Complex division, real part

Percentage Accurate: 62.0% → 78.3%

Time: 10.0s

Alternatives: 8

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 62.0% 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: 78.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b}{c} \cdot d\\ \mathbf{if}\;c \leq -2.9 \cdot 10^{+70}:\\ \;\;\;\;\frac{a + t\_0}{c}\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{a \cdot \left(c + b \cdot \frac{d}{a}\right)}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \left(t\_0 - a \cdot \left(\frac{d}{c} \cdot \frac{d}{c}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (* (/ b c) d)))
   (if (<= c -2.9e+70)
     (/ (+ a t_0) c)
     (if (<= c 3.6e-95)
       (/ (+ b (* a (/ c d))) d)
       (if (<= c 1.25e+14)
         (/ (* a (+ c (* b (/ d a)))) (+ (* c c) (* d d)))
         (/ (+ a (- t_0 (* a (* (/ d c) (/ d c))))) c))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b / c) * d;
	double tmp;
	if (c <= -2.9e+70) {
		tmp = (a + t_0) / c;
	} else if (c <= 3.6e-95) {
		tmp = (b + (a * (c / d))) / d;
	} else if (c <= 1.25e+14) {
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d));
	} else {
		tmp = (a + (t_0 - (a * ((d / c) * (d / c))))) / 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) :: t_0
    real(8) :: tmp
    t_0 = (b / c) * d
    if (c <= (-2.9d+70)) then
        tmp = (a + t_0) / c
    else if (c <= 3.6d-95) then
        tmp = (b + (a * (c / d))) / d
    else if (c <= 1.25d+14) then
        tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d))
    else
        tmp = (a + (t_0 - (a * ((d / c) * (d / c))))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (b / c) * d;
	double tmp;
	if (c <= -2.9e+70) {
		tmp = (a + t_0) / c;
	} else if (c <= 3.6e-95) {
		tmp = (b + (a * (c / d))) / d;
	} else if (c <= 1.25e+14) {
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d));
	} else {
		tmp = (a + (t_0 - (a * ((d / c) * (d / c))))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b / c) * d
	tmp = 0
	if c <= -2.9e+70:
		tmp = (a + t_0) / c
	elif c <= 3.6e-95:
		tmp = (b + (a * (c / d))) / d
	elif c <= 1.25e+14:
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d))
	else:
		tmp = (a + (t_0 - (a * ((d / c) * (d / c))))) / c
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b / c) * d)
	tmp = 0.0
	if (c <= -2.9e+70)
		tmp = Float64(Float64(a + t_0) / c);
	elseif (c <= 3.6e-95)
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	elseif (c <= 1.25e+14)
		tmp = Float64(Float64(a * Float64(c + Float64(b * Float64(d / a)))) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = Float64(Float64(a + Float64(t_0 - Float64(a * Float64(Float64(d / c) * Float64(d / c))))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b / c) * d;
	tmp = 0.0;
	if (c <= -2.9e+70)
		tmp = (a + t_0) / c;
	elseif (c <= 3.6e-95)
		tmp = (b + (a * (c / d))) / d;
	elseif (c <= 1.25e+14)
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d));
	else
		tmp = (a + (t_0 - (a * ((d / c) * (d / c))))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b / c), $MachinePrecision] * d), $MachinePrecision]}, If[LessEqual[c, -2.9e+70], N[(N[(a + t$95$0), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 3.6e-95], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 1.25e+14], N[(N[(a * N[(c + N[(b * N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(t$95$0 - N[(a * N[(N[(d / c), $MachinePrecision] * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.8999999999999998e70

   1. Initial program 36.0%

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

   3. Taylor expanded in c around inf 85.9%

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

      1. *-commutative 85.9%

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

   5. Simplified 85.9%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

   7. Applied egg-rr 89.6%

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

   if -2.8999999999999998e70 < c < 3.6e-95

   1. Initial program 66.1%

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

   3. Taylor expanded in d around inf 85.3%

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

      1. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   if 3.6e-95 < c < 1.25e14

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 94.5%

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

      1. associate-/l* 94.7%

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

   5. Simplified 94.7%

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

   if 1.25e14 < c

   1. Initial program 43.9%

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

   3. Taylor expanded in c around inf 68.6%

      \[\leadsto \color{blue}{\frac{a + \left(-1 \cdot \frac{a \cdot {d}^{2}}{{c}^{2}} + \frac{b \cdot d}{c}\right)}{c}} \]
   4. Step-by-step derivation

      1. +-commutative 68.6%

         \[\leadsto \frac{a + \color{blue}{\left(\frac{b \cdot d}{c} + -1 \cdot \frac{a \cdot {d}^{2}}{{c}^{2}}\right)}}{c} \]

      2. mul-1-neg 68.6%

         \[\leadsto \frac{a + \left(\frac{b \cdot d}{c} + \color{blue}{\left(-\frac{a \cdot {d}^{2}}{{c}^{2}}\right)}\right)}{c} \]

      3. unsub-neg 68.6%

         \[\leadsto \frac{a + \color{blue}{\left(\frac{b \cdot d}{c} - \frac{a \cdot {d}^{2}}{{c}^{2}}\right)}}{c} \]

      4. *-commutative 68.6%

         \[\leadsto \frac{a + \left(\frac{\color{blue}{d \cdot b}}{c} - \frac{a \cdot {d}^{2}}{{c}^{2}}\right)}{c} \]

      5. associate-/l* 72.3%

         \[\leadsto \frac{a + \left(\color{blue}{d \cdot \frac{b}{c}} - \frac{a \cdot {d}^{2}}{{c}^{2}}\right)}{c} \]

      6. associate-/l* 74.6%

         \[\leadsto \frac{a + \left(d \cdot \frac{b}{c} - \color{blue}{a \cdot \frac{{d}^{2}}{{c}^{2}}}\right)}{c} \]

   5. Simplified 74.6%

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

      1. unpow2 74.6%

         \[\leadsto \frac{a + \left(d \cdot \frac{b}{c} - a \cdot \frac{\color{blue}{d \cdot d}}{{c}^{2}}\right)}{c} \]

      2. unpow2 74.6%

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

      3. times-frac 81.8%

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

   7. Applied egg-rr 81.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+70}:\\ \;\;\;\;\frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{a \cdot \left(c + b \cdot \frac{d}{a}\right)}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \left(\frac{b}{c} \cdot d - a \cdot \left(\frac{d}{c} \cdot \frac{d}{c}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{if}\;c \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-95}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{+14}:\\ \;\;\;\;\frac{a \cdot \left(c + b \cdot \frac{d}{a}\right)}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ a (* (/ b c) d)) c)))
   (if (<= c -1.25e+71)
     t_0
     (if (<= c 3.2e-95)
       (/ (+ b (* a (/ c d))) d)
       (if (<= c 1.06e+14)
         (/ (* a (+ c (* b (/ d a)))) (+ (* c c) (* d d)))
         t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a + ((b / c) * d)) / c;
	double tmp;
	if (c <= -1.25e+71) {
		tmp = t_0;
	} else if (c <= 3.2e-95) {
		tmp = (b + (a * (c / d))) / d;
	} else if (c <= 1.06e+14) {
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * 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 + ((b / c) * d)) / c
    if (c <= (-1.25d+71)) then
        tmp = t_0
    else if (c <= 3.2d-95) then
        tmp = (b + (a * (c / d))) / d
    else if (c <= 1.06d+14) then
        tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * 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 + ((b / c) * d)) / c;
	double tmp;
	if (c <= -1.25e+71) {
		tmp = t_0;
	} else if (c <= 3.2e-95) {
		tmp = (b + (a * (c / d))) / d;
	} else if (c <= 1.06e+14) {
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a + ((b / c) * d)) / c
	tmp = 0
	if c <= -1.25e+71:
		tmp = t_0
	elif c <= 3.2e-95:
		tmp = (b + (a * (c / d))) / d
	elif c <= 1.06e+14:
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d))
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a + Float64(Float64(b / c) * d)) / c)
	tmp = 0.0
	if (c <= -1.25e+71)
		tmp = t_0;
	elseif (c <= 3.2e-95)
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	elseif (c <= 1.06e+14)
		tmp = Float64(Float64(a * Float64(c + Float64(b * Float64(d / a)))) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a + ((b / c) * d)) / c;
	tmp = 0.0;
	if (c <= -1.25e+71)
		tmp = t_0;
	elseif (c <= 3.2e-95)
		tmp = (b + (a * (c / d))) / d;
	elseif (c <= 1.06e+14)
		tmp = (a * (c + (b * (d / a)))) / ((c * c) + (d * d));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a + N[(N[(b / c), $MachinePrecision] * d), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -1.25e+71], t$95$0, If[LessEqual[c, 3.2e-95], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 1.06e+14], N[(N[(a * N[(c + N[(b * N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.24999999999999993e71 or 1.06e14 < c

   1. Initial program 39.9%

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

   3. Taylor expanded in c around inf 81.9%

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

      1. *-commutative 81.9%

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

   5. Simplified 81.9%

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

      1. associate-*r/ 85.6%

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

      2. *-commutative 85.6%

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

   7. Applied egg-rr 85.6%

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

   if -1.24999999999999993e71 < c < 3.1999999999999997e-95

   1. Initial program 66.1%

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

   3. Taylor expanded in d around inf 85.3%

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

      1. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   if 3.1999999999999997e-95 < c < 1.06e14

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 94.5%

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

      1. associate-/l* 94.7%

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

   5. Simplified 94.7%

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

Alternative 3: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{if}\;c \leq -1.28 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{+14}:\\ \;\;\;\;\frac{c \cdot a + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ a (* (/ b c) d)) c)))
   (if (<= c -1.28e+71)
     t_0
     (if (<= c 5.1e-99)
       (/ (+ b (* a (/ c d))) d)
       (if (<= c 1.28e+14) (/ (+ (* c a) (* b d)) (+ (* c c) (* d d))) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a + ((b / c) * d)) / c;
	double tmp;
	if (c <= -1.28e+71) {
		tmp = t_0;
	} else if (c <= 5.1e-99) {
		tmp = (b + (a * (c / d))) / d;
	} else if (c <= 1.28e+14) {
		tmp = ((c * a) + (b * d)) / ((c * c) + (d * 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 + ((b / c) * d)) / c
    if (c <= (-1.28d+71)) then
        tmp = t_0
    else if (c <= 5.1d-99) then
        tmp = (b + (a * (c / d))) / d
    else if (c <= 1.28d+14) then
        tmp = ((c * a) + (b * d)) / ((c * c) + (d * 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 + ((b / c) * d)) / c;
	double tmp;
	if (c <= -1.28e+71) {
		tmp = t_0;
	} else if (c <= 5.1e-99) {
		tmp = (b + (a * (c / d))) / d;
	} else if (c <= 1.28e+14) {
		tmp = ((c * a) + (b * d)) / ((c * c) + (d * d));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a + ((b / c) * d)) / c
	tmp = 0
	if c <= -1.28e+71:
		tmp = t_0
	elif c <= 5.1e-99:
		tmp = (b + (a * (c / d))) / d
	elif c <= 1.28e+14:
		tmp = ((c * a) + (b * d)) / ((c * c) + (d * d))
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a + Float64(Float64(b / c) * d)) / c)
	tmp = 0.0
	if (c <= -1.28e+71)
		tmp = t_0;
	elseif (c <= 5.1e-99)
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	elseif (c <= 1.28e+14)
		tmp = Float64(Float64(Float64(c * a) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a + ((b / c) * d)) / c;
	tmp = 0.0;
	if (c <= -1.28e+71)
		tmp = t_0;
	elseif (c <= 5.1e-99)
		tmp = (b + (a * (c / d))) / d;
	elseif (c <= 1.28e+14)
		tmp = ((c * a) + (b * d)) / ((c * c) + (d * d));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a + N[(N[(b / c), $MachinePrecision] * d), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -1.28e+71], t$95$0, If[LessEqual[c, 5.1e-99], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 1.28e+14], N[(N[(N[(c * a), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.2800000000000001e71 or 1.28e14 < c

   1. Initial program 39.9%

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

   3. Taylor expanded in c around inf 81.9%

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

      1. *-commutative 81.9%

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

   5. Simplified 81.9%

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

      1. associate-*r/ 85.6%

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

      2. *-commutative 85.6%

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

   7. Applied egg-rr 85.6%

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

   if -1.2800000000000001e71 < c < 5.0999999999999999e-99

   1. Initial program 66.1%

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

   3. Taylor expanded in d around inf 85.3%

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

      1. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   if 5.0999999999999999e-99 < c < 1.28e14

   1. Initial program 94.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.28 \cdot 10^{+71}:\\ \;\;\;\;\frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{+14}:\\ \;\;\;\;\frac{c \cdot a + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{b}{c} \cdot d}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+70} \lor \neg \left(c \leq 2.5 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.9e+70) (not (<= c 2.5e-79)))
   (/ (+ a (* (/ b c) d)) c)
   (/ (+ b (* a (/ c d))) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.9e+70) || !(c <= 2.5e-79)) {
		tmp = (a + ((b / c) * d)) / c;
	} else {
		tmp = (b + (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 <= (-2.9d+70)) .or. (.not. (c <= 2.5d-79))) then
        tmp = (a + ((b / c) * d)) / c
    else
        tmp = (b + (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 <= -2.9e+70) || !(c <= 2.5e-79)) {
		tmp = (a + ((b / c) * d)) / c;
	} else {
		tmp = (b + (a * (c / d))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.9e+70) or not (c <= 2.5e-79):
		tmp = (a + ((b / c) * d)) / c
	else:
		tmp = (b + (a * (c / d))) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.9e+70) || !(c <= 2.5e-79))
		tmp = Float64(Float64(a + Float64(Float64(b / c) * d)) / c);
	else
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.9e+70) || ~((c <= 2.5e-79)))
		tmp = (a + ((b / c) * d)) / c;
	else
		tmp = (b + (a * (c / d))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.9e+70], N[Not[LessEqual[c, 2.5e-79]], $MachinePrecision]], N[(N[(a + N[(N[(b / c), $MachinePrecision] * d), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.8999999999999998e70 or 2.5e-79 < c

   1. Initial program 47.8%

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

   3. Taylor expanded in c around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

      1. associate-*r/ 81.0%

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

      2. *-commutative 81.0%

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

   7. Applied egg-rr 81.0%

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

   if -2.8999999999999998e70 < c < 2.5e-79

   1. Initial program 67.4%

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

   3. Taylor expanded in d around inf 84.8%

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

      1. associate-/l* 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+70} \lor \neg \left(c \leq 2.5 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{-19} \lor \neg \left(c \leq 1.3 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -6e-19) (not (<= c 1.3e-80)))
   (/ (+ a (* (/ b c) d)) c)
   (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -6e-19) || !(c <= 1.3e-80)) {
		tmp = (a + ((b / c) * d)) / 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 <= (-6d-19)) .or. (.not. (c <= 1.3d-80))) then
        tmp = (a + ((b / c) * d)) / 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 <= -6e-19) || !(c <= 1.3e-80)) {
		tmp = (a + ((b / c) * d)) / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -6e-19) or not (c <= 1.3e-80):
		tmp = (a + ((b / c) * d)) / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -6e-19) || !(c <= 1.3e-80))
		tmp = Float64(Float64(a + Float64(Float64(b / c) * d)) / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -6e-19) || ~((c <= 1.3e-80)))
		tmp = (a + ((b / c) * d)) / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -6e-19], N[Not[LessEqual[c, 1.3e-80]], $MachinePrecision]], N[(N[(a + N[(N[(b / c), $MachinePrecision] * d), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.99999999999999985e-19 or 1.3e-80 < c

   1. Initial program 50.4%

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

   3. Taylor expanded in c around inf 74.0%

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

      1. *-commutative 74.0%

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

   5. Simplified 74.0%

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

      1. associate-*r/ 76.1%

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

      2. *-commutative 76.1%

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

   7. Applied egg-rr 76.1%

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

   if -5.99999999999999985e-19 < c < 1.3e-80

   1. Initial program 67.5%

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

   3. Taylor expanded in c around 0 68.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{-19} \lor \neg \left(c \leq 1.3 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{a + \frac{b}{c} \cdot d}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-21} \lor \neg \left(c \leq 1.85 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -1.5e-21) (not (<= c 1.85e-79)))
   (/ (+ a (* b (/ d c))) c)
   (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.5e-21) || !(c <= 1.85e-79)) {
		tmp = (a + (b * (d / c))) / 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 <= (-1.5d-21)) .or. (.not. (c <= 1.85d-79))) then
        tmp = (a + (b * (d / c))) / 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 <= -1.5e-21) || !(c <= 1.85e-79)) {
		tmp = (a + (b * (d / c))) / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -1.5e-21) or not (c <= 1.85e-79):
		tmp = (a + (b * (d / c))) / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -1.5e-21) || !(c <= 1.85e-79))
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -1.5e-21) || ~((c <= 1.85e-79)))
		tmp = (a + (b * (d / c))) / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -1.5e-21], N[Not[LessEqual[c, 1.85e-79]], $MachinePrecision]], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.49999999999999996e-21 or 1.85000000000000009e-79 < c

   1. Initial program 50.4%

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

      1. div-inv 50.3%

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

      2. fma-define 50.3%

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

      3. add-sqr-sqrt 50.3%

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

      4. pow2 50.3%

         \[\leadsto \mathsf{fma}\left(a, c, b \cdot d\right) \cdot \frac{1}{\color{blue}{{\left(\sqrt{c \cdot c + d \cdot d}\right)}^{2}}} \]

      5. hypot-define 50.3%

         \[\leadsto \mathsf{fma}\left(a, c, b \cdot d\right) \cdot \frac{1}{{\color{blue}{\left(\mathsf{hypot}\left(c, d\right)\right)}}^{2}} \]

   4. Applied egg-rr 50.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, c, b \cdot d\right) \cdot \frac{1}{{\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}}} \]

   5. Taylor expanded in c around inf 74.0%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   if -1.49999999999999996e-21 < c < 1.85000000000000009e-79

   1. Initial program 67.5%

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

   3. Taylor expanded in c around 0 68.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-21} \lor \neg \left(c \leq 1.85 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-21} \lor \neg \left(c \leq 14500000000\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -3.2e-21) (not (<= c 14500000000.0))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -3.2e-21) || !(c <= 14500000000.0)) {
		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 <= (-3.2d-21)) .or. (.not. (c <= 14500000000.0d0))) 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 <= -3.2e-21) || !(c <= 14500000000.0)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -3.2e-21) or not (c <= 14500000000.0):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -3.2e-21) || !(c <= 14500000000.0))
		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 <= -3.2e-21) || ~((c <= 14500000000.0)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -3.2e-21], N[Not[LessEqual[c, 14500000000.0]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.2000000000000002e-21 or 1.45e10 < c

   1. Initial program 44.0%

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

   3. Taylor expanded in c around inf 63.5%

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

   if -3.2000000000000002e-21 < c < 1.45e10

   1. Initial program 71.4%

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

   3. Taylor expanded in c around 0 64.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-21} \lor \neg \left(c \leq 14500000000\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.0% 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 57.6%

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

3. Taylor expanded in c around inf 40.4%

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

Developer Target 1: 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 2024180 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (fabs d) (fabs c)) (/ (+ a (* b (/ d c))) (+ c (* d (/ d c)))) (/ (+ b (* a (/ c d))) (+ d (* c (/ c d))))))

  (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))