Complex division, real part

Percentage Accurate: 62.0% → 85.8%

Time: 10.3s

Alternatives: 11

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 62.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) 2e+299)
   (* (/ 1.0 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
   (/ (+ a (* b (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((a * c) + (b * d)) / ((c * c) + (d * d))) <= 2e+299) {
		tmp = (1.0 / hypot(c, d)) * (fma(a, c, (b * d)) / hypot(c, d));
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d))) <= 2e+299)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(fma(a, c, Float64(b * d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+299], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d))) < 2.0000000000000001e299

   1. Initial program 77.6%

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

      1. *-un-lft-identity 77.6%

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

      2. associate-*r/ 77.6%

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

      3. fma-define 77.6%

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

      4. add-sqr-sqrt 77.6%

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

      5. times-frac 77.6%

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

      6. fma-define 77.6%

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

      7. hypot-define 77.6%

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

      8. fma-define 77.6%

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

      9. fma-define 77.6%

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

      10. hypot-define 97.7%

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

   4. Applied egg-rr 97.7%

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

   if 2.0000000000000001e299 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 13.9%

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

   3. Taylor expanded in c around inf 54.9%

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

      1. associate-/l* 63.5%

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

   5. Simplified 63.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{-\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + \frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -3.6e+65)
   (/ (+ a (* b (/ d c))) (- (hypot c d)))
   (if (<= c -2.5e-108)
     (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
     (if (<= c 8.5e-18) (/ (+ b (/ (* a c) d)) d) (/ (+ a (* d (/ b c))) c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.6e+65) {
		tmp = (a + (b * (d / c))) / -hypot(c, d);
	} else if (c <= -2.5e-108) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 8.5e-18) {
		tmp = (b + ((a * c) / d)) / d;
	} else {
		tmp = (a + (d * (b / c))) / c;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.6e+65) {
		tmp = (a + (b * (d / c))) / -Math.hypot(c, d);
	} else if (c <= -2.5e-108) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 8.5e-18) {
		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 c <= -3.6e+65:
		tmp = (a + (b * (d / c))) / -math.hypot(c, d)
	elif c <= -2.5e-108:
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
	elif c <= 8.5e-18:
		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 (c <= -3.6e+65)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / Float64(-hypot(c, d)));
	elseif (c <= -2.5e-108)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 8.5e-18)
		tmp = Float64(Float64(b + Float64(Float64(a * c) / d)) / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -3.6e+65)
		tmp = (a + (b * (d / c))) / -hypot(c, d);
	elseif (c <= -2.5e-108)
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	elseif (c <= 8.5e-18)
		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[LessEqual[c, -3.6e+65], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision])), $MachinePrecision], If[LessEqual[c, -2.5e-108], N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e-18], N[(N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.59999999999999978e65

   1. Initial program 32.2%

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

      1. *-un-lft-identity 32.2%

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

      2. associate-*r/ 32.2%

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

      3. fma-define 32.2%

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

      4. add-sqr-sqrt 32.2%

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

      5. times-frac 32.0%

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

      6. fma-define 32.0%

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

      7. hypot-define 32.0%

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

      8. fma-define 32.0%

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

      9. fma-define 32.0%

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

      10. hypot-define 57.6%

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

   4. Applied egg-rr 57.6%

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

   5. Taylor expanded in c around -inf 77.7%

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

      1. associate-*l/ 77.9%

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

      2. *-un-lft-identity 77.9%

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

      3. frac-2neg 77.9%

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

   7. Applied egg-rr 80.7%

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

   if -3.59999999999999978e65 < c < -2.5e-108

   1. Initial program 94.4%

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

   if -2.5e-108 < c < 8.4999999999999995e-18

   1. Initial program 73.4%

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

   3. Taylor expanded in d around inf 88.9%

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

   if 8.4999999999999995e-18 < c

   1. Initial program 50.6%

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

   3. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{-\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + \frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-106}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + \frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -3.4e+70)
   (/ (+ a (* b (/ d c))) c)
   (if (<= c -3e-106)
     (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
     (if (<= c 3.6e-13) (/ (+ b (/ (* a c) d)) d) (/ (+ a (* d (/ b c))) c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.4e+70) {
		tmp = (a + (b * (d / c))) / c;
	} else if (c <= -3e-106) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 3.6e-13) {
		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 (c <= (-3.4d+70)) then
        tmp = (a + (b * (d / c))) / c
    else if (c <= (-3d-106)) then
        tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
    else if (c <= 3.6d-13) 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 (c <= -3.4e+70) {
		tmp = (a + (b * (d / c))) / c;
	} else if (c <= -3e-106) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (c <= 3.6e-13) {
		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 c <= -3.4e+70:
		tmp = (a + (b * (d / c))) / c
	elif c <= -3e-106:
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
	elif c <= 3.6e-13:
		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 (c <= -3.4e+70)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	elseif (c <= -3e-106)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (c <= 3.6e-13)
		tmp = Float64(Float64(b + Float64(Float64(a * c) / d)) / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -3.4e+70)
		tmp = (a + (b * (d / c))) / c;
	elseif (c <= -3e-106)
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	elseif (c <= 3.6e-13)
		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[LessEqual[c, -3.4e+70], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, -3e-106], N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e-13], N[(N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.4000000000000001e70

   1. Initial program 32.2%

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

   3. Taylor expanded in c around inf 77.7%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

   if -3.4000000000000001e70 < c < -3.00000000000000019e-106

   1. Initial program 94.4%

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

   if -3.00000000000000019e-106 < c < 3.5999999999999998e-13

   1. Initial program 73.4%

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

   3. Taylor expanded in d around inf 88.9%

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

   if 3.5999999999999998e-13 < c

   1. Initial program 50.6%

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

   3. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-106}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + \frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-43} \lor \neg \left(c \leq 8.8 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -1.4e-43) (not (<= c 8.8e-22)))
   (/ (+ a (* b (/ d c))) c)
   (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.4e-43) || !(c <= 8.8e-22)) {
		tmp = (a + (b * (d / c))) / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((c <= (-1.4d-43)) .or. (.not. (c <= 8.8d-22))) then
        tmp = (a + (b * (d / c))) / c
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.4e-43) || !(c <= 8.8e-22)) {
		tmp = (a + (b * (d / c))) / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -1.4e-43) or not (c <= 8.8e-22):
		tmp = (a + (b * (d / c))) / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -1.4e-43) || !(c <= 8.8e-22))
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -1.4e-43) || ~((c <= 8.8e-22)))
		tmp = (a + (b * (d / c))) / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -1.4e-43], N[Not[LessEqual[c, 8.8e-22]], $MachinePrecision]], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.3999999999999999e-43 or 8.8000000000000002e-22 < c

   1. Initial program 52.5%

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

   3. Taylor expanded in c around inf 74.5%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

   if -1.3999999999999999e-43 < c < 8.8000000000000002e-22

   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 0 67.1%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-43} \lor \neg \left(c \leq 8.8 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -7.5e-46)
   (/ (+ a (* b (/ d c))) c)
   (if (<= c 6.5e-19) (/ b d) (/ (+ a (* d (/ b c))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -7.5e-46) {
		tmp = (a + (b * (d / c))) / c;
	} else if (c <= 6.5e-19) {
		tmp = b / 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 (c <= (-7.5d-46)) then
        tmp = (a + (b * (d / c))) / c
    else if (c <= 6.5d-19) then
        tmp = b / 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 (c <= -7.5e-46) {
		tmp = (a + (b * (d / c))) / c;
	} else if (c <= 6.5e-19) {
		tmp = b / d;
	} else {
		tmp = (a + (d * (b / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -7.5e-46:
		tmp = (a + (b * (d / c))) / c
	elif c <= 6.5e-19:
		tmp = b / d
	else:
		tmp = (a + (d * (b / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -7.5e-46)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	elseif (c <= 6.5e-19)
		tmp = Float64(b / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -7.5e-46)
		tmp = (a + (b * (d / c))) / c;
	elseif (c <= 6.5e-19)
		tmp = b / d;
	else
		tmp = (a + (d * (b / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -7.5e-46], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 6.5e-19], N[(b / d), $MachinePrecision], N[(N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.50000000000000027e-46

   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 inf 73.8%

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

      1. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

   if -7.50000000000000027e-46 < c < 6.5000000000000001e-19

   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 0 67.1%

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

   if 6.5000000000000001e-19 < c

   1. Initial program 50.6%

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

   3. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-14}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -3.5e-43)
   (/ (+ a (/ b (/ c d))) c)
   (if (<= c 2.45e-14) (/ b d) (/ (+ a (* d (/ b c))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.5e-43) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 2.45e-14) {
		tmp = b / 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 (c <= (-3.5d-43)) then
        tmp = (a + (b / (c / d))) / c
    else if (c <= 2.45d-14) then
        tmp = b / 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 (c <= -3.5e-43) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 2.45e-14) {
		tmp = b / d;
	} else {
		tmp = (a + (d * (b / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -3.5e-43:
		tmp = (a + (b / (c / d))) / c
	elif c <= 2.45e-14:
		tmp = b / d
	else:
		tmp = (a + (d * (b / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -3.5e-43)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / c);
	elseif (c <= 2.45e-14)
		tmp = Float64(b / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -3.5e-43)
		tmp = (a + (b / (c / d))) / c;
	elseif (c <= 2.45e-14)
		tmp = b / d;
	else
		tmp = (a + (d * (b / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -3.5e-43], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 2.45e-14], N[(b / d), $MachinePrecision], N[(N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.49999999999999997e-43

   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 inf 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. associate-*r/ 73.8%

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

      2. associate-*l/ 75.5%

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

      3. *-commutative 75.5%

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

      4. clear-num 75.5%

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

      5. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -3.49999999999999997e-43 < c < 2.44999999999999997e-14

   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 0 67.1%

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

   if 2.44999999999999997e-14 < c

   1. Initial program 50.6%

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

   3. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-14}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -4.2e-42)
   (/ (+ a (/ b (/ c d))) c)
   (if (<= c 1.65e-13) (/ (+ b (* a (/ c d))) d) (/ (+ a (* d (/ b c))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -4.2e-42) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 1.65e-13) {
		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 (c <= (-4.2d-42)) then
        tmp = (a + (b / (c / d))) / c
    else if (c <= 1.65d-13) 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 (c <= -4.2e-42) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 1.65e-13) {
		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 c <= -4.2e-42:
		tmp = (a + (b / (c / d))) / c
	elif c <= 1.65e-13:
		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 (c <= -4.2e-42)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / c);
	elseif (c <= 1.65e-13)
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -4.2e-42)
		tmp = (a + (b / (c / d))) / c;
	elseif (c <= 1.65e-13)
		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[LessEqual[c, -4.2e-42], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 1.65e-13], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.20000000000000013e-42

   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 inf 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. associate-*r/ 73.8%

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

      2. associate-*l/ 75.5%

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

      3. *-commutative 75.5%

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

      4. clear-num 75.5%

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

      5. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -4.20000000000000013e-42 < c < 1.65e-13

   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 d around inf 86.0%

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

      1. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

   if 1.65e-13 < c

   1. Initial program 50.6%

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

   3. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -4.8e-43)
   (/ (+ a (/ b (/ c d))) c)
   (if (<= c 8.4e-13) (/ (+ b (/ a (/ d c))) d) (/ (+ a (* d (/ b c))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -4.8e-43) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 8.4e-13) {
		tmp = (b + (a / (d / c))) / 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 (c <= (-4.8d-43)) then
        tmp = (a + (b / (c / d))) / c
    else if (c <= 8.4d-13) then
        tmp = (b + (a / (d / c))) / 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 (c <= -4.8e-43) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 8.4e-13) {
		tmp = (b + (a / (d / c))) / d;
	} else {
		tmp = (a + (d * (b / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -4.8e-43:
		tmp = (a + (b / (c / d))) / c
	elif c <= 8.4e-13:
		tmp = (b + (a / (d / c))) / d
	else:
		tmp = (a + (d * (b / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -4.8e-43)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / c);
	elseif (c <= 8.4e-13)
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -4.8e-43)
		tmp = (a + (b / (c / d))) / c;
	elseif (c <= 8.4e-13)
		tmp = (b + (a / (d / c))) / d;
	else
		tmp = (a + (d * (b / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -4.8e-43], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 8.4e-13], N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.8000000000000004e-43

   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 inf 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. associate-*r/ 73.8%

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

      2. associate-*l/ 75.5%

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

      3. *-commutative 75.5%

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

      4. clear-num 75.5%

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

      5. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -4.8000000000000004e-43 < c < 8.39999999999999955e-13

   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 d around inf 86.0%

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

      1. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

      1. clear-num 84.7%

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

      2. un-div-inv 84.7%

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

   7. Applied egg-rr 84.7%

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

   if 8.39999999999999955e-13 < c

   1. Initial program 50.6%

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

   3. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + \frac{a}{\frac{d}{c}}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{b + \frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -5.8e-42)
   (/ (+ a (/ b (/ c d))) c)
   (if (<= c 2.2e-17) (/ (+ b (/ (* a c) d)) d) (/ (+ a (* d (/ b c))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -5.8e-42) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 2.2e-17) {
		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 (c <= (-5.8d-42)) then
        tmp = (a + (b / (c / d))) / c
    else if (c <= 2.2d-17) 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 (c <= -5.8e-42) {
		tmp = (a + (b / (c / d))) / c;
	} else if (c <= 2.2e-17) {
		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 c <= -5.8e-42:
		tmp = (a + (b / (c / d))) / c
	elif c <= 2.2e-17:
		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 (c <= -5.8e-42)
		tmp = Float64(Float64(a + Float64(b / Float64(c / d))) / c);
	elseif (c <= 2.2e-17)
		tmp = Float64(Float64(b + Float64(Float64(a * c) / d)) / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -5.8e-42)
		tmp = (a + (b / (c / d))) / c;
	elseif (c <= 2.2e-17)
		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[LessEqual[c, -5.8e-42], N[(N[(a + N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 2.2e-17], N[(N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(d * N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.8000000000000006e-42

   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 inf 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. associate-*r/ 73.8%

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

      2. associate-*l/ 75.5%

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

      3. *-commutative 75.5%

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

      4. clear-num 75.5%

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

      5. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -5.8000000000000006e-42 < c < 2.2e-17

   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 d around inf 86.0%

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

   if 2.2e-17 < c

   1. Initial program 50.6%

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

   3. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 81.3%

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

   5. Applied egg-rr 81.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{a + \frac{b}{\frac{c}{d}}}{c}\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{b + \frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \frac{b}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{-42} \lor \neg \left(c \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.3e-42) (not (<= c 2e-18))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.3e-42) || !(c <= 2e-18)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((c <= (-2.3d-42)) .or. (.not. (c <= 2d-18))) then
        tmp = a / c
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.3e-42) || !(c <= 2e-18)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.3e-42) or not (c <= 2e-18):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.3e-42) || !(c <= 2e-18))
		tmp = Float64(a / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.3e-42) || ~((c <= 2e-18)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.3e-42], N[Not[LessEqual[c, 2e-18]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.30000000000000004e-42 or 2.0000000000000001e-18 < c

   1. Initial program 52.5%

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

   3. Taylor expanded in c around inf 65.8%

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

   if -2.30000000000000004e-42 < c < 2.0000000000000001e-18

   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 0 67.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{-42} \lor \neg \left(c \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.1% 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 63.2%

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

3. Taylor expanded in c around inf 42.6%

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

4. Final simplification 42.6%

   \[\leadsto \frac{a}{c} \]
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 2024071 
(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))))