Complex division, real part

Percentage Accurate: 61.0% → 80.4%

Time: 8.5s

Alternatives: 12

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: 61.0% 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: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -0.72:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq 1.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{elif}\;d \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;\frac{d \cdot b + a \cdot c}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -0.72)
   (/ (+ b (/ a (/ d c))) d)
   (if (<= d 1.7e-101)
     (/ (+ a (/ (* d b) c)) c)
     (if (<= d 1.05e+85)
       (/ (+ (* d b) (* a c)) (+ (* c c) (* d d)))
       (/ (+ b (* c (/ a d))) d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.72) {
		tmp = (b + (a / (d / c))) / d;
	} else if (d <= 1.7e-101) {
		tmp = (a + ((d * b) / c)) / c;
	} else if (d <= 1.05e+85) {
		tmp = ((d * b) + (a * c)) / ((c * c) + (d * d));
	} else {
		tmp = (b + (c * (a / 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 (d <= (-0.72d0)) then
        tmp = (b + (a / (d / c))) / d
    else if (d <= 1.7d-101) then
        tmp = (a + ((d * b) / c)) / c
    else if (d <= 1.05d+85) then
        tmp = ((d * b) + (a * c)) / ((c * c) + (d * d))
    else
        tmp = (b + (c * (a / d))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.72) {
		tmp = (b + (a / (d / c))) / d;
	} else if (d <= 1.7e-101) {
		tmp = (a + ((d * b) / c)) / c;
	} else if (d <= 1.05e+85) {
		tmp = ((d * b) + (a * c)) / ((c * c) + (d * d));
	} else {
		tmp = (b + (c * (a / d))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -0.72:
		tmp = (b + (a / (d / c))) / d
	elif d <= 1.7e-101:
		tmp = (a + ((d * b) / c)) / c
	elif d <= 1.05e+85:
		tmp = ((d * b) + (a * c)) / ((c * c) + (d * d))
	else:
		tmp = (b + (c * (a / d))) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -0.72)
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) / d);
	elseif (d <= 1.7e-101)
		tmp = Float64(Float64(a + Float64(Float64(d * b) / c)) / c);
	elseif (d <= 1.05e+85)
		tmp = Float64(Float64(Float64(d * b) + Float64(a * c)) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = Float64(Float64(b + Float64(c * Float64(a / d))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -0.72)
		tmp = (b + (a / (d / c))) / d;
	elseif (d <= 1.7e-101)
		tmp = (a + ((d * b) / c)) / c;
	elseif (d <= 1.05e+85)
		tmp = ((d * b) + (a * c)) / ((c * c) + (d * d));
	else
		tmp = (b + (c * (a / d))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -0.72], N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 1.7e-101], N[(N[(a + N[(N[(d * b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 1.05e+85], N[(N[(N[(d * b), $MachinePrecision] + N[(a * c), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(c * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if d < -0.71999999999999997

   1. Initial program 40.5%

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

   3. Taylor expanded in d around inf 77.6%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

      1. clear-num 80.4%

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

      2. un-div-inv 80.4%

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

   7. Applied egg-rr 80.4%

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

   if -0.71999999999999997 < d < 1.69999999999999995e-101

   1. Initial program 77.6%

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

   3. Taylor expanded in c around inf 87.8%

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

   if 1.69999999999999995e-101 < d < 1.05000000000000005e85

   1. Initial program 87.8%

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

   if 1.05000000000000005e85 < d

   1. Initial program 37.1%

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

   3. Taylor expanded in d around inf 81.2%

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

      1. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

      1. clear-num 89.8%

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

      2. un-div-inv 89.8%

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

   7. Applied egg-rr 89.8%

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

      1. associate-/r/ 90.6%

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

   9. Applied egg-rr 90.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -0.72:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq 1.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{elif}\;d \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;\frac{d \cdot b + a \cdot c}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -2.25 \cdot 10^{+24}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq -1.75:\\ \;\;\;\;\frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;d \leq 1.32 \cdot 10^{+21}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.6e+76)
   (/ b d)
   (if (<= d -2.25e+24)
     (/ (+ a (* b (/ d c))) c)
     (if (<= d -1.75)
       (/ (/ (* a c) d) d)
       (if (<= d 1.32e+21) (/ (+ a (/ (* d b) c)) c) (/ b d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.6e+76) {
		tmp = b / d;
	} else if (d <= -2.25e+24) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= -1.75) {
		tmp = ((a * c) / d) / d;
	} else if (d <= 1.32e+21) {
		tmp = (a + ((d * b) / 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 (d <= (-1.6d+76)) then
        tmp = b / d
    else if (d <= (-2.25d+24)) then
        tmp = (a + (b * (d / c))) / c
    else if (d <= (-1.75d0)) then
        tmp = ((a * c) / d) / d
    else if (d <= 1.32d+21) then
        tmp = (a + ((d * b) / 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 (d <= -1.6e+76) {
		tmp = b / d;
	} else if (d <= -2.25e+24) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= -1.75) {
		tmp = ((a * c) / d) / d;
	} else if (d <= 1.32e+21) {
		tmp = (a + ((d * b) / c)) / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.6e+76:
		tmp = b / d
	elif d <= -2.25e+24:
		tmp = (a + (b * (d / c))) / c
	elif d <= -1.75:
		tmp = ((a * c) / d) / d
	elif d <= 1.32e+21:
		tmp = (a + ((d * b) / c)) / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.6e+76)
		tmp = Float64(b / d);
	elseif (d <= -2.25e+24)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	elseif (d <= -1.75)
		tmp = Float64(Float64(Float64(a * c) / d) / d);
	elseif (d <= 1.32e+21)
		tmp = Float64(Float64(a + Float64(Float64(d * b) / c)) / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.6e+76)
		tmp = b / d;
	elseif (d <= -2.25e+24)
		tmp = (a + (b * (d / c))) / c;
	elseif (d <= -1.75)
		tmp = ((a * c) / d) / d;
	elseif (d <= 1.32e+21)
		tmp = (a + ((d * b) / c)) / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.6e+76], N[(b / d), $MachinePrecision], If[LessEqual[d, -2.25e+24], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, -1.75], N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 1.32e+21], N[(N[(a + N[(N[(d * b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -1.59999999999999988e76 or 1.32e21 < d

   1. Initial program 40.6%

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

   3. Taylor expanded in c around 0 79.4%

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

   if -1.59999999999999988e76 < d < -2.2500000000000001e24

   1. Initial program 46.2%

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

   3. Taylor expanded in c around inf 56.1%

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

      1. associate-/l* 64.9%

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

   5. Simplified 64.9%

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

   if -2.2500000000000001e24 < d < -1.75

   1. Initial program 100.0%

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

   3. Taylor expanded in d around inf 100.0%

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

      1. associate-/l* 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in b around 0 81.1%

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

      1. associate-/l* 80.8%

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

   8. Simplified 80.8%

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

      1. associate-*r/ 81.1%

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

      2. unpow2 81.1%

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

      3. associate-/r* 81.1%

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

      4. associate-/l* 80.5%

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

   10. Applied egg-rr 80.5%

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

   11. Taylor expanded in a around 0 81.1%

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

   if -1.75 < d < 1.32e21

   1. Initial program 79.5%

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

   3. Taylor expanded in c around inf 82.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -2.25 \cdot 10^{+24}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq -1.75:\\ \;\;\;\;\frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;d \leq 1.32 \cdot 10^{+21}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -0.9:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq 2.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{elif}\;d \leq 3.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 5.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -0.9)
   (/ (+ b (/ a (/ d c))) d)
   (if (<= d 2.4e-41)
     (/ (+ a (/ (* d b) c)) c)
     (if (<= d 3.8e-12)
       (/ (* d b) (+ (* c c) (* d d)))
       (if (<= d 5.6e+47)
         (/ (+ a (* b (/ d c))) c)
         (/ (+ b (* c (/ a d))) d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.9) {
		tmp = (b + (a / (d / c))) / d;
	} else if (d <= 2.4e-41) {
		tmp = (a + ((d * b) / c)) / c;
	} else if (d <= 3.8e-12) {
		tmp = (d * b) / ((c * c) + (d * d));
	} else if (d <= 5.6e+47) {
		tmp = (a + (b * (d / c))) / c;
	} else {
		tmp = (b + (c * (a / 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 (d <= (-0.9d0)) then
        tmp = (b + (a / (d / c))) / d
    else if (d <= 2.4d-41) then
        tmp = (a + ((d * b) / c)) / c
    else if (d <= 3.8d-12) then
        tmp = (d * b) / ((c * c) + (d * d))
    else if (d <= 5.6d+47) then
        tmp = (a + (b * (d / c))) / c
    else
        tmp = (b + (c * (a / d))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.9) {
		tmp = (b + (a / (d / c))) / d;
	} else if (d <= 2.4e-41) {
		tmp = (a + ((d * b) / c)) / c;
	} else if (d <= 3.8e-12) {
		tmp = (d * b) / ((c * c) + (d * d));
	} else if (d <= 5.6e+47) {
		tmp = (a + (b * (d / c))) / c;
	} else {
		tmp = (b + (c * (a / d))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -0.9:
		tmp = (b + (a / (d / c))) / d
	elif d <= 2.4e-41:
		tmp = (a + ((d * b) / c)) / c
	elif d <= 3.8e-12:
		tmp = (d * b) / ((c * c) + (d * d))
	elif d <= 5.6e+47:
		tmp = (a + (b * (d / c))) / c
	else:
		tmp = (b + (c * (a / d))) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -0.9)
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) / d);
	elseif (d <= 2.4e-41)
		tmp = Float64(Float64(a + Float64(Float64(d * b) / c)) / c);
	elseif (d <= 3.8e-12)
		tmp = Float64(Float64(d * b) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 5.6e+47)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	else
		tmp = Float64(Float64(b + Float64(c * Float64(a / d))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -0.9)
		tmp = (b + (a / (d / c))) / d;
	elseif (d <= 2.4e-41)
		tmp = (a + ((d * b) / c)) / c;
	elseif (d <= 3.8e-12)
		tmp = (d * b) / ((c * c) + (d * d));
	elseif (d <= 5.6e+47)
		tmp = (a + (b * (d / c))) / c;
	else
		tmp = (b + (c * (a / d))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -0.9], N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 2.4e-41], N[(N[(a + N[(N[(d * b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 3.8e-12], N[(N[(d * b), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 5.6e+47], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(c * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if d < -0.900000000000000022

   1. Initial program 40.5%

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

   3. Taylor expanded in d around inf 77.6%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

      1. clear-num 80.4%

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

      2. un-div-inv 80.4%

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

   7. Applied egg-rr 80.4%

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

   if -0.900000000000000022 < d < 2.40000000000000022e-41

   1. Initial program 77.8%

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

   3. Taylor expanded in c around inf 86.4%

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

   if 2.40000000000000022e-41 < d < 3.79999999999999996e-12

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0 90.7%

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

   if 3.79999999999999996e-12 < d < 5.59999999999999976e47

   1. Initial program 77.1%

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

   3. Taylor expanded in c around inf 75.7%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   if 5.59999999999999976e47 < d

   1. Initial program 45.1%

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

   3. Taylor expanded in d around inf 81.6%

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

      1. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. un-div-inv 89.1%

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

   7. Applied egg-rr 89.1%

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

      1. associate-/r/ 89.8%

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

   9. Applied egg-rr 89.8%

      \[\leadsto \frac{b + \color{blue}{\frac{a}{d} \cdot c}}{d} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -0.9:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq 2.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{elif}\;d \leq 3.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 5.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.26 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq -0.28:\\ \;\;\;\;\frac{a}{d} \cdot \frac{c}{d}\\ \mathbf{elif}\;d \leq -1.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{d \cdot \frac{b}{c}}{c}\\ \mathbf{elif}\;d \leq 1.55 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.26e+76)
   (/ b d)
   (if (<= d -1.4e+37)
     (/ a c)
     (if (<= d -0.28)
       (* (/ a d) (/ c d))
       (if (<= d -1.6e-70)
         (/ (* d (/ b c)) c)
         (if (<= d 1.55e-40) (/ a c) (/ b d)))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.26e+76) {
		tmp = b / d;
	} else if (d <= -1.4e+37) {
		tmp = a / c;
	} else if (d <= -0.28) {
		tmp = (a / d) * (c / d);
	} else if (d <= -1.6e-70) {
		tmp = (d * (b / c)) / c;
	} else if (d <= 1.55e-40) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= (-1.26d+76)) then
        tmp = b / d
    else if (d <= (-1.4d+37)) then
        tmp = a / c
    else if (d <= (-0.28d0)) then
        tmp = (a / d) * (c / d)
    else if (d <= (-1.6d-70)) then
        tmp = (d * (b / c)) / c
    else if (d <= 1.55d-40) then
        tmp = a / c
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.26e+76) {
		tmp = b / d;
	} else if (d <= -1.4e+37) {
		tmp = a / c;
	} else if (d <= -0.28) {
		tmp = (a / d) * (c / d);
	} else if (d <= -1.6e-70) {
		tmp = (d * (b / c)) / c;
	} else if (d <= 1.55e-40) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.26e+76:
		tmp = b / d
	elif d <= -1.4e+37:
		tmp = a / c
	elif d <= -0.28:
		tmp = (a / d) * (c / d)
	elif d <= -1.6e-70:
		tmp = (d * (b / c)) / c
	elif d <= 1.55e-40:
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.26e+76)
		tmp = Float64(b / d);
	elseif (d <= -1.4e+37)
		tmp = Float64(a / c);
	elseif (d <= -0.28)
		tmp = Float64(Float64(a / d) * Float64(c / d));
	elseif (d <= -1.6e-70)
		tmp = Float64(Float64(d * Float64(b / c)) / c);
	elseif (d <= 1.55e-40)
		tmp = Float64(a / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.26e+76)
		tmp = b / d;
	elseif (d <= -1.4e+37)
		tmp = a / c;
	elseif (d <= -0.28)
		tmp = (a / d) * (c / d);
	elseif (d <= -1.6e-70)
		tmp = (d * (b / c)) / c;
	elseif (d <= 1.55e-40)
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.26e+76], N[(b / d), $MachinePrecision], If[LessEqual[d, -1.4e+37], N[(a / c), $MachinePrecision], If[LessEqual[d, -0.28], N[(N[(a / d), $MachinePrecision] * N[(c / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -1.6e-70], N[(N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 1.55e-40], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -1.26000000000000007e76 or 1.55000000000000005e-40 < d

   1. Initial program 48.2%

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

   3. Taylor expanded in c around 0 72.5%

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

   if -1.26000000000000007e76 < d < -1.3999999999999999e37 or -1.5999999999999999e-70 < d < 1.55000000000000005e-40

   1. Initial program 74.5%

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

   3. Taylor expanded in c around inf 69.1%

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

   if -1.3999999999999999e37 < d < -0.28000000000000003

   1. Initial program 86.5%

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

   3. Taylor expanded in d around inf 86.1%

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

      1. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in b around 0 58.3%

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

      1. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

      1. associate-*r/ 58.3%

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

      2. unpow2 58.3%

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

      3. associate-/r* 58.3%

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

      4. associate-/l* 57.9%

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

   10. Applied egg-rr 57.9%

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

       1. *-commutative 57.9%

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

       2. associate-/l* 57.9%

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

   12. Applied egg-rr 57.9%

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

   if -0.28000000000000003 < d < -1.5999999999999999e-70

   1. Initial program 84.4%

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

   3. Taylor expanded in c around inf 85.5%

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

   4. Taylor expanded in a around 0 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-*r/ 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.26 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq -0.28:\\ \;\;\;\;\frac{a}{d} \cdot \frac{c}{d}\\ \mathbf{elif}\;d \leq -1.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{d \cdot \frac{b}{c}}{c}\\ \mathbf{elif}\;d \leq 1.55 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.26 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq -0.45:\\ \;\;\;\;\frac{\frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq -2.75 \cdot 10^{-70}:\\ \;\;\;\;\frac{d \cdot \frac{b}{c}}{c}\\ \mathbf{elif}\;d \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.26e+76)
   (/ b d)
   (if (<= d -1.05e+38)
     (/ a c)
     (if (<= d -0.45)
       (/ (/ a (/ d c)) d)
       (if (<= d -2.75e-70)
         (/ (* d (/ b c)) c)
         (if (<= d 1.15e-40) (/ a c) (/ b d)))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.26e+76) {
		tmp = b / d;
	} else if (d <= -1.05e+38) {
		tmp = a / c;
	} else if (d <= -0.45) {
		tmp = (a / (d / c)) / d;
	} else if (d <= -2.75e-70) {
		tmp = (d * (b / c)) / c;
	} else if (d <= 1.15e-40) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= (-1.26d+76)) then
        tmp = b / d
    else if (d <= (-1.05d+38)) then
        tmp = a / c
    else if (d <= (-0.45d0)) then
        tmp = (a / (d / c)) / d
    else if (d <= (-2.75d-70)) then
        tmp = (d * (b / c)) / c
    else if (d <= 1.15d-40) then
        tmp = a / c
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.26e+76) {
		tmp = b / d;
	} else if (d <= -1.05e+38) {
		tmp = a / c;
	} else if (d <= -0.45) {
		tmp = (a / (d / c)) / d;
	} else if (d <= -2.75e-70) {
		tmp = (d * (b / c)) / c;
	} else if (d <= 1.15e-40) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.26e+76:
		tmp = b / d
	elif d <= -1.05e+38:
		tmp = a / c
	elif d <= -0.45:
		tmp = (a / (d / c)) / d
	elif d <= -2.75e-70:
		tmp = (d * (b / c)) / c
	elif d <= 1.15e-40:
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.26e+76)
		tmp = Float64(b / d);
	elseif (d <= -1.05e+38)
		tmp = Float64(a / c);
	elseif (d <= -0.45)
		tmp = Float64(Float64(a / Float64(d / c)) / d);
	elseif (d <= -2.75e-70)
		tmp = Float64(Float64(d * Float64(b / c)) / c);
	elseif (d <= 1.15e-40)
		tmp = Float64(a / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.26e+76)
		tmp = b / d;
	elseif (d <= -1.05e+38)
		tmp = a / c;
	elseif (d <= -0.45)
		tmp = (a / (d / c)) / d;
	elseif (d <= -2.75e-70)
		tmp = (d * (b / c)) / c;
	elseif (d <= 1.15e-40)
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.26e+76], N[(b / d), $MachinePrecision], If[LessEqual[d, -1.05e+38], N[(a / c), $MachinePrecision], If[LessEqual[d, -0.45], N[(N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, -2.75e-70], N[(N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 1.15e-40], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -1.26000000000000007e76 or 1.15e-40 < d

   1. Initial program 48.2%

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

   3. Taylor expanded in c around 0 72.5%

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

   if -1.26000000000000007e76 < d < -1.05e38 or -2.75e-70 < d < 1.15e-40

   1. Initial program 74.5%

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

   3. Taylor expanded in c around inf 69.1%

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

   if -1.05e38 < d < -0.450000000000000011

   1. Initial program 86.5%

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

   3. Taylor expanded in d around inf 86.1%

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

      1. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in b around 0 58.3%

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

      1. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

      1. associate-*r/ 58.3%

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

      2. unpow2 58.3%

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

      3. associate-/r* 58.3%

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

      4. associate-/l* 57.9%

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

   10. Applied egg-rr 57.9%

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

       1. clear-num 85.7%

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

       2. un-div-inv 85.9%

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

   12. Applied egg-rr 58.1%

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

   if -0.450000000000000011 < d < -2.75e-70

   1. Initial program 84.4%

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

   3. Taylor expanded in c around inf 85.5%

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

   4. Taylor expanded in a around 0 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-*r/ 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.26 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq -0.45:\\ \;\;\;\;\frac{\frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq -2.75 \cdot 10^{-70}:\\ \;\;\;\;\frac{d \cdot \frac{b}{c}}{c}\\ \mathbf{elif}\;d \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -1.05 \cdot 10^{+32}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq -1.05:\\ \;\;\;\;\frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;d \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{d \cdot \frac{b}{c}}{c}\\ \mathbf{elif}\;d \leq 7.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.6e+76)
   (/ b d)
   (if (<= d -1.05e+32)
     (/ a c)
     (if (<= d -1.05)
       (/ (/ (* a c) d) d)
       (if (<= d -2.4e-70)
         (/ (* d (/ b c)) c)
         (if (<= d 7.7e-41) (/ a c) (/ b d)))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.6e+76) {
		tmp = b / d;
	} else if (d <= -1.05e+32) {
		tmp = a / c;
	} else if (d <= -1.05) {
		tmp = ((a * c) / d) / d;
	} else if (d <= -2.4e-70) {
		tmp = (d * (b / c)) / c;
	} else if (d <= 7.7e-41) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= (-1.6d+76)) then
        tmp = b / d
    else if (d <= (-1.05d+32)) then
        tmp = a / c
    else if (d <= (-1.05d0)) then
        tmp = ((a * c) / d) / d
    else if (d <= (-2.4d-70)) then
        tmp = (d * (b / c)) / c
    else if (d <= 7.7d-41) then
        tmp = a / c
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.6e+76) {
		tmp = b / d;
	} else if (d <= -1.05e+32) {
		tmp = a / c;
	} else if (d <= -1.05) {
		tmp = ((a * c) / d) / d;
	} else if (d <= -2.4e-70) {
		tmp = (d * (b / c)) / c;
	} else if (d <= 7.7e-41) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.6e+76:
		tmp = b / d
	elif d <= -1.05e+32:
		tmp = a / c
	elif d <= -1.05:
		tmp = ((a * c) / d) / d
	elif d <= -2.4e-70:
		tmp = (d * (b / c)) / c
	elif d <= 7.7e-41:
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.6e+76)
		tmp = Float64(b / d);
	elseif (d <= -1.05e+32)
		tmp = Float64(a / c);
	elseif (d <= -1.05)
		tmp = Float64(Float64(Float64(a * c) / d) / d);
	elseif (d <= -2.4e-70)
		tmp = Float64(Float64(d * Float64(b / c)) / c);
	elseif (d <= 7.7e-41)
		tmp = Float64(a / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.6e+76)
		tmp = b / d;
	elseif (d <= -1.05e+32)
		tmp = a / c;
	elseif (d <= -1.05)
		tmp = ((a * c) / d) / d;
	elseif (d <= -2.4e-70)
		tmp = (d * (b / c)) / c;
	elseif (d <= 7.7e-41)
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.6e+76], N[(b / d), $MachinePrecision], If[LessEqual[d, -1.05e+32], N[(a / c), $MachinePrecision], If[LessEqual[d, -1.05], N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, -2.4e-70], N[(N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 7.7e-41], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -1.59999999999999988e76 or 7.6999999999999997e-41 < d

   1. Initial program 48.2%

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

   3. Taylor expanded in c around 0 72.5%

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

   if -1.59999999999999988e76 < d < -1.05e32 or -2.4000000000000001e-70 < d < 7.6999999999999997e-41

   1. Initial program 74.5%

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

   3. Taylor expanded in c around inf 69.1%

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

   if -1.05e32 < d < -1.05000000000000004

   1. Initial program 86.5%

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

   3. Taylor expanded in d around inf 86.1%

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

      1. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in b around 0 58.3%

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

      1. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

      1. associate-*r/ 58.3%

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

      2. unpow2 58.3%

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

      3. associate-/r* 58.3%

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

      4. associate-/l* 57.9%

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

   10. Applied egg-rr 57.9%

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

   11. Taylor expanded in a around 0 58.3%

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

   if -1.05000000000000004 < d < -2.4000000000000001e-70

   1. Initial program 84.4%

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

   3. Taylor expanded in c around inf 85.5%

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

   4. Taylor expanded in a around 0 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-*r/ 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq -1.05 \cdot 10^{+32}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{elif}\;d \leq -1.05:\\ \;\;\;\;\frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;d \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{d \cdot \frac{b}{c}}{c}\\ \mathbf{elif}\;d \leq 7.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.36 \cdot 10^{+76} \lor \neg \left(d \leq 4.65 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.36e+76) (not (<= d 4.65e+20)))
   (/ b d)
   (/ (+ a (* b (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.36e+76) || !(d <= 4.65e+20)) {
		tmp = b / d;
	} else {
		tmp = (a + (b * (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) :: tmp
    if ((d <= (-1.36d+76)) .or. (.not. (d <= 4.65d+20))) then
        tmp = b / d
    else
        tmp = (a + (b * (d / c))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.36e+76) || !(d <= 4.65e+20)) {
		tmp = b / d;
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.36e+76) or not (d <= 4.65e+20):
		tmp = b / d
	else:
		tmp = (a + (b * (d / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.36e+76) || !(d <= 4.65e+20))
		tmp = Float64(b / d);
	else
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -1.36e+76) || ~((d <= 4.65e+20)))
		tmp = b / d;
	else
		tmp = (a + (b * (d / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -1.36e+76], N[Not[LessEqual[d, 4.65e+20]], $MachinePrecision]], N[(b / d), $MachinePrecision], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -1.36000000000000004e76 or 4.65e20 < d

   1. Initial program 40.6%

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

   3. Taylor expanded in c around 0 79.4%

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

   if -1.36000000000000004e76 < d < 4.65e20

   1. Initial program 77.8%

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

   3. Taylor expanded in c around inf 78.2%

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

      1. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.36 \cdot 10^{+76} \lor \neg \left(d \leq 4.65 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -0.8 \lor \neg \left(d \leq 3.8 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -0.8) (not (<= d 3.8e+46)))
   (/ (+ b (* a (/ c d))) d)
   (/ (+ a (/ (* d b) c)) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -0.8) || !(d <= 3.8e+46)) {
		tmp = (b + (a * (c / d))) / d;
	} else {
		tmp = (a + ((d * b) / 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) :: tmp
    if ((d <= (-0.8d0)) .or. (.not. (d <= 3.8d+46))) then
        tmp = (b + (a * (c / d))) / d
    else
        tmp = (a + ((d * b) / c)) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -0.8) || !(d <= 3.8e+46)) {
		tmp = (b + (a * (c / d))) / d;
	} else {
		tmp = (a + ((d * b) / c)) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -0.8) or not (d <= 3.8e+46):
		tmp = (b + (a * (c / d))) / d
	else:
		tmp = (a + ((d * b) / c)) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -0.8) || !(d <= 3.8e+46))
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	else
		tmp = Float64(Float64(a + Float64(Float64(d * b) / c)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -0.8) || ~((d <= 3.8e+46)))
		tmp = (b + (a * (c / d))) / d;
	else
		tmp = (a + ((d * b) / c)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -0.8], N[Not[LessEqual[d, 3.8e+46]], $MachinePrecision]], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(N[(d * b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -0.80000000000000004 or 3.7999999999999999e46 < d

   1. Initial program 42.4%

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

   3. Taylor expanded in d around inf 79.2%

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

      1. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   if -0.80000000000000004 < d < 3.7999999999999999e46

   1. Initial program 79.5%

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

   3. Taylor expanded in c around inf 81.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -0.8 \lor \neg \left(d \leq 3.8 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -0.42:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;d \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -0.42)
   (/ (+ b (* a (/ c d))) d)
   (if (<= d 6.5e+46) (/ (+ a (/ (* d b) c)) c) (/ (+ b (* c (/ a d))) d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.42) {
		tmp = (b + (a * (c / d))) / d;
	} else if (d <= 6.5e+46) {
		tmp = (a + ((d * b) / c)) / c;
	} else {
		tmp = (b + (c * (a / 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 (d <= (-0.42d0)) then
        tmp = (b + (a * (c / d))) / d
    else if (d <= 6.5d+46) then
        tmp = (a + ((d * b) / c)) / c
    else
        tmp = (b + (c * (a / d))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.42) {
		tmp = (b + (a * (c / d))) / d;
	} else if (d <= 6.5e+46) {
		tmp = (a + ((d * b) / c)) / c;
	} else {
		tmp = (b + (c * (a / d))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -0.42:
		tmp = (b + (a * (c / d))) / d
	elif d <= 6.5e+46:
		tmp = (a + ((d * b) / c)) / c
	else:
		tmp = (b + (c * (a / d))) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -0.42)
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	elseif (d <= 6.5e+46)
		tmp = Float64(Float64(a + Float64(Float64(d * b) / c)) / c);
	else
		tmp = Float64(Float64(b + Float64(c * Float64(a / d))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -0.42)
		tmp = (b + (a * (c / d))) / d;
	elseif (d <= 6.5e+46)
		tmp = (a + ((d * b) / c)) / c;
	else
		tmp = (b + (c * (a / d))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -0.42], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 6.5e+46], N[(N[(a + N[(N[(d * b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(c * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d < -0.419999999999999984

   1. Initial program 40.5%

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

   3. Taylor expanded in d around inf 77.6%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

   if -0.419999999999999984 < d < 6.50000000000000008e46

   1. Initial program 79.5%

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

   3. Taylor expanded in c around inf 81.8%

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

   if 6.50000000000000008e46 < d

   1. Initial program 45.1%

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

   3. Taylor expanded in d around inf 81.6%

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

      1. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. un-div-inv 89.1%

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

   7. Applied egg-rr 89.1%

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

      1. associate-/r/ 89.8%

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

   9. Applied egg-rr 89.8%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -0.42:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;d \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -0.65:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -0.65)
   (/ (+ b (/ a (/ d c))) d)
   (if (<= d 5.2e+46) (/ (+ a (/ (* d b) c)) c) (/ (+ b (* c (/ a d))) d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.65) {
		tmp = (b + (a / (d / c))) / d;
	} else if (d <= 5.2e+46) {
		tmp = (a + ((d * b) / c)) / c;
	} else {
		tmp = (b + (c * (a / 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 (d <= (-0.65d0)) then
        tmp = (b + (a / (d / c))) / d
    else if (d <= 5.2d+46) then
        tmp = (a + ((d * b) / c)) / c
    else
        tmp = (b + (c * (a / d))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -0.65) {
		tmp = (b + (a / (d / c))) / d;
	} else if (d <= 5.2e+46) {
		tmp = (a + ((d * b) / c)) / c;
	} else {
		tmp = (b + (c * (a / d))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -0.65:
		tmp = (b + (a / (d / c))) / d
	elif d <= 5.2e+46:
		tmp = (a + ((d * b) / c)) / c
	else:
		tmp = (b + (c * (a / d))) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -0.65)
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) / d);
	elseif (d <= 5.2e+46)
		tmp = Float64(Float64(a + Float64(Float64(d * b) / c)) / c);
	else
		tmp = Float64(Float64(b + Float64(c * Float64(a / d))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -0.65)
		tmp = (b + (a / (d / c))) / d;
	elseif (d <= 5.2e+46)
		tmp = (a + ((d * b) / c)) / c;
	else
		tmp = (b + (c * (a / d))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -0.65], N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 5.2e+46], N[(N[(a + N[(N[(d * b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(c * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d < -0.650000000000000022

   1. Initial program 40.5%

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

   3. Taylor expanded in d around inf 77.6%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

      1. clear-num 80.4%

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

      2. un-div-inv 80.4%

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

   7. Applied egg-rr 80.4%

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

   if -0.650000000000000022 < d < 5.20000000000000027e46

   1. Initial program 79.5%

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

   3. Taylor expanded in c around inf 81.8%

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

   if 5.20000000000000027e46 < d

   1. Initial program 45.1%

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

   3. Taylor expanded in d around inf 81.6%

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

      1. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. un-div-inv 89.1%

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

   7. Applied egg-rr 89.1%

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

      1. associate-/r/ 89.8%

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

   9. Applied egg-rr 89.8%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -0.65:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{elif}\;d \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{a + \frac{d \cdot b}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -3.6 \cdot 10^{+76} \lor \neg \left(d \leq 1.45 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -3.6e+76) (not (<= d 1.45e-40))) (/ b d) (/ a c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.6e+76) || !(d <= 1.45e-40)) {
		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 ((d <= (-3.6d+76)) .or. (.not. (d <= 1.45d-40))) 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 ((d <= -3.6e+76) || !(d <= 1.45e-40)) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -3.6e+76) or not (d <= 1.45e-40):
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -3.6e+76) || !(d <= 1.45e-40))
		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 ((d <= -3.6e+76) || ~((d <= 1.45e-40)))
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -3.6e+76], N[Not[LessEqual[d, 1.45e-40]], $MachinePrecision]], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -3.6000000000000003e76 or 1.4499999999999999e-40 < d

   1. Initial program 48.2%

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

   3. Taylor expanded in c around 0 72.5%

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

   if -3.6000000000000003e76 < d < 1.4499999999999999e-40

   1. Initial program 76.1%

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

   3. Taylor expanded in c around inf 62.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -3.6 \cdot 10^{+76} \lor \neg \left(d \leq 1.45 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.3% 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 62.7%

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

3. Taylor expanded in c around inf 40.9%

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

4. Final simplification 40.9%

   \[\leadsto \frac{a}{c} \]
5. Add Preprocessing

Developer target: 99.3% 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 2024074 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :alt
  (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))))