Complex division, real part

Percentage Accurate: 61.9% → 81.6%

Time: 10.4s

Alternatives: 9

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.9% 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: 81.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot c + b \cdot d\\ t_1 := c \cdot c + d \cdot d\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{a + \frac{d}{c} \cdot b}{c}\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{t\_0}{t\_1}\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-89}:\\ \;\;\;\;\frac{b + \frac{c \cdot a}{d}}{d}\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{1}{t\_1} \cdot t\_0\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\frac{c}{b}} + a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (+ (* a c) (* b d))) (t_1 (+ (* c c) (* d d))))
   (if (<= c -2.1e+139)
     (/ (+ a (* (/ d c) b)) c)
     (if (<= c -7.8e-74)
       (/ t_0 t_1)
       (if (<= c 1.55e-89)
         (/ (+ b (/ (* c a) d)) d)
         (if (<= c 9.8e-36)
           (* (/ 1.0 t_1) t_0)
           (if (<= c 1.6e+17)
             (/ (+ b (/ c (/ d a))) d)
             (/ (+ (/ d (/ c b)) a) c))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a * c) + (b * d);
	double t_1 = (c * c) + (d * d);
	double tmp;
	if (c <= -2.1e+139) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= -7.8e-74) {
		tmp = t_0 / t_1;
	} else if (c <= 1.55e-89) {
		tmp = (b + ((c * a) / d)) / d;
	} else if (c <= 9.8e-36) {
		tmp = (1.0 / t_1) * t_0;
	} else if (c <= 1.6e+17) {
		tmp = (b + (c / (d / a))) / d;
	} else {
		tmp = ((d / (c / b)) + a) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (a * c) + (b * d)
    t_1 = (c * c) + (d * d)
    if (c <= (-2.1d+139)) then
        tmp = (a + ((d / c) * b)) / c
    else if (c <= (-7.8d-74)) then
        tmp = t_0 / t_1
    else if (c <= 1.55d-89) then
        tmp = (b + ((c * a) / d)) / d
    else if (c <= 9.8d-36) then
        tmp = (1.0d0 / t_1) * t_0
    else if (c <= 1.6d+17) then
        tmp = (b + (c / (d / a))) / d
    else
        tmp = ((d / (c / b)) + a) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (a * c) + (b * d);
	double t_1 = (c * c) + (d * d);
	double tmp;
	if (c <= -2.1e+139) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= -7.8e-74) {
		tmp = t_0 / t_1;
	} else if (c <= 1.55e-89) {
		tmp = (b + ((c * a) / d)) / d;
	} else if (c <= 9.8e-36) {
		tmp = (1.0 / t_1) * t_0;
	} else if (c <= 1.6e+17) {
		tmp = (b + (c / (d / a))) / d;
	} else {
		tmp = ((d / (c / b)) + a) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a * c) + (b * d)
	t_1 = (c * c) + (d * d)
	tmp = 0
	if c <= -2.1e+139:
		tmp = (a + ((d / c) * b)) / c
	elif c <= -7.8e-74:
		tmp = t_0 / t_1
	elif c <= 1.55e-89:
		tmp = (b + ((c * a) / d)) / d
	elif c <= 9.8e-36:
		tmp = (1.0 / t_1) * t_0
	elif c <= 1.6e+17:
		tmp = (b + (c / (d / a))) / d
	else:
		tmp = ((d / (c / b)) + a) / c
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a * c) + Float64(b * d))
	t_1 = Float64(Float64(c * c) + Float64(d * d))
	tmp = 0.0
	if (c <= -2.1e+139)
		tmp = Float64(Float64(a + Float64(Float64(d / c) * b)) / c);
	elseif (c <= -7.8e-74)
		tmp = Float64(t_0 / t_1);
	elseif (c <= 1.55e-89)
		tmp = Float64(Float64(b + Float64(Float64(c * a) / d)) / d);
	elseif (c <= 9.8e-36)
		tmp = Float64(Float64(1.0 / t_1) * t_0);
	elseif (c <= 1.6e+17)
		tmp = Float64(Float64(b + Float64(c / Float64(d / a))) / d);
	else
		tmp = Float64(Float64(Float64(d / Float64(c / b)) + a) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a * c) + (b * d);
	t_1 = (c * c) + (d * d);
	tmp = 0.0;
	if (c <= -2.1e+139)
		tmp = (a + ((d / c) * b)) / c;
	elseif (c <= -7.8e-74)
		tmp = t_0 / t_1;
	elseif (c <= 1.55e-89)
		tmp = (b + ((c * a) / d)) / d;
	elseif (c <= 9.8e-36)
		tmp = (1.0 / t_1) * t_0;
	elseif (c <= 1.6e+17)
		tmp = (b + (c / (d / a))) / d;
	else
		tmp = ((d / (c / b)) + a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.1e+139], N[(N[(a + N[(N[(d / c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, -7.8e-74], N[(t$95$0 / t$95$1), $MachinePrecision], If[LessEqual[c, 1.55e-89], N[(N[(b + N[(N[(c * a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 9.8e-36], N[(N[(1.0 / t$95$1), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[c, 1.6e+17], N[(N[(b + N[(c / N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(N[(d / N[(c / b), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -2.0999999999999999e139

   1. Initial program 20.9%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -2.0999999999999999e139 < c < -7.8000000000000003e-74

   1. Initial program 84.5%

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

   if -7.8000000000000003e-74 < c < 1.54999999999999998e-89

   1. Initial program 68.3%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.54999999999999998e-89 < c < 9.7999999999999994e-36

   1. Initial program 83.3%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 9.7999999999999994e-36 < c < 1.6e17

   1. Initial program 77.2%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.6e17 < c

   1. Initial program 44.8%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 2: 81.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+138}:\\ \;\;\;\;\frac{a + \frac{d}{c} \cdot b}{c}\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{b + \frac{c \cdot a}{d}}{d}\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\frac{c}{b}} + a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (<= c -7.5e+138)
     (/ (+ a (* (/ d c) b)) c)
     (if (<= c -7e-74)
       t_0
       (if (<= c 7.5e-88)
         (/ (+ b (/ (* c a) d)) d)
         (if (<= c 1.35e-38)
           t_0
           (if (<= c 1.2e+18)
             (/ (+ b (/ c (/ d a))) d)
             (/ (+ (/ d (/ c b)) a) c))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double tmp;
	if (c <= -7.5e+138) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= -7e-74) {
		tmp = t_0;
	} else if (c <= 7.5e-88) {
		tmp = (b + ((c * a) / d)) / d;
	} else if (c <= 1.35e-38) {
		tmp = t_0;
	} else if (c <= 1.2e+18) {
		tmp = (b + (c / (d / a))) / d;
	} else {
		tmp = ((d / (c / b)) + a) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
    if (c <= (-7.5d+138)) then
        tmp = (a + ((d / c) * b)) / c
    else if (c <= (-7d-74)) then
        tmp = t_0
    else if (c <= 7.5d-88) then
        tmp = (b + ((c * a) / d)) / d
    else if (c <= 1.35d-38) then
        tmp = t_0
    else if (c <= 1.2d+18) then
        tmp = (b + (c / (d / a))) / d
    else
        tmp = ((d / (c / b)) + a) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double tmp;
	if (c <= -7.5e+138) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= -7e-74) {
		tmp = t_0;
	} else if (c <= 7.5e-88) {
		tmp = (b + ((c * a) / d)) / d;
	} else if (c <= 1.35e-38) {
		tmp = t_0;
	} else if (c <= 1.2e+18) {
		tmp = (b + (c / (d / a))) / d;
	} else {
		tmp = ((d / (c / b)) + a) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d))
	tmp = 0
	if c <= -7.5e+138:
		tmp = (a + ((d / c) * b)) / c
	elif c <= -7e-74:
		tmp = t_0
	elif c <= 7.5e-88:
		tmp = (b + ((c * a) / d)) / d
	elif c <= 1.35e-38:
		tmp = t_0
	elif c <= 1.2e+18:
		tmp = (b + (c / (d / a))) / d
	else:
		tmp = ((d / (c / b)) + a) / c
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (c <= -7.5e+138)
		tmp = Float64(Float64(a + Float64(Float64(d / c) * b)) / c);
	elseif (c <= -7e-74)
		tmp = t_0;
	elseif (c <= 7.5e-88)
		tmp = Float64(Float64(b + Float64(Float64(c * a) / d)) / d);
	elseif (c <= 1.35e-38)
		tmp = t_0;
	elseif (c <= 1.2e+18)
		tmp = Float64(Float64(b + Float64(c / Float64(d / a))) / d);
	else
		tmp = Float64(Float64(Float64(d / Float64(c / b)) + a) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (c <= -7.5e+138)
		tmp = (a + ((d / c) * b)) / c;
	elseif (c <= -7e-74)
		tmp = t_0;
	elseif (c <= 7.5e-88)
		tmp = (b + ((c * a) / d)) / d;
	elseif (c <= 1.35e-38)
		tmp = t_0;
	elseif (c <= 1.2e+18)
		tmp = (b + (c / (d / a))) / d;
	else
		tmp = ((d / (c / b)) + a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = 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, -7.5e+138], N[(N[(a + N[(N[(d / c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, -7e-74], t$95$0, If[LessEqual[c, 7.5e-88], N[(N[(b + N[(N[(c * a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 1.35e-38], t$95$0, If[LessEqual[c, 1.2e+18], N[(N[(b + N[(c / N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(N[(d / N[(c / b), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.4999999999999999e138

   1. Initial program 20.9%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -7.4999999999999999e138 < c < -7.00000000000000029e-74 or 7.50000000000000041e-88 < c < 1.35000000000000003e-38

   1. Initial program 84.0%

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

   if -7.00000000000000029e-74 < c < 7.50000000000000041e-88

   1. Initial program 68.7%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.35000000000000003e-38 < c < 1.2e18

   1. Initial program 77.2%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.2e18 < c

   1. Initial program 44.8%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 78.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -135000:\\ \;\;\;\;\frac{a + \frac{d}{c} \cdot b}{c}\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{b + \frac{c \cdot a}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{d}{\frac{c}{b}} + a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -135000.0)
   (/ (+ a (* (/ d c) b)) c)
   (if (<= c 2.5e+16) (/ (+ b (/ (* c a) d)) d) (/ (+ (/ d (/ c b)) a) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -135000.0) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= 2.5e+16) {
		tmp = (b + ((c * a) / d)) / d;
	} else {
		tmp = ((d / (c / b)) + a) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (c <= (-135000.0d0)) then
        tmp = (a + ((d / c) * b)) / c
    else if (c <= 2.5d+16) then
        tmp = (b + ((c * a) / d)) / d
    else
        tmp = ((d / (c / b)) + a) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -135000.0) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= 2.5e+16) {
		tmp = (b + ((c * a) / d)) / d;
	} else {
		tmp = ((d / (c / b)) + a) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -135000.0:
		tmp = (a + ((d / c) * b)) / c
	elif c <= 2.5e+16:
		tmp = (b + ((c * a) / d)) / d
	else:
		tmp = ((d / (c / b)) + a) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -135000.0)
		tmp = Float64(Float64(a + Float64(Float64(d / c) * b)) / c);
	elseif (c <= 2.5e+16)
		tmp = Float64(Float64(b + Float64(Float64(c * a) / d)) / d);
	else
		tmp = Float64(Float64(Float64(d / Float64(c / b)) + a) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -135000.0)
		tmp = (a + ((d / c) * b)) / c;
	elseif (c <= 2.5e+16)
		tmp = (b + ((c * a) / d)) / d;
	else
		tmp = ((d / (c / b)) + a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -135000.0], N[(N[(a + N[(N[(d / c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 2.5e+16], N[(N[(b + N[(N[(c * a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(N[(d / N[(c / b), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -135000

   1. Initial program 47.8%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -135000 < c < 2.5e16

   1. Initial program 72.7%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.5e16 < c

   1. Initial program 44.8%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5000000:\\ \;\;\;\;\frac{a + \frac{d}{c} \cdot b}{c}\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+17}:\\ \;\;\;\;\frac{b + \frac{c \cdot a}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{\frac{c}{d}} + a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -5000000.0)
   (/ (+ a (* (/ d c) b)) c)
   (if (<= c 7e+17) (/ (+ b (/ (* c a) d)) d) (/ (+ (/ b (/ c d)) a) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -5000000.0) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= 7e+17) {
		tmp = (b + ((c * a) / d)) / d;
	} else {
		tmp = ((b / (c / d)) + a) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (c <= (-5000000.0d0)) then
        tmp = (a + ((d / c) * b)) / c
    else if (c <= 7d+17) then
        tmp = (b + ((c * a) / d)) / d
    else
        tmp = ((b / (c / d)) + a) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -5000000.0) {
		tmp = (a + ((d / c) * b)) / c;
	} else if (c <= 7e+17) {
		tmp = (b + ((c * a) / d)) / d;
	} else {
		tmp = ((b / (c / d)) + a) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -5000000.0:
		tmp = (a + ((d / c) * b)) / c
	elif c <= 7e+17:
		tmp = (b + ((c * a) / d)) / d
	else:
		tmp = ((b / (c / d)) + a) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -5000000.0)
		tmp = Float64(Float64(a + Float64(Float64(d / c) * b)) / c);
	elseif (c <= 7e+17)
		tmp = Float64(Float64(b + Float64(Float64(c * a) / d)) / d);
	else
		tmp = Float64(Float64(Float64(b / Float64(c / d)) + a) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -5000000.0)
		tmp = (a + ((d / c) * b)) / c;
	elseif (c <= 7e+17)
		tmp = (b + ((c * a) / d)) / d;
	else
		tmp = ((b / (c / d)) + a) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -5000000.0], N[(N[(a + N[(N[(d / c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 7e+17], N[(N[(b + N[(N[(c * a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -5e6

   1. Initial program 47.8%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -5e6 < c < 7e17

   1. Initial program 72.7%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 7e17 < c

   1. Initial program 44.8%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a + \frac{d}{c} \cdot b}{c}\\ \mathbf{if}\;c \leq -38000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{b + \frac{c \cdot a}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ a (* (/ d c) b)) c)))
   (if (<= c -38000.0) t_0 (if (<= c 5.6e+16) (/ (+ b (/ (* c a) d)) d) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a + ((d / c) * b)) / c;
	double tmp;
	if (c <= -38000.0) {
		tmp = t_0;
	} else if (c <= 5.6e+16) {
		tmp = (b + ((c * a) / d)) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a + ((d / c) * b)) / c
    if (c <= (-38000.0d0)) then
        tmp = t_0
    else if (c <= 5.6d+16) then
        tmp = (b + ((c * a) / d)) / d
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (a + ((d / c) * b)) / c;
	double tmp;
	if (c <= -38000.0) {
		tmp = t_0;
	} else if (c <= 5.6e+16) {
		tmp = (b + ((c * a) / d)) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a + ((d / c) * b)) / c
	tmp = 0
	if c <= -38000.0:
		tmp = t_0
	elif c <= 5.6e+16:
		tmp = (b + ((c * a) / d)) / d
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a + Float64(Float64(d / c) * b)) / c)
	tmp = 0.0
	if (c <= -38000.0)
		tmp = t_0;
	elseif (c <= 5.6e+16)
		tmp = Float64(Float64(b + Float64(Float64(c * a) / d)) / d);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a + ((d / c) * b)) / c;
	tmp = 0.0;
	if (c <= -38000.0)
		tmp = t_0;
	elseif (c <= 5.6e+16)
		tmp = (b + ((c * a) / d)) / d;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a + N[(N[(d / c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -38000.0], t$95$0, If[LessEqual[c, 5.6e+16], N[(N[(b + N[(N[(c * a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if c < -38000 or 5.6e16 < c

   1. Initial program 46.5%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -38000 < c < 5.6e16

   1. Initial program 72.7%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 77.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a + \frac{d}{c} \cdot b}{c}\\ \mathbf{if}\;c \leq -240000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{b + \frac{c}{\frac{d}{a}}}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ a (* (/ d c) b)) c)))
   (if (<= c -240000.0)
     t_0
     (if (<= c 2.6e+15) (/ (+ b (/ c (/ d a))) d) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a + ((d / c) * b)) / c;
	double tmp;
	if (c <= -240000.0) {
		tmp = t_0;
	} else if (c <= 2.6e+15) {
		tmp = (b + (c / (d / a))) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a + ((d / c) * b)) / c
    if (c <= (-240000.0d0)) then
        tmp = t_0
    else if (c <= 2.6d+15) then
        tmp = (b + (c / (d / a))) / d
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (a + ((d / c) * b)) / c;
	double tmp;
	if (c <= -240000.0) {
		tmp = t_0;
	} else if (c <= 2.6e+15) {
		tmp = (b + (c / (d / a))) / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a + ((d / c) * b)) / c
	tmp = 0
	if c <= -240000.0:
		tmp = t_0
	elif c <= 2.6e+15:
		tmp = (b + (c / (d / a))) / d
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a + Float64(Float64(d / c) * b)) / c)
	tmp = 0.0
	if (c <= -240000.0)
		tmp = t_0;
	elseif (c <= 2.6e+15)
		tmp = Float64(Float64(b + Float64(c / Float64(d / a))) / d);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a + ((d / c) * b)) / c;
	tmp = 0.0;
	if (c <= -240000.0)
		tmp = t_0;
	elseif (c <= 2.6e+15)
		tmp = (b + (c / (d / a))) / d;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a + N[(N[(d / c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -240000.0], t$95$0, If[LessEqual[c, 2.6e+15], N[(N[(b + N[(c / N[(d / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if c < -2.4e5 or 2.6e15 < c

   1. Initial program 46.5%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -2.4e5 < c < 2.6e15

   1. Initial program 72.7%

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

   3. Taylor expanded in d around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 70.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a + \frac{d}{c} \cdot b}{c}\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{-73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 0.95:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ a (* (/ d c) b)) c)))
   (if (<= c -5.6e-73) t_0 (if (<= c 0.95) (/ b d) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (a + ((d / c) * b)) / c;
	double tmp;
	if (c <= -5.6e-73) {
		tmp = t_0;
	} else if (c <= 0.95) {
		tmp = b / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (a + ((d / c) * b)) / c
    if (c <= (-5.6d-73)) then
        tmp = t_0
    else if (c <= 0.95d0) then
        tmp = b / d
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (a + ((d / c) * b)) / c;
	double tmp;
	if (c <= -5.6e-73) {
		tmp = t_0;
	} else if (c <= 0.95) {
		tmp = b / d;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (a + ((d / c) * b)) / c
	tmp = 0
	if c <= -5.6e-73:
		tmp = t_0
	elif c <= 0.95:
		tmp = b / d
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(a + Float64(Float64(d / c) * b)) / c)
	tmp = 0.0
	if (c <= -5.6e-73)
		tmp = t_0;
	elseif (c <= 0.95)
		tmp = Float64(b / d);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (a + ((d / c) * b)) / c;
	tmp = 0.0;
	if (c <= -5.6e-73)
		tmp = t_0;
	elseif (c <= 0.95)
		tmp = b / d;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a + N[(N[(d / c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[c, -5.6e-73], t$95$0, If[LessEqual[c, 0.95], N[(b / d), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if c < -5.60000000000000023e-73 or 0.94999999999999996 < c

   1. Initial program 51.1%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -5.60000000000000023e-73 < c < 0.94999999999999996

   1. Initial program 70.3%

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

   3. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 64.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1750000:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1750000.0) (/ b d) (if (<= d 7.2e-47) (/ a c) (/ b d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1750000.0) {
		tmp = b / d;
	} else if (d <= 7.2e-47) {
		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 <= (-1750000.0d0)) then
        tmp = b / d
    else if (d <= 7.2d-47) 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 <= -1750000.0) {
		tmp = b / d;
	} else if (d <= 7.2e-47) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1750000.0:
		tmp = b / d
	elif d <= 7.2e-47:
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1750000.0)
		tmp = Float64(b / d);
	elseif (d <= 7.2e-47)
		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 <= -1750000.0)
		tmp = b / d;
	elseif (d <= 7.2e-47)
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1750000.0], N[(b / d), $MachinePrecision], If[LessEqual[d, 7.2e-47], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if d < -1.75e6 or 7.19999999999999982e-47 < d

   1. Initial program 53.1%

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

   3. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.75e6 < d < 7.19999999999999982e-47

   1. Initial program 67.8%

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

   3. Taylor expanded in c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 43.0% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.3%

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

3. Taylor expanded in c around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. 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 2024110 
(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))))