / (d / c)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -3.8e+44) or not (c <= 72.0):
		tmp = a / c
	else:
		tmp = (1.0 / d) * (b + (a / (d / c)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -3.8e+44) || !(c <= 72.0))
		tmp = Float64(a / c);
	else
		tmp = Float64(Float64(1.0 / d) * Float64(b + Float64(a / Float64(d / c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -3.8e+44) || ~((c <= 72.0)))
		tmp = a / c;
	else
		tmp = (1.0 / d) * (b + (a / (d / c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -3.8e+44], N[Not[LessEqual[c, 72.0]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(N[(1.0 / d), $MachinePrecision] * N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.8000000000000002e44 or 72 < c

   1. Initial program 51.4%

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

   2. Taylor expanded in c around inf 70.5%

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

   if -3.8000000000000002e44 < c < 72

   1. Initial program 70.1%

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

      1. *-un-lft-identity 70.1%

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

      2. add-sqr-sqrt 70.1%

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

      3. times-frac 70.1%

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

      4. hypot-def 70.1%

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

      5. fma-def 70.1%

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

      6. hypot-def 82.0%

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

   3. Applied egg-rr 82.0%

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

   4. Taylor expanded in c around 0 72.3%

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

      1. *-commutative 72.3%

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

      2. unpow2 72.3%

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

      3. times-frac 74.5%

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

   6. Applied egg-rr 74.5%

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

      1. +-commutative 74.5%

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

      2. frac-times 72.3%

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

      3. *-un-lft-identity 72.3%

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

      4. frac-times 75.6%

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

      5. *-commutative 75.6%

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

      6. div-inv 75.5%

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

      7. distribute-rgt-out 75.6%

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

      8. *-commutative 75.6%

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

      9. associate-/l* 76.9%

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

   8. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{1}{d} \cdot \left(\frac{a}{\frac{d}{c}} + b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+44} \lor \neg \left(c \leq 72\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{d} \cdot \left(b + \frac{a}{\frac{d}{c}}\right)\\ \end{array} \]

Alternative 6: 64.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+45} \lor \neg \left(c \leq 2.2 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -4e+45) (not (<= c 2.2e-73))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4e+45) || !(c <= 2.2e-73)) {
		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 <= (-4d+45)) .or. (.not. (c <= 2.2d-73))) 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 <= -4e+45) || !(c <= 2.2e-73)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -4e+45) or not (c <= 2.2e-73):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -4e+45) || !(c <= 2.2e-73))
		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 <= -4e+45) || ~((c <= 2.2e-73)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -4e+45], N[Not[LessEqual[c, 2.2e-73]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.9999999999999997e45 or 2.2e-73 < c

   1. Initial program 54.4%

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

   2. Taylor expanded in c around inf 67.0%

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

   if -3.9999999999999997e45 < c < 2.2e-73

   1. Initial program 70.2%

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

   2. Taylor expanded in c around 0 66.6%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+45} \lor \neg \left(c \leq 2.2 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]

Alternative 7: 44.1% 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 62.2%

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

2. Taylor expanded in c around inf 42.3%

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

3. Final simplification 42.3%

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

Developer target: 99.5% 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 2023331 
(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))))