Complex division, real part

Percentage Accurate: 60.7% → 78.2%

Time: 5.8s

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: 60.7% 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: 78.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{if}\;c \leq -4.6 \cdot 10^{+151}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-65}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(\frac{c}{d}, \frac{a}{d}, \frac{b}{d}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (+ (/ a c) (* (/ d c) (/ b c)))))
   (if (<= c -4.6e+151)
     t_0
     (if (<= c -1.25e-65)
       (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
       (if (<= c 2.2e+54) (fma (/ c d) (/ a d) (/ b d)) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a / c) + ((d / c) * (b / c));
	double tmp;
	if (c <= -4.6e+151) {
		tmp = t_0;
	} else if (c <= -1.25e-65) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 2.2e+54) {
		tmp = fma((c / d), (a / d), (b / d));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a / c) + Float64(Float64(d / c) * Float64(b / c)))
	tmp = 0.0
	if (c <= -4.6e+151)
		tmp = t_0;
	elseif (c <= -1.25e-65)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 2.2e+54)
		tmp = fma(Float64(c / d), Float64(a / d), Float64(b / d));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a / c), $MachinePrecision] + N[(N[(d / c), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.6e+151], t$95$0, If[LessEqual[c, -1.25e-65], N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+54], N[(N[(c / d), $MachinePrecision] * N[(a / d), $MachinePrecision] + N[(b / d), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.6000000000000002e151 or 2.1999999999999999e54 < c

   1. Initial program 35.6%

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

   2. Taylor expanded in c around inf 80.5%

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

      1. associate-/l* 82.8%

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

      2. associate-/r/ 82.9%

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

      3. unpow2 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in d around 0 80.5%

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

      1. unpow2 80.5%

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

      2. times-frac 91.4%

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

   7. Simplified 91.4%

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

   if -4.6000000000000002e151 < c < -1.24999999999999996e-65

   1. Initial program 81.5%

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

   if -1.24999999999999996e-65 < c < 2.1999999999999999e54

   1. Initial program 64.9%

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

   2. Taylor expanded in c around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. unpow2 83.8%

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

      3. times-frac 84.9%

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

      4. fma-def 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+151}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-65}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(\frac{c}{d}, \frac{a}{d}, \frac{b}{d}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \end{array} \]

Alternative 2: 83.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 5 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) 5e+170)
   (/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
   (+ (/ a c) (* (/ d c) (/ b c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((a * c) + (b * d)) / ((c * c) + (d * d))) <= 5e+170) {
		tmp = (fma(a, c, (b * d)) / hypot(c, d)) / hypot(c, d);
	} else {
		tmp = (a / c) + ((d / c) * (b / c));
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d))) <= 5e+170)
		tmp = Float64(Float64(fma(a, c, Float64(b * d)) / hypot(c, d)) / hypot(c, d));
	else
		tmp = Float64(Float64(a / c) + Float64(Float64(d / c) * Float64(b / c)));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+170], N[(N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] + N[(N[(d / c), $MachinePrecision] * N[(b / c), $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))) < 4.99999999999999977e170

   1. Initial program 71.5%

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

      1. *-un-lft-identity 71.5%

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

      2. add-sqr-sqrt 71.5%

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

      3. times-frac 71.5%

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

      4. hypot-def 71.5%

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

      5. fma-def 71.5%

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

      6. hypot-def 94.8%

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

   3. Applied egg-rr 94.8%

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

      1. associate-*l/ 95.0%

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

      2. *-un-lft-identity 95.0%

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

   5. Applied egg-rr 95.0%

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

   if 4.99999999999999977e170 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 10.8%

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

   2. Taylor expanded in c around inf 47.3%

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

      1. associate-/l* 51.0%

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

      2. associate-/r/ 51.0%

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

      3. unpow2 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in d around 0 47.3%

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

      1. unpow2 47.3%

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

      2. times-frac 59.8%

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

   7. Simplified 59.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 5 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \end{array} \]

Alternative 3: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+55}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (+ (/ a c) (* (/ d c) (/ b c)))))
   (if (<= c -2.5e+153)
     t_0
     (if (<= c -3.8e-64)
       (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
       (if (<= c 1.85e+55) (+ (/ b d) (* (/ c d) (/ a d))) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a / c) + ((d / c) * (b / c));
	double tmp;
	if (c <= -2.5e+153) {
		tmp = t_0;
	} else if (c <= -3.8e-64) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 1.85e+55) {
		tmp = (b / d) + ((c / d) * (a / d));
	} else {
		tmp = t_0;
	}
	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) :: tmp
    t_0 = (a / c) + ((d / c) * (b / c))
    if (c <= (-2.5d+153)) then
        tmp = t_0
    else if (c <= (-3.8d-64)) then
        tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
    else if (c <= 1.85d+55) then
        tmp = (b / d) + ((c / d) * (a / d))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (a / c) + ((d / c) * (b / c));
	double tmp;
	if (c <= -2.5e+153) {
		tmp = t_0;
	} else if (c <= -3.8e-64) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 1.85e+55) {
		tmp = (b / d) + ((c / d) * (a / d));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a / c) + ((d / c) * (b / c))
	tmp = 0
	if c <= -2.5e+153:
		tmp = t_0
	elif c <= -3.8e-64:
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
	elif c <= 1.85e+55:
		tmp = (b / d) + ((c / d) * (a / d))
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a / c) + Float64(Float64(d / c) * Float64(b / c)))
	tmp = 0.0
	if (c <= -2.5e+153)
		tmp = t_0;
	elseif (c <= -3.8e-64)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 1.85e+55)
		tmp = Float64(Float64(b / d) + Float64(Float64(c / d) * Float64(a / d)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a / c) + ((d / c) * (b / c));
	tmp = 0.0;
	if (c <= -2.5e+153)
		tmp = t_0;
	elseif (c <= -3.8e-64)
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	elseif (c <= 1.85e+55)
		tmp = (b / d) + ((c / d) * (a / d));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a / c), $MachinePrecision] + N[(N[(d / c), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e+153], t$95$0, If[LessEqual[c, -3.8e-64], N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e+55], N[(N[(b / d), $MachinePrecision] + N[(N[(c / d), $MachinePrecision] * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.50000000000000009e153 or 1.8500000000000001e55 < c

   1. Initial program 35.6%

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

   2. Taylor expanded in c around inf 80.5%

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

      1. associate-/l* 82.8%

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

      2. associate-/r/ 82.9%

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

      3. unpow2 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in d around 0 80.5%

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

      1. unpow2 80.5%

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

      2. times-frac 91.4%

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

   7. Simplified 91.4%

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

   if -2.50000000000000009e153 < c < -3.8000000000000002e-64

   1. Initial program 81.5%

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

   if -3.8000000000000002e-64 < c < 1.8500000000000001e55

   1. Initial program 64.9%

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

      1. *-un-lft-identity 64.9%

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

      2. add-sqr-sqrt 64.9%

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

      3. times-frac 64.9%

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

      4. hypot-def 64.9%

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

      5. fma-def 64.9%

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

      6. hypot-def 79.0%

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

   3. Applied egg-rr 79.0%

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

   4. Taylor expanded in c around 0 83.8%

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

      1. unpow2 83.8%

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

      2. times-frac 84.9%

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

   6. Simplified 84.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+55}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \end{array} \]

Alternative 4: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.8 \cdot 10^{-64} \lor \neg \left(c \leq 2.3 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -8.8e-64) (not (<= c 2.3e+53)))
   (+ (/ a c) (* (/ d c) (/ b c)))
   (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -8.8e-64) || !(c <= 2.3e+53)) {
		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 ((c <= (-8.8d-64)) .or. (.not. (c <= 2.3d+53))) 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 ((c <= -8.8e-64) || !(c <= 2.3e+53)) {
		tmp = (a / c) + ((d / c) * (b / c));
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -8.8e-64) or not (c <= 2.3e+53):
		tmp = (a / c) + ((d / c) * (b / c))
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -8.8e-64) || !(c <= 2.3e+53))
		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 ((c <= -8.8e-64) || ~((c <= 2.3e+53)))
		tmp = (a / c) + ((d / c) * (b / c));
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -8.8e-64], N[Not[LessEqual[c, 2.3e+53]], $MachinePrecision]], 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 c < -8.7999999999999998e-64 or 2.3000000000000002e53 < c

   1. Initial program 47.4%

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

   2. Taylor expanded in c around inf 75.9%

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

      1. associate-/l* 77.8%

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

      2. associate-/r/ 76.8%

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

      3. unpow2 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in d around 0 75.9%

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

      1. unpow2 75.9%

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

      2. times-frac 84.0%

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

   7. Simplified 84.0%

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

   if -8.7999999999999998e-64 < c < 2.3000000000000002e53

   1. Initial program 64.9%

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

   2. Taylor expanded in c around 0 75.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.8 \cdot 10^{-64} \lor \neg \left(c \leq 2.3 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]

Alternative 5: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-60} \lor \neg \left(c \leq 5 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -1.1e-60) (not (<= c 5e+56)))
   (+ (/ 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 <= -1.1e-60) || !(c <= 5e+56)) {
		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 <= (-1.1d-60)) .or. (.not. (c <= 5d+56))) 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 <= -1.1e-60) || !(c <= 5e+56)) {
		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 <= -1.1e-60) or not (c <= 5e+56):
		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 <= -1.1e-60) || !(c <= 5e+56))
		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 <= -1.1e-60) || ~((c <= 5e+56)))
		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, -1.1e-60], N[Not[LessEqual[c, 5e+56]], $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 < -1.0999999999999999e-60 or 5.00000000000000024e56 < c

   1. Initial program 47.4%

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

   2. Taylor expanded in c around inf 75.9%

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

      1. associate-/l* 77.8%

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

      2. associate-/r/ 76.8%

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

      3. unpow2 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in d around 0 75.9%

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

      1. unpow2 75.9%

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

      2. times-frac 84.0%

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

   7. Simplified 84.0%

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

   if -1.0999999999999999e-60 < c < 5.00000000000000024e56

   1. Initial program 64.9%

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

      1. *-un-lft-identity 64.9%

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

      2. add-sqr-sqrt 64.9%

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

      3. times-frac 64.9%

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

      4. hypot-def 64.9%

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

      5. fma-def 64.9%

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

      6. hypot-def 79.0%

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

   3. Applied egg-rr 79.0%

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

   4. Taylor expanded in c around 0 83.8%

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

      1. unpow2 83.8%

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

      2. times-frac 84.9%

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

   6. Simplified 84.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-60} \lor \neg \left(c \leq 5 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{a}{c} + \frac{d}{c} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{c}{d} \cdot \frac{a}{d}\\ \end{array} \]

Alternative 6: 62.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.3 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -5.3e-61) (/ a c) (if (<= c 9.5e+54) (/ b d) (/ a c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -5.3e-61) {
		tmp = a / c;
	} else if (c <= 9.5e+54) {
		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 <= (-5.3d-61)) then
        tmp = a / c
    else if (c <= 9.5d+54) 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 <= -5.3e-61) {
		tmp = a / c;
	} else if (c <= 9.5e+54) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -5.3e-61:
		tmp = a / c
	elif c <= 9.5e+54:
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -5.3e-61)
		tmp = Float64(a / c);
	elseif (c <= 9.5e+54)
		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 <= -5.3e-61)
		tmp = a / c;
	elseif (c <= 9.5e+54)
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -5.3e-61], N[(a / c), $MachinePrecision], If[LessEqual[c, 9.5e+54], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -5.3e-61 or 9.4999999999999999e54 < c

   1. Initial program 47.4%

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

   2. Taylor expanded in c around inf 72.5%

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

   if -5.3e-61 < c < 9.4999999999999999e54

   1. Initial program 64.9%

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

   2. Taylor expanded in c around 0 75.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.3 \cdot 10^{-61}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]

Alternative 7: 42.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \frac{a}{c} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.6%

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

2. Taylor expanded in c around inf 45.4%

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

3. Final simplification 45.4%

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

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 2023240 
(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))))