Complex division, real part

Percentage Accurate: 61.6% → 90.3%

Time: 9.0s

Alternatives: 10

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.6% 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: 90.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{\mathsf{hypot}\left(c, d\right)}\\ t_1 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ t_2 := \frac{1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_0 \cdot \frac{d}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;t\_2 \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \left(d \cdot t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (fma a (/ c d) b) (hypot c d)))
        (t_1 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))
        (t_2 (/ 1.0 (hypot c d))))
   (if (<= t_1 (- INFINITY))
     (* t_0 (/ d (hypot c d)))
     (if (<= t_1 5e+295)
       (* t_2 (/ (fma a c (* b d)) (hypot c d)))
       (* t_2 (* d t_0))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(a, (c / d), b) / hypot(c, d);
	double t_1 = ((a * c) + (b * d)) / ((c * c) + (d * d));
	double t_2 = 1.0 / hypot(c, d);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_0 * (d / hypot(c, d));
	} else if (t_1 <= 5e+295) {
		tmp = t_2 * (fma(a, c, (b * d)) / hypot(c, d));
	} else {
		tmp = t_2 * (d * t_0);
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(fma(a, Float64(c / d), b) / hypot(c, d))
	t_1 = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)))
	t_2 = Float64(1.0 / hypot(c, d))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_0 * Float64(d / hypot(c, d)));
	elseif (t_1 <= 5e+295)
		tmp = Float64(t_2 * Float64(fma(a, c, Float64(b * d)) / hypot(c, d)));
	else
		tmp = Float64(t_2 * Float64(d * 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] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t$95$0 * N[(d / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+295], N[(t$95$2 * N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * N[(d * t$95$0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d))) < -inf.0

   1. Initial program 50.1%

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

   3. Taylor expanded in d around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. add-sqr-sqrt 50.1%

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

      3. hypot-undefine 50.1%

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

      4. hypot-undefine 50.1%

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

      5. times-frac 94.9%

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

      6. +-commutative 94.9%

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

      7. associate-/l* 99.8%

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

      8. fma-define 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d))) < 4.99999999999999991e295

   1. Initial program 81.1%

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

      1. *-un-lft-identity 81.1%

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

      2. associate-*r/ 81.1%

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

      3. fma-define 81.1%

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

      4. add-sqr-sqrt 81.0%

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

      5. times-frac 81.0%

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

      6. fma-define 81.0%

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

      7. hypot-define 81.0%

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

      8. fma-define 81.0%

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

      9. fma-define 81.0%

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

      10. hypot-define 98.4%

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

   4. Applied egg-rr 98.4%

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

   if 4.99999999999999991e295 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 17.2%

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

   3. Taylor expanded in d around inf 17.2%

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

      1. *-un-lft-identity 17.2%

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

      2. add-sqr-sqrt 17.2%

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

      3. hypot-undefine 17.2%

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

      4. hypot-undefine 17.2%

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

      5. times-frac 24.1%

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

      6. +-commutative 24.1%

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

      7. associate-/l* 24.1%

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

      8. fma-define 24.1%

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

   5. Applied egg-rr 24.1%

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

      1. associate-/l* 78.5%

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

   7. Simplified 78.5%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(d \cdot \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{\mathsf{hypot}\left(c, d\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{d}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \left(d \cdot \frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{\mathsf{hypot}\left(c, d\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 10^{+293}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{d}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+293)))
     (* (/ (fma a (/ c d) b) (hypot c d)) (/ d (hypot c d)))
     (* (/ 1.0 (hypot c d)) (/ (fma a c (* b d)) (hypot c d))))))

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 ((t_0 <= -((double) INFINITY)) || !(t_0 <= 1e+293)) {
		tmp = (fma(a, (c / d), b) / hypot(c, d)) * (d / hypot(c, d));
	} else {
		tmp = (1.0 / hypot(c, d)) * (fma(a, c, (b * d)) / hypot(c, d));
	}
	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 ((t_0 <= Float64(-Inf)) || !(t_0 <= 1e+293))
		tmp = Float64(Float64(fma(a, Float64(c / d), b) / hypot(c, d)) * Float64(d / hypot(c, d)));
	else
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(fma(a, c, Float64(b * d)) / hypot(c, d)));
	end
	return 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[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 1e+293]], $MachinePrecision]], N[(N[(N[(a * N[(c / d), $MachinePrecision] + b), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(d / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d))) < -inf.0 or 9.9999999999999992e292 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 24.8%

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

   3. Taylor expanded in d around inf 24.8%

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

      1. *-commutative 24.8%

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

      2. add-sqr-sqrt 24.8%

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

      3. hypot-undefine 24.8%

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

      4. hypot-undefine 24.8%

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

      5. times-frac 71.6%

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

      6. +-commutative 71.6%

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

      7. associate-/l* 83.1%

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

      8. fma-define 83.1%

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

   5. Applied egg-rr 83.1%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d))) < 9.9999999999999992e292

   1. Initial program 80.9%

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

      1. *-un-lft-identity 80.9%

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

      2. associate-*r/ 80.9%

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

      3. fma-define 80.9%

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

      4. add-sqr-sqrt 80.9%

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

      5. times-frac 80.9%

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

      6. fma-define 80.9%

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

      7. hypot-define 80.9%

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

      8. fma-define 80.9%

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

      9. fma-define 80.9%

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

      10. hypot-define 98.4%

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

   4. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq -\infty \lor \neg \left(\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 10^{+293}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(a, \frac{c}{d}, b\right)}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{d}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 10^{+293}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) 1e+293)
   (* (/ 1.0 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
   (/ (+ b (* a (/ c d))) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((a * c) + (b * d)) / ((c * c) + (d * d))) <= 1e+293) {
		tmp = (1.0 / hypot(c, d)) * (fma(a, c, (b * d)) / hypot(c, d));
	} else {
		tmp = (b + (a * (c / d))) / d;
	}
	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))) <= 1e+293)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(fma(a, c, Float64(b * d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	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], 1e+293], 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[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $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))) < 9.9999999999999992e292

   1. Initial program 77.7%

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

      1. *-un-lft-identity 77.7%

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

      2. associate-*r/ 77.7%

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

      3. fma-define 77.7%

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

      4. add-sqr-sqrt 77.7%

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

      5. times-frac 77.7%

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

      6. fma-define 77.7%

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

      7. hypot-define 77.7%

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

      8. fma-define 77.7%

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

      9. fma-define 77.7%

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

      10. hypot-define 95.4%

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

   4. Applied egg-rr 95.4%

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

   if 9.9999999999999992e292 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 18.3%

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

   3. Taylor expanded in d around inf 59.5%

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

      1. associate-/l* 68.4%

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

   5. Simplified 68.4%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \leq 10^{+293}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(a, c, b \cdot d\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{if}\;d \leq -5.1 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq -1.55 \cdot 10^{-139}:\\ \;\;\;\;\frac{d \cdot \left(b + \frac{a \cdot c}{d}\right)}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 5.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{a + d \cdot \left(b \cdot \frac{1}{c}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ b (* a (/ c d))) d)))
   (if (<= d -5.1e+101)
     t_0
     (if (<= d -1.55e-139)
       (/ (* d (+ b (/ (* a c) d))) (+ (* c c) (* d d)))
       (if (<= d 5.3e+19) (/ (+ a (* d (* b (/ 1.0 c)))) c) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b + (a * (c / d))) / d;
	double tmp;
	if (d <= -5.1e+101) {
		tmp = t_0;
	} else if (d <= -1.55e-139) {
		tmp = (d * (b + ((a * c) / d))) / ((c * c) + (d * d));
	} else if (d <= 5.3e+19) {
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (b + (a * (c / d))) / d
    if (d <= (-5.1d+101)) then
        tmp = t_0
    else if (d <= (-1.55d-139)) then
        tmp = (d * (b + ((a * c) / d))) / ((c * c) + (d * d))
    else if (d <= 5.3d+19) then
        tmp = (a + (d * (b * (1.0d0 / c)))) / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (b + (a * (c / d))) / d;
	double tmp;
	if (d <= -5.1e+101) {
		tmp = t_0;
	} else if (d <= -1.55e-139) {
		tmp = (d * (b + ((a * c) / d))) / ((c * c) + (d * d));
	} else if (d <= 5.3e+19) {
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b + (a * (c / d))) / d
	tmp = 0
	if d <= -5.1e+101:
		tmp = t_0
	elif d <= -1.55e-139:
		tmp = (d * (b + ((a * c) / d))) / ((c * c) + (d * d))
	elif d <= 5.3e+19:
		tmp = (a + (d * (b * (1.0 / c)))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b + Float64(a * Float64(c / d))) / d)
	tmp = 0.0
	if (d <= -5.1e+101)
		tmp = t_0;
	elseif (d <= -1.55e-139)
		tmp = Float64(Float64(d * Float64(b + Float64(Float64(a * c) / d))) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 5.3e+19)
		tmp = Float64(Float64(a + Float64(d * Float64(b * Float64(1.0 / c)))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b + (a * (c / d))) / d;
	tmp = 0.0;
	if (d <= -5.1e+101)
		tmp = t_0;
	elseif (d <= -1.55e-139)
		tmp = (d * (b + ((a * c) / d))) / ((c * c) + (d * d));
	elseif (d <= 5.3e+19)
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -5.1e+101], t$95$0, If[LessEqual[d, -1.55e-139], N[(N[(d * N[(b + N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 5.3e+19], N[(N[(a + N[(d * N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d < -5.09999999999999995e101 or 5.3e19 < d

   1. Initial program 39.1%

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

   3. Taylor expanded in d around inf 80.9%

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

      1. associate-/l* 88.0%

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

   5. Simplified 88.0%

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

   if -5.09999999999999995e101 < d < -1.55e-139

   1. Initial program 86.5%

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

   3. Taylor expanded in d around inf 86.5%

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

   if -1.55e-139 < d < 5.3e19

   1. Initial program 69.9%

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

   3. Taylor expanded in c around inf 85.1%

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

      1. div-inv 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*l* 86.1%

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

   5. Applied egg-rr 86.1%

      \[\leadsto \frac{a + \color{blue}{d \cdot \left(b \cdot \frac{1}{c}\right)}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -5.1 \cdot 10^{+101}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;d \leq -1.55 \cdot 10^{-139}:\\ \;\;\;\;\frac{d \cdot \left(b + \frac{a \cdot c}{d}\right)}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 5.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{a + d \cdot \left(b \cdot \frac{1}{c}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{if}\;d \leq -1.92 \cdot 10^{+99}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq -1.9 \cdot 10^{-139}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{a + d \cdot \left(b \cdot \frac{1}{c}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ b (* a (/ c d))) d)))
   (if (<= d -1.92e+99)
     t_0
     (if (<= d -1.9e-139)
       (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
       (if (<= d 2.6e+19) (/ (+ a (* d (* b (/ 1.0 c)))) c) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b + (a * (c / d))) / d;
	double tmp;
	if (d <= -1.92e+99) {
		tmp = t_0;
	} else if (d <= -1.9e-139) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 2.6e+19) {
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (b + (a * (c / d))) / d
    if (d <= (-1.92d+99)) then
        tmp = t_0
    else if (d <= (-1.9d-139)) then
        tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
    else if (d <= 2.6d+19) then
        tmp = (a + (d * (b * (1.0d0 / c)))) / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (b + (a * (c / d))) / d;
	double tmp;
	if (d <= -1.92e+99) {
		tmp = t_0;
	} else if (d <= -1.9e-139) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 2.6e+19) {
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b + (a * (c / d))) / d
	tmp = 0
	if d <= -1.92e+99:
		tmp = t_0
	elif d <= -1.9e-139:
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
	elif d <= 2.6e+19:
		tmp = (a + (d * (b * (1.0 / c)))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b + Float64(a * Float64(c / d))) / d)
	tmp = 0.0
	if (d <= -1.92e+99)
		tmp = t_0;
	elseif (d <= -1.9e-139)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 2.6e+19)
		tmp = Float64(Float64(a + Float64(d * Float64(b * Float64(1.0 / c)))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b + (a * (c / d))) / d;
	tmp = 0.0;
	if (d <= -1.92e+99)
		tmp = t_0;
	elseif (d <= -1.9e-139)
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	elseif (d <= 2.6e+19)
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -1.92e+99], t$95$0, If[LessEqual[d, -1.9e-139], N[(N[(N[(a * c), $MachinePrecision] + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2.6e+19], N[(N[(a + N[(d * N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d < -1.9199999999999999e99 or 2.6e19 < d

   1. Initial program 39.1%

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

   3. Taylor expanded in d around inf 80.9%

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

      1. associate-/l* 88.0%

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

   5. Simplified 88.0%

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

   if -1.9199999999999999e99 < d < -1.90000000000000004e-139

   1. Initial program 86.5%

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

   if -1.90000000000000004e-139 < d < 2.6e19

   1. Initial program 69.9%

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

   3. Taylor expanded in c around inf 85.1%

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

      1. div-inv 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*l* 86.1%

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

   5. Applied egg-rr 86.1%

      \[\leadsto \frac{a + \color{blue}{d \cdot \left(b \cdot \frac{1}{c}\right)}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.92 \cdot 10^{+99}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{elif}\;d \leq -1.9 \cdot 10^{-139}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{a + d \cdot \left(b \cdot \frac{1}{c}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -3 \lor \neg \left(d \leq 3.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \left(b \cdot \frac{1}{c}\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -3.0) (not (<= d 3.5e+21)))
   (/ (+ b (* a (/ c d))) d)
   (/ (+ a (* d (* b (/ 1.0 c)))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.0) || !(d <= 3.5e+21)) {
		tmp = (b + (a * (c / d))) / d;
	} else {
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-3.0d0)) .or. (.not. (d <= 3.5d+21))) then
        tmp = (b + (a * (c / d))) / d
    else
        tmp = (a + (d * (b * (1.0d0 / c)))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.0) || !(d <= 3.5e+21)) {
		tmp = (b + (a * (c / d))) / d;
	} else {
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -3.0) or not (d <= 3.5e+21):
		tmp = (b + (a * (c / d))) / d
	else:
		tmp = (a + (d * (b * (1.0 / c)))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -3.0) || !(d <= 3.5e+21))
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	else
		tmp = Float64(Float64(a + Float64(d * Float64(b * Float64(1.0 / c)))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -3.0) || ~((d <= 3.5e+21)))
		tmp = (b + (a * (c / d))) / d;
	else
		tmp = (a + (d * (b * (1.0 / c)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -3.0], N[Not[LessEqual[d, 3.5e+21]], $MachinePrecision]], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(d * N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -3 or 3.5e21 < d

   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 d around inf 77.1%

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

      1. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   if -3 < d < 3.5e21

   1. Initial program 74.5%

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

   3. Taylor expanded in c around inf 83.1%

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

      1. div-inv 83.1%

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

      2. *-commutative 83.1%

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

      3. associate-*l* 84.0%

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

   5. Applied egg-rr 84.0%

      \[\leadsto \frac{a + \color{blue}{d \cdot \left(b \cdot \frac{1}{c}\right)}}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -3 \lor \neg \left(d \leq 3.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + d \cdot \left(b \cdot \frac{1}{c}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.1 \cdot 10^{+25} \lor \neg \left(d \leq 6.1 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.1e+25) (not (<= d 6.1e+19)))
   (/ b d)
   (/ (+ a (* b (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.1e+25) || !(d <= 6.1e+19)) {
		tmp = b / d;
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-1.1d+25)) .or. (.not. (d <= 6.1d+19))) then
        tmp = b / d
    else
        tmp = (a + (b * (d / c))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.1e+25) || !(d <= 6.1e+19)) {
		tmp = b / d;
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.1e+25) or not (d <= 6.1e+19):
		tmp = b / d
	else:
		tmp = (a + (b * (d / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.1e+25) || !(d <= 6.1e+19))
		tmp = Float64(b / d);
	else
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -1.1e+25) || ~((d <= 6.1e+19)))
		tmp = b / d;
	else
		tmp = (a + (b * (d / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -1.1e+25], N[Not[LessEqual[d, 6.1e+19]], $MachinePrecision]], N[(b / d), $MachinePrecision], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -1.1e25 or 6.1e19 < d

   1. Initial program 45.8%

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

   3. Taylor expanded in c around 0 70.2%

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

   if -1.1e25 < d < 6.1e19

   1. Initial program 75.1%

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

   3. Taylor expanded in c around inf 81.1%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.1 \cdot 10^{+25} \lor \neg \left(d \leq 6.1 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -3.75 \lor \neg \left(d \leq 6.1 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -3.75) (not (<= d 6.1e+19)))
   (/ (+ b (* a (/ c d))) d)
   (/ (+ a (* b (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.75) || !(d <= 6.1e+19)) {
		tmp = (b + (a * (c / d))) / d;
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-3.75d0)) .or. (.not. (d <= 6.1d+19))) then
        tmp = (b + (a * (c / d))) / d
    else
        tmp = (a + (b * (d / c))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.75) || !(d <= 6.1e+19)) {
		tmp = (b + (a * (c / d))) / d;
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -3.75) or not (d <= 6.1e+19):
		tmp = (b + (a * (c / d))) / d
	else:
		tmp = (a + (b * (d / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -3.75) || !(d <= 6.1e+19))
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	else
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -3.75) || ~((d <= 6.1e+19)))
		tmp = (b + (a * (c / d))) / d;
	else
		tmp = (a + (b * (d / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -3.75], N[Not[LessEqual[d, 6.1e+19]], $MachinePrecision]], N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -3.75 or 6.1e19 < d

   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 d around inf 77.1%

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

      1. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   if -3.75 < d < 6.1e19

   1. Initial program 74.5%

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

   3. Taylor expanded in c around inf 83.1%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -3.75 \lor \neg \left(d \leq 6.1 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+44} \lor \neg \left(c \leq 1.2 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -5.2e+44) (not (<= c 1.2e+88))) (/ a c) (/ b d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -5.2e+44) || !(c <= 1.2e+88)) {
		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 <= (-5.2d+44)) .or. (.not. (c <= 1.2d+88))) 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 <= -5.2e+44) || !(c <= 1.2e+88)) {
		tmp = a / c;
	} else {
		tmp = b / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -5.2e+44) or not (c <= 1.2e+88):
		tmp = a / c
	else:
		tmp = b / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -5.2e+44) || !(c <= 1.2e+88))
		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 <= -5.2e+44) || ~((c <= 1.2e+88)))
		tmp = a / c;
	else
		tmp = b / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -5.2e+44], N[Not[LessEqual[c, 1.2e+88]], $MachinePrecision]], N[(a / c), $MachinePrecision], N[(b / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.1999999999999998e44 or 1.2e88 < c

   1. Initial program 47.5%

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

   3. Taylor expanded in c around inf 66.7%

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

   if -5.1999999999999998e44 < c < 1.2e88

   1. Initial program 68.5%

      \[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d} \]
   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 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+44} \lor \neg \left(c \leq 1.2 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.8% 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 60.5%

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

3. Taylor expanded in c around inf 37.7%

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

4. Final simplification 37.7%

   \[\leadsto \frac{a}{c} \]
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 2024078 
(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))))