Complex division, real part

Percentage Accurate: 61.6% → 83.9%

Time: 8.2s

Alternatives: 7

Speedup: 1.6×

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: 61.6% 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: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(d, d, c \cdot c\right)\\ t_1 := \mathsf{fma}\left(b, \frac{d}{t\_0}, \frac{a \cdot c}{t\_0}\right)\\ t_2 := \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{if}\;d \leq -2 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;d \leq -2 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-137}:\\ \;\;\;\;\frac{a + \frac{\mathsf{fma}\left(d, -\frac{d \cdot a}{c}, d \cdot b\right)}{c}}{c}\\ \mathbf{elif}\;d \leq 2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (fma d d (* c c)))
        (t_1 (fma b (/ d t_0) (/ (* a c) t_0)))
        (t_2 (/ (fma a (/ c d) b) d)))
   (if (<= d -2e+142)
     t_2
     (if (<= d -2e-134)
       t_1
       (if (<= d 6e-137)
         (/ (+ a (/ (fma d (- (/ (* d a) c)) (* d b)) c)) c)
         (if (<= d 2e+100) t_1 t_2))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(d, d, (c * c));
	double t_1 = fma(b, (d / t_0), ((a * c) / t_0));
	double t_2 = fma(a, (c / d), b) / d;
	double tmp;
	if (d <= -2e+142) {
		tmp = t_2;
	} else if (d <= -2e-134) {
		tmp = t_1;
	} else if (d <= 6e-137) {
		tmp = (a + (fma(d, -((d * a) / c), (d * b)) / c)) / c;
	} else if (d <= 2e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = fma(d, d, Float64(c * c))
	t_1 = fma(b, Float64(d / t_0), Float64(Float64(a * c) / t_0))
	t_2 = Float64(fma(a, Float64(c / d), b) / d)
	tmp = 0.0
	if (d <= -2e+142)
		tmp = t_2;
	elseif (d <= -2e-134)
		tmp = t_1;
	elseif (d <= 6e-137)
		tmp = Float64(Float64(a + Float64(fma(d, Float64(-Float64(Float64(d * a) / c)), Float64(d * b)) / c)) / c);
	elseif (d <= 2e+100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(d * d + N[(c * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(b * N[(d / t$95$0), $MachinePrecision] + N[(N[(a * c), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -2e+142], t$95$2, If[LessEqual[d, -2e-134], t$95$1, If[LessEqual[d, 6e-137], N[(N[(a + N[(N[(d * (-N[(N[(d * a), $MachinePrecision] / c), $MachinePrecision]) + N[(d * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 2e+100], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if d < -2.0000000000000001e142 or 2.00000000000000003e100 < d

   1. Initial program 38.2%

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

   3. Taylor expanded in d around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 95.3

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

   5. Applied rewrites 95.3%

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

   if -2.0000000000000001e142 < d < -2.00000000000000008e-134 or 5.9999999999999996e-137 < d < 2.00000000000000003e100

   1. Initial program 78.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. unpow2 N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

      13. unpow2 N/A

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

      14. lower-fma.f64 N/A

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

      15. unpow2 N/A

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

      16. lower-*.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if -2.00000000000000008e-134 < d < 5.9999999999999996e-137

   1. Initial program 60.2%

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

   3. Taylor expanded in c around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. div-sub N/A

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

      7. unsub-neg N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. lower-/.f64 N/A

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

   5. Applied rewrites 92.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -2 \cdot 10^{+142}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{elif}\;d \leq -2 \cdot 10^{-134}:\\ \;\;\;\;\mathsf{fma}\left(b, \frac{d}{\mathsf{fma}\left(d, d, c \cdot c\right)}, \frac{a \cdot c}{\mathsf{fma}\left(d, d, c \cdot c\right)}\right)\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-137}:\\ \;\;\;\;\frac{a + \frac{\mathsf{fma}\left(d, -\frac{d \cdot a}{c}, d \cdot b\right)}{c}}{c}\\ \mathbf{elif}\;d \leq 2 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(b, \frac{d}{\mathsf{fma}\left(d, d, c \cdot c\right)}, \frac{a \cdot c}{\mathsf{fma}\left(d, d, c \cdot c\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + d \cdot b}{c \cdot c + d \cdot d}\\ t_1 := \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{if}\;d \leq -1 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;d \leq -2 \cdot 10^{-134}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-137}:\\ \;\;\;\;\frac{a + \frac{\mathsf{fma}\left(d, -\frac{d \cdot a}{c}, d \cdot b\right)}{c}}{c}\\ \mathbf{elif}\;d \leq 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* d b)) (+ (* c c) (* d d))))
        (t_1 (/ (fma a (/ c d) b) d)))
   (if (<= d -1e+132)
     t_1
     (if (<= d -2e-134)
       t_0
       (if (<= d 6e-137)
         (/ (+ a (/ (fma d (- (/ (* d a) c)) (* d b)) c)) c)
         (if (<= d 1e+75) t_0 t_1))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (d * b)) / ((c * c) + (d * d));
	double t_1 = fma(a, (c / d), b) / d;
	double tmp;
	if (d <= -1e+132) {
		tmp = t_1;
	} else if (d <= -2e-134) {
		tmp = t_0;
	} else if (d <= 6e-137) {
		tmp = (a + (fma(d, -((d * a) / c), (d * b)) / c)) / c;
	} else if (d <= 1e+75) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(a * c) + Float64(d * b)) / Float64(Float64(c * c) + Float64(d * d)))
	t_1 = Float64(fma(a, Float64(c / d), b) / d)
	tmp = 0.0
	if (d <= -1e+132)
		tmp = t_1;
	elseif (d <= -2e-134)
		tmp = t_0;
	elseif (d <= 6e-137)
		tmp = Float64(Float64(a + Float64(fma(d, Float64(-Float64(Float64(d * a) / c)), Float64(d * b)) / c)) / c);
	elseif (d <= 1e+75)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(a * c), $MachinePrecision] + N[(d * b), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -1e+132], t$95$1, If[LessEqual[d, -2e-134], t$95$0, If[LessEqual[d, 6e-137], N[(N[(a + N[(N[(d * (-N[(N[(d * a), $MachinePrecision] / c), $MachinePrecision]) + N[(d * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 1e+75], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if d < -9.99999999999999991e131 or 9.99999999999999927e74 < d

   1. Initial program 40.7%

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

   3. Taylor expanded in d around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 94.9

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

   5. Applied rewrites 94.9%

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

   if -9.99999999999999991e131 < d < -2.00000000000000008e-134 or 5.9999999999999996e-137 < d < 9.99999999999999927e74

   1. Initial program 80.0%

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

   if -2.00000000000000008e-134 < d < 5.9999999999999996e-137

   1. Initial program 60.2%

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

   3. Taylor expanded in c around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. unpow2 N/A

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

      5. associate-/r* N/A

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

      6. div-sub N/A

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

      7. unsub-neg N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. lower-/.f64 N/A

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

   5. Applied rewrites 92.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1 \cdot 10^{+132}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{elif}\;d \leq -2 \cdot 10^{-134}:\\ \;\;\;\;\frac{a \cdot c + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-137}:\\ \;\;\;\;\frac{a + \frac{\mathsf{fma}\left(d, -\frac{d \cdot a}{c}, d \cdot b\right)}{c}}{c}\\ \mathbf{elif}\;d \leq 10^{+75}:\\ \;\;\;\;\frac{a \cdot c + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + d \cdot b}{c \cdot c + d \cdot d}\\ t_1 := \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{if}\;d \leq -1 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;d \leq -2 \cdot 10^{-134}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-137}:\\ \;\;\;\;\frac{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}{c}\\ \mathbf{elif}\;d \leq 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* d b)) (+ (* c c) (* d d))))
        (t_1 (/ (fma a (/ c d) b) d)))
   (if (<= d -1e+132)
     t_1
     (if (<= d -2e-134)
       t_0
       (if (<= d 6e-137) (/ (fma b (/ d c) a) c) (if (<= d 1e+75) t_0 t_1))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((a * c) + (d * b)) / ((c * c) + (d * d));
	double t_1 = fma(a, (c / d), b) / d;
	double tmp;
	if (d <= -1e+132) {
		tmp = t_1;
	} else if (d <= -2e-134) {
		tmp = t_0;
	} else if (d <= 6e-137) {
		tmp = fma(b, (d / c), a) / c;
	} else if (d <= 1e+75) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(a * c) + Float64(d * b)) / Float64(Float64(c * c) + Float64(d * d)))
	t_1 = Float64(fma(a, Float64(c / d), b) / d)
	tmp = 0.0
	if (d <= -1e+132)
		tmp = t_1;
	elseif (d <= -2e-134)
		tmp = t_0;
	elseif (d <= 6e-137)
		tmp = Float64(fma(b, Float64(d / c), a) / c);
	elseif (d <= 1e+75)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(a * c), $MachinePrecision] + N[(d * b), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -1e+132], t$95$1, If[LessEqual[d, -2e-134], t$95$0, If[LessEqual[d, 6e-137], N[(N[(b * N[(d / c), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 1e+75], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if d < -9.99999999999999991e131 or 9.99999999999999927e74 < d

   1. Initial program 40.7%

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

   3. Taylor expanded in d around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 94.9

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

   5. Applied rewrites 94.9%

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

   if -9.99999999999999991e131 < d < -2.00000000000000008e-134 or 5.9999999999999996e-137 < d < 9.99999999999999927e74

   1. Initial program 80.0%

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

   if -2.00000000000000008e-134 < d < 5.9999999999999996e-137

   1. Initial program 60.2%

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

   3. Taylor expanded in c around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 90.4

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

   5. Applied rewrites 90.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1 \cdot 10^{+132}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{elif}\;d \leq -2 \cdot 10^{-134}:\\ \;\;\;\;\frac{a \cdot c + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-137}:\\ \;\;\;\;\frac{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}{c}\\ \mathbf{elif}\;d \leq 10^{+75}:\\ \;\;\;\;\frac{a \cdot c + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{if}\;d \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 2000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma a (/ c d) b) d)))
   (if (<= d -5e+15) t_0 (if (<= d 2000000.0) (/ (fma b (/ d c) a) c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(a, (c / d), b) / d;
	double tmp;
	if (d <= -5e+15) {
		tmp = t_0;
	} else if (d <= 2000000.0) {
		tmp = fma(b, (d / c), a) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(a, Float64(c / d), b) / d)
	tmp = 0.0
	if (d <= -5e+15)
		tmp = t_0;
	elseif (d <= 2000000.0)
		tmp = Float64(fma(b, Float64(d / c), a) / c);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -5e+15], t$95$0, If[LessEqual[d, 2000000.0], N[(N[(b * N[(d / c), $MachinePrecision] + a), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -5e15 or 2e6 < d

   1. Initial program 51.9%

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

   3. Taylor expanded in d around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   if -5e15 < d < 2e6

   1. Initial program 68.0%

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

   3. Taylor expanded in c around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 81.3

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

   5. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(b, \frac{d}{c}, a\right)}{c}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{d}\\ \mathbf{if}\;d \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 2000000:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma a (/ c d) b) d)))
   (if (<= d -5e+15) t_0 (if (<= d 2000000.0) (/ a c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(a, (c / d), b) / d;
	double tmp;
	if (d <= -5e+15) {
		tmp = t_0;
	} else if (d <= 2000000.0) {
		tmp = a / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(a, Float64(c / d), b) / d)
	tmp = 0.0
	if (d <= -5e+15)
		tmp = t_0;
	elseif (d <= 2000000.0)
		tmp = Float64(a / c);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -5e+15], t$95$0, If[LessEqual[d, 2000000.0], N[(a / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -5e15 or 2e6 < d

   1. Initial program 51.9%

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

   3. Taylor expanded in d around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   if -5e15 < d < 2e6

   1. Initial program 68.0%

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

   3. Taylor expanded in c around inf

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

      1. lower-/.f64 64.6

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

   5. Applied rewrites 64.6%

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

Alternative 6: 63.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{b}{d}\\ \mathbf{elif}\;d \leq 2000000:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -5e+15) (/ b d) (if (<= d 2000000.0) (/ a c) (/ b d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -5e+15) {
		tmp = b / d;
	} else if (d <= 2000000.0) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= (-5d+15)) then
        tmp = b / d
    else if (d <= 2000000.0d0) then
        tmp = a / c
    else
        tmp = b / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -5e+15) {
		tmp = b / d;
	} else if (d <= 2000000.0) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -5e+15:
		tmp = b / d
	elif d <= 2000000.0:
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -5e+15)
		tmp = Float64(b / d);
	elseif (d <= 2000000.0)
		tmp = Float64(a / c);
	else
		tmp = Float64(b / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -5e+15)
		tmp = b / d;
	elseif (d <= 2000000.0)
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -5e+15], N[(b / d), $MachinePrecision], If[LessEqual[d, 2000000.0], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if d < -5e15 or 2e6 < d

   1. Initial program 51.9%

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

   3. Taylor expanded in c around 0

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

      1. lower-/.f64 70.3

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

   5. Applied rewrites 70.3%

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

   if -5e15 < d < 2e6

   1. Initial program 68.0%

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

   3. Taylor expanded in c around inf

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

      1. lower-/.f64 64.6

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

   5. Applied rewrites 64.6%

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

Alternative 7: 42.4% accurate, 3.2× 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 60.0%

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

3. Taylor expanded in c around inf

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

   1. lower-/.f64 40.1

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

5. Applied rewrites 40.1%

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

Developer Target 1: 99.4% accurate, 0.6× 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 2024212 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

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

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