Complex division, real part

Percentage Accurate: 62.5% → 84.3%

Time: 8.6s

Alternatives: 8

Speedup: 0.8×

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: 62.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot a + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{if}\;d \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{elif}\;d \leq -9 \cdot 10^{-101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* c a) (* d b)) (+ (* c c) (* d d)))))
   (if (<= d -3.6e+113)
     (/ (+ b (/ c (/ d a))) d)
     (if (<= d -9e-101)
       t_0
       (if (<= d 1.5e-129)
         (/ (+ a (* b (/ d c))) c)
         (if (<= d 5.2e+63) t_0 (/ (+ b (/ a (/ d c))) d)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -3.6e+113) {
		tmp = (b + (c / (d / a))) / d;
	} else if (d <= -9e-101) {
		tmp = t_0;
	} else if (d <= 1.5e-129) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= 5.2e+63) {
		tmp = t_0;
	} else {
		tmp = (b + (a / (d / 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) :: t_0
    real(8) :: tmp
    t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d))
    if (d <= (-3.6d+113)) then
        tmp = (b + (c / (d / a))) / d
    else if (d <= (-9d-101)) then
        tmp = t_0
    else if (d <= 1.5d-129) then
        tmp = (a + (b * (d / c))) / c
    else if (d <= 5.2d+63) then
        tmp = t_0
    else
        tmp = (b + (a / (d / c))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -3.6e+113) {
		tmp = (b + (c / (d / a))) / d;
	} else if (d <= -9e-101) {
		tmp = t_0;
	} else if (d <= 1.5e-129) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= 5.2e+63) {
		tmp = t_0;
	} else {
		tmp = (b + (a / (d / c))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d))
	tmp = 0
	if d <= -3.6e+113:
		tmp = (b + (c / (d / a))) / d
	elif d <= -9e-101:
		tmp = t_0
	elif d <= 1.5e-129:
		tmp = (a + (b * (d / c))) / c
	elif d <= 5.2e+63:
		tmp = t_0
	else:
		tmp = (b + (a / (d / c))) / d
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * a) + Float64(d * b)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (d <= -3.6e+113)
		tmp = Float64(Float64(b + Float64(c / Float64(d / a))) / d);
	elseif (d <= -9e-101)
		tmp = t_0;
	elseif (d <= 1.5e-129)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	elseif (d <= 5.2e+63)
		tmp = t_0;
	else
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (d <= -3.6e+113)
		tmp = (b + (c / (d / a))) / d;
	elseif (d <= -9e-101)
		tmp = t_0;
	elseif (d <= 1.5e-129)
		tmp = (a + (b * (d / c))) / c;
	elseif (d <= 5.2e+63)
		tmp = t_0;
	else
		tmp = (b + (a / (d / c))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * a), $MachinePrecision] + N[(d * b), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -3.6e+113], N[(N[(b + N[(c / N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, -9e-101], t$95$0, If[LessEqual[d, 1.5e-129], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 5.2e+63], t$95$0, N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -3.59999999999999992e113

   1. Initial program 26.9%

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

   3. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \frac{a \cdot c}{d}\right), \color{blue}{d}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a \cdot c}{d}\right)\right), d\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(a \cdot c\right), d\right)\right), d\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(c \cdot a\right), d\right)\right), d\right) \]

      5. *-lowering-*.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, a\right), d\right)\right), d\right) \]

   5. Simplified 76.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(c \cdot \frac{a}{d}\right)\right), d\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(c \cdot \frac{1}{\frac{d}{a}}\right)\right), d\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{c}{\frac{d}{a}}\right)\right), d\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(c, \left(\frac{d}{a}\right)\right)\right), d\right) \]

      5. /-lowering-/.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(c, \mathsf{/.f64}\left(d, a\right)\right)\right), d\right) \]

   7. Applied egg-rr 89.6%

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

   if -3.59999999999999992e113 < d < -8.9999999999999997e-101 or 1.4999999999999999e-129 < d < 5.2000000000000002e63

   1. Initial program 88.8%

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

   if -8.9999999999999997e-101 < d < 1.4999999999999999e-129

   1. Initial program 72.5%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a + \frac{b \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b \cdot d}{c}\right)\right), c\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot d\right), c\right)\right), c\right) \]

      4. *-lowering-*.f64 89.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), c\right)\right), c\right) \]

   5. Simplified 89.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{d}{c}\right)\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{d}{c} \cdot b\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{d}{c}\right), b\right)\right), c\right) \]

      4. /-lowering-/.f64 89.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{/.f64}\left(d, c\right), b\right)\right), c\right) \]

   7. Applied egg-rr 89.9%

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

   if 5.2000000000000002e63 < d

   1. Initial program 27.0%

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

   3. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \frac{a \cdot c}{d}\right), \color{blue}{d}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a \cdot c}{d}\right)\right), d\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(a \cdot c\right), d\right)\right), d\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(c \cdot a\right), d\right)\right), d\right) \]

      5. *-lowering-*.f64 79.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, a\right), d\right)\right), d\right) \]

   5. Simplified 79.0%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{d}{c \cdot a}}\right)\right), d\right) \]

      2. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{\frac{d}{c}}{a}}\right)\right), d\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a}{\frac{d}{c}}\right)\right), d\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), d\right) \]

      5. /-lowering-/.f64 86.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), d\right) \]

   7. Applied egg-rr 86.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{elif}\;d \leq -9 \cdot 10^{-101}:\\ \;\;\;\;\frac{c \cdot a + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{c \cdot a + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -4.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{elif}\;d \leq 1.18 \cdot 10^{-73}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;d \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -4.5e-98)
   (/ (+ b (/ c (/ d a))) d)
   (if (<= d 1.18e-73)
     (/ (+ a (/ b (/ c d))) c)
     (if (<= d 3.6e+48)
       (/ (* d b) (+ (* c c) (* d d)))
       (/ (+ b (/ a (/ d c))) d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -4.5e-98) {
		tmp = (b + (c / (d / a))) / d;
	} else if (d <= 1.18e-73) {
		tmp = (a + (b / (c / d))) / c;
	} else if (d <= 3.6e+48) {
		tmp = (d * b) / ((c * c) + (d * d));
	} else {
		tmp = (b + (a / (d / 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 (d <= (-4.5d-98)) then
        tmp = (b + (c / (d / a))) / d
    else if (d <= 1.18d-73) then
        tmp = (a + (b / (c / d))) / c
    else if (d <= 3.6d+48) then
        tmp = (d * b) / ((c * c) + (d * d))
    else
        tmp = (b + (a / (d / c))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -4.5e-98) {
		tmp = (b + (c / (d / a))) / d;
	} else if (d <= 1.18e-73) {
		tmp = (a + (b / (c / d))) / c;
	} else if (d <= 3.6e+48) {
		tmp = (d * b) / ((c * c) + (d * d));
	} else {
		tmp = (b + (a / (d / c))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -4.5e-98:
		tmp = (b + (c / (d / a))) / d
	elif d <= 1.18e-73:
		tmp = (a + (b / (c / d))) / c
	elif d <= 3.6e+48:
		tmp = (d * b) / ((c * c) + (d * d))
	else:
		tmp = (b + (a / (d / c))) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -4.5e-98)
		tmp = Float64(Float64(b + Float64(c / Float64(d / a))) / d);
	elseif (d <= 1.18e-73)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / c);
	elseif (d <= 3.6e+48)
		tmp = Float64(Float64(d * b) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -4.5e-98)
		tmp = (b + (c / (d / a))) / d;
	elseif (d <= 1.18e-73)
		tmp = (a + (b / (c / d))) / c;
	elseif (d <= 3.6e+48)
		tmp = (d * b) / ((c * c) + (d * d));
	else
		tmp = (b + (a / (d / c))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -4.5e-98], N[(N[(b + N[(c / N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 1.18e-73], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 3.6e+48], N[(N[(d * b), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if d < -4.49999999999999997e-98

   1. Initial program 61.2%

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

   3. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \frac{a \cdot c}{d}\right), \color{blue}{d}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a \cdot c}{d}\right)\right), d\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(a \cdot c\right), d\right)\right), d\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(c \cdot a\right), d\right)\right), d\right) \]

      5. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, a\right), d\right)\right), d\right) \]

   5. Simplified 71.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(c \cdot \frac{a}{d}\right)\right), d\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(c \cdot \frac{1}{\frac{d}{a}}\right)\right), d\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{c}{\frac{d}{a}}\right)\right), d\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(c, \left(\frac{d}{a}\right)\right)\right), d\right) \]

      5. /-lowering-/.f64 77.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(c, \mathsf{/.f64}\left(d, a\right)\right)\right), d\right) \]

   7. Applied egg-rr 77.4%

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

   if -4.49999999999999997e-98 < d < 1.17999999999999993e-73

   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

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a + \frac{b \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b \cdot d}{c}\right)\right), c\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot d\right), c\right)\right), c\right) \]

      4. *-lowering-*.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), c\right)\right), c\right) \]

   5. Simplified 88.1%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{d}{c}\right)\right), c\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{1}{\frac{c}{d}}\right)\right), c\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b}{\frac{c}{d}}\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \left(\frac{c}{d}\right)\right)\right), c\right) \]

      5. /-lowering-/.f64 88.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(c, d\right)\right)\right), c\right) \]

   7. Applied egg-rr 88.2%

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

   if 1.17999999999999993e-73 < d < 3.59999999999999983e48

   1. Initial program 83.1%

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

   3. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot d\right), \color{blue}{\left({c}^{2} + {d}^{2}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), \left(\color{blue}{{c}^{2}} + {d}^{2}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), \mathsf{+.f64}\left(\left({c}^{2}\right), \color{blue}{\left({d}^{2}\right)}\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), \mathsf{+.f64}\left(\left(c \cdot c\right), \left({\color{blue}{d}}^{2}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \left({\color{blue}{d}}^{2}\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \left(d \cdot \color{blue}{d}\right)\right)\right) \]

      7. *-lowering-*.f64 75.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \mathsf{*.f64}\left(d, \color{blue}{d}\right)\right)\right) \]

   5. Simplified 75.4%

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

   if 3.59999999999999983e48 < d

   1. Initial program 31.4%

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

   3. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \frac{a \cdot c}{d}\right), \color{blue}{d}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a \cdot c}{d}\right)\right), d\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(a \cdot c\right), d\right)\right), d\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(c \cdot a\right), d\right)\right), d\right) \]

      5. *-lowering-*.f64 78.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, a\right), d\right)\right), d\right) \]

   5. Simplified 78.3%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{d}{c \cdot a}}\right)\right), d\right) \]

      2. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{\frac{d}{c}}{a}}\right)\right), d\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a}{\frac{d}{c}}\right)\right), d\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), d\right) \]

      5. /-lowering-/.f64 85.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), d\right) \]

   7. Applied egg-rr 85.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -4.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{elif}\;d \leq 1.18 \cdot 10^{-73}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;d \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -4.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{elif}\;d \leq 8.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -4.5e-98)
   (/ (+ b (/ c (/ d a))) d)
   (if (<= d 8.5e+48) (/ (+ a (/ b (/ c d))) c) (/ (+ b (/ a (/ d c))) d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -4.5e-98) {
		tmp = (b + (c / (d / a))) / d;
	} else if (d <= 8.5e+48) {
		tmp = (a + (b / (c / d))) / c;
	} else {
		tmp = (b + (a / (d / 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 (d <= (-4.5d-98)) then
        tmp = (b + (c / (d / a))) / d
    else if (d <= 8.5d+48) then
        tmp = (a + (b / (c / d))) / c
    else
        tmp = (b + (a / (d / c))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -4.5e-98) {
		tmp = (b + (c / (d / a))) / d;
	} else if (d <= 8.5e+48) {
		tmp = (a + (b / (c / d))) / c;
	} else {
		tmp = (b + (a / (d / c))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -4.5e-98:
		tmp = (b + (c / (d / a))) / d
	elif d <= 8.5e+48:
		tmp = (a + (b / (c / d))) / c
	else:
		tmp = (b + (a / (d / c))) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -4.5e-98)
		tmp = Float64(Float64(b + Float64(c / Float64(d / a))) / d);
	elseif (d <= 8.5e+48)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / c);
	else
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -4.5e-98)
		tmp = (b + (c / (d / a))) / d;
	elseif (d <= 8.5e+48)
		tmp = (a + (b / (c / d))) / c;
	else
		tmp = (b + (a / (d / c))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -4.5e-98], N[(N[(b + N[(c / N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 8.5e+48], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d < -4.49999999999999997e-98

   1. Initial program 61.2%

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

   3. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \frac{a \cdot c}{d}\right), \color{blue}{d}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a \cdot c}{d}\right)\right), d\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(a \cdot c\right), d\right)\right), d\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(c \cdot a\right), d\right)\right), d\right) \]

      5. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, a\right), d\right)\right), d\right) \]

   5. Simplified 71.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(c \cdot \frac{a}{d}\right)\right), d\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(c \cdot \frac{1}{\frac{d}{a}}\right)\right), d\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{c}{\frac{d}{a}}\right)\right), d\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(c, \left(\frac{d}{a}\right)\right)\right), d\right) \]

      5. /-lowering-/.f64 77.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(c, \mathsf{/.f64}\left(d, a\right)\right)\right), d\right) \]

   7. Applied egg-rr 77.4%

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

   if -4.49999999999999997e-98 < d < 8.5000000000000001e48

   1. Initial program 76.2%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a + \frac{b \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b \cdot d}{c}\right)\right), c\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot d\right), c\right)\right), c\right) \]

      4. *-lowering-*.f64 81.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), c\right)\right), c\right) \]

   5. Simplified 81.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{d}{c}\right)\right), c\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{1}{\frac{c}{d}}\right)\right), c\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b}{\frac{c}{d}}\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \left(\frac{c}{d}\right)\right)\right), c\right) \]

      5. /-lowering-/.f64 81.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(c, d\right)\right)\right), c\right) \]

   7. Applied egg-rr 81.9%

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

   if 8.5000000000000001e48 < d

   1. Initial program 31.4%

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

   3. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \frac{a \cdot c}{d}\right), \color{blue}{d}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a \cdot c}{d}\right)\right), d\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(a \cdot c\right), d\right)\right), d\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(c \cdot a\right), d\right)\right), d\right) \]

      5. *-lowering-*.f64 78.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, a\right), d\right)\right), d\right) \]

   5. Simplified 78.3%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{d}{c \cdot a}}\right)\right), d\right) \]

      2. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{\frac{d}{c}}{a}}\right)\right), d\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a}{\frac{d}{c}}\right)\right), d\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), d\right) \]

      5. /-lowering-/.f64 85.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), d\right) \]

   7. Applied egg-rr 85.6%

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

Alternative 4: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{if}\;d \leq -4.4 \cdot 10^{-98}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 1.25 \cdot 10^{+51}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ b (/ a (/ d c))) d)))
   (if (<= d -4.4e-98)
     t_0
     (if (<= d 1.25e+51) (/ (+ a (/ b (/ c d))) c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b + (a / (d / c))) / d;
	double tmp;
	if (d <= -4.4e-98) {
		tmp = t_0;
	} else if (d <= 1.25e+51) {
		tmp = (a + (b / (c / d))) / c;
	} 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 = (b + (a / (d / c))) / d
    if (d <= (-4.4d-98)) then
        tmp = t_0
    else if (d <= 1.25d+51) then
        tmp = (a + (b / (c / d))) / c
    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 = (b + (a / (d / c))) / d;
	double tmp;
	if (d <= -4.4e-98) {
		tmp = t_0;
	} else if (d <= 1.25e+51) {
		tmp = (a + (b / (c / d))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b + (a / (d / c))) / d
	tmp = 0
	if d <= -4.4e-98:
		tmp = t_0
	elif d <= 1.25e+51:
		tmp = (a + (b / (c / d))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b + Float64(a / Float64(d / c))) / d)
	tmp = 0.0
	if (d <= -4.4e-98)
		tmp = t_0;
	elseif (d <= 1.25e+51)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b + (a / (d / c))) / d;
	tmp = 0.0;
	if (d <= -4.4e-98)
		tmp = t_0;
	elseif (d <= 1.25e+51)
		tmp = (a + (b / (c / d))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -4.4e-98], t$95$0, If[LessEqual[d, 1.25e+51], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -4.39999999999999993e-98 or 1.25e51 < d

   1. Initial program 49.9%

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

   3. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \frac{a \cdot c}{d}\right), \color{blue}{d}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a \cdot c}{d}\right)\right), d\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(a \cdot c\right), d\right)\right), d\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(c \cdot a\right), d\right)\right), d\right) \]

      5. *-lowering-*.f64 73.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, a\right), d\right)\right), d\right) \]

   5. Simplified 73.9%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{d}{c \cdot a}}\right)\right), d\right) \]

      2. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{1}{\frac{\frac{d}{c}}{a}}\right)\right), d\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(\frac{a}{\frac{d}{c}}\right)\right), d\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), d\right) \]

      5. /-lowering-/.f64 80.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), d\right) \]

   7. Applied egg-rr 80.5%

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

   if -4.39999999999999993e-98 < d < 1.25e51

   1. Initial program 76.2%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a + \frac{b \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b \cdot d}{c}\right)\right), c\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot d\right), c\right)\right), c\right) \]

      4. *-lowering-*.f64 81.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), c\right)\right), c\right) \]

   5. Simplified 81.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{d}{c}\right)\right), c\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{1}{\frac{c}{d}}\right)\right), c\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b}{\frac{c}{d}}\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \left(\frac{c}{d}\right)\right)\right), c\right) \]

      5. /-lowering-/.f64 81.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(c, d\right)\right)\right), c\right) \]

   7. Applied egg-rr 81.9%

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

Alternative 5: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -6 \cdot 10^{-6}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 1.25 \cdot 10^{+77}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -6e-6)
   (/ b d)
   (if (<= d 1.25e+77) (/ (+ a (/ b (/ c d))) c) (/ b d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -6e-6) {
		tmp = b / d;
	} else if (d <= 1.25e+77) {
		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 (d <= (-6d-6)) then
        tmp = b / d
    else if (d <= 1.25d+77) 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 (d <= -6e-6) {
		tmp = b / d;
	} else if (d <= 1.25e+77) {
		tmp = (a + (b / (c / d))) / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -6e-6:
		tmp = b / d
	elif d <= 1.25e+77:
		tmp = (a + (b / (c / d))) / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -6e-6)
		tmp = Float64(b / d);
	elseif (d <= 1.25e+77)
		tmp = Float64(Float64(a + Float64(b / Float64(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 (d <= -6e-6)
		tmp = b / d;
	elseif (d <= 1.25e+77)
		tmp = (a + (b / (c / d))) / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -6e-6], N[(b / d), $MachinePrecision], If[LessEqual[d, 1.25e+77], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if d < -6.0000000000000002e-6 or 1.25000000000000001e77 < d

   1. Initial program 40.9%

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

   3. Taylor expanded in c around 0

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

      1. /-lowering-/.f64 71.4%

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{d}\right) \]

   5. Simplified 71.4%

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

   if -6.0000000000000002e-6 < d < 1.25000000000000001e77

   1. Initial program 78.5%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a + \frac{b \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b \cdot d}{c}\right)\right), c\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot d\right), c\right)\right), c\right) \]

      4. *-lowering-*.f64 75.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), c\right)\right), c\right) \]

   5. Simplified 75.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{d}{c}\right)\right), c\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{1}{\frac{c}{d}}\right)\right), c\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b}{\frac{c}{d}}\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \left(\frac{c}{d}\right)\right)\right), c\right) \]

      5. /-lowering-/.f64 76.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(c, d\right)\right)\right), c\right) \]

   7. Applied egg-rr 76.5%

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

Alternative 6: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.72 \cdot 10^{-13}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 3.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.72e-13)
   (/ b d)
   (if (<= d 3.7e+77) (/ (+ a (* b (/ d c))) c) (/ b d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.72e-13) {
		tmp = b / d;
	} else if (d <= 3.7e+77) {
		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 (d <= (-1.72d-13)) then
        tmp = b / d
    else if (d <= 3.7d+77) 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 (d <= -1.72e-13) {
		tmp = b / d;
	} else if (d <= 3.7e+77) {
		tmp = (a + (b * (d / c))) / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.72e-13:
		tmp = b / d
	elif d <= 3.7e+77:
		tmp = (a + (b * (d / c))) / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.72e-13)
		tmp = Float64(b / d);
	elseif (d <= 3.7e+77)
		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 (d <= -1.72e-13)
		tmp = b / d;
	elseif (d <= 3.7e+77)
		tmp = (a + (b * (d / c))) / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.72e-13], N[(b / d), $MachinePrecision], If[LessEqual[d, 3.7e+77], 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 d < -1.71999999999999999e-13 or 3.69999999999999995e77 < d

   1. Initial program 40.9%

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

   3. Taylor expanded in c around 0

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

      1. /-lowering-/.f64 71.4%

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{d}\right) \]

   5. Simplified 71.4%

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

   if -1.71999999999999999e-13 < d < 3.69999999999999995e77

   1. Initial program 78.5%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a + \frac{b \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b \cdot d}{c}\right)\right), c\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(b \cdot d\right), c\right)\right), c\right) \]

      4. *-lowering-*.f64 75.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, d\right), c\right)\right), c\right) \]

   5. Simplified 75.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot \frac{d}{c}\right)\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{d}{c} \cdot b\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{d}{c}\right), b\right)\right), c\right) \]

      4. /-lowering-/.f64 76.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{/.f64}\left(d, c\right), b\right)\right), c\right) \]

   7. Applied egg-rr 76.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.72 \cdot 10^{-13}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 3.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -4.1 \cdot 10^{-98}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 3.35 \cdot 10^{-71}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -4.1e-98) (/ b d) (if (<= d 3.35e-71) (/ a c) (/ b d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -4.1e-98) {
		tmp = b / d;
	} else if (d <= 3.35e-71) {
		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 <= (-4.1d-98)) then
        tmp = b / d
    else if (d <= 3.35d-71) 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 <= -4.1e-98) {
		tmp = b / d;
	} else if (d <= 3.35e-71) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -4.1e-98:
		tmp = b / d
	elif d <= 3.35e-71:
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -4.1e-98)
		tmp = Float64(b / d);
	elseif (d <= 3.35e-71)
		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 <= -4.1e-98)
		tmp = b / d;
	elseif (d <= 3.35e-71)
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -4.1e-98], N[(b / d), $MachinePrecision], If[LessEqual[d, 3.35e-71], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if d < -4.0999999999999998e-98 or 3.3499999999999999e-71 < d

   1. Initial program 54.8%

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

   3. Taylor expanded in c around 0

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

      1. /-lowering-/.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{d}\right) \]

   5. Simplified 62.8%

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

   if -4.0999999999999998e-98 < d < 3.3499999999999999e-71

   1. Initial program 74.8%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 65.9%

         \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{c}\right) \]

   5. Simplified 65.9%

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

Alternative 8: 42.1% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.9%

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

3. Taylor expanded in c around inf

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

   1. /-lowering-/.f64 37.7%

      \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{c}\right) \]

5. Simplified 37.7%

   \[\leadsto \color{blue}{\frac{a}{c}} \]
6. 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 2024191 
(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))))