Complex division, real part

Percentage Accurate: 61.9% → 86.9%

Time: 10.3s

Alternatives: 9

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 86.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{\frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}\right)\\ t_1 := \frac{1}{\mathsf{hypot}\left(d, c\right)}\\ \mathbf{if}\;d \leq -6.9 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(b, \frac{1}{d}, c \cdot \left(t\_1 \cdot \left(a \cdot t\_1\right)\right)\right)\\ \mathbf{elif}\;d \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 1.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq 2.9 \cdot 10^{+155}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0
         (fma
          b
          (/ d (pow (hypot d c) 2.0))
          (* c (/ (/ a (hypot d c)) (hypot d c)))))
        (t_1 (/ 1.0 (hypot d c))))
   (if (<= d -6.9e+149)
     (fma b (/ 1.0 d) (* c (* t_1 (* a t_1))))
     (if (<= d -5.5e-82)
       t_0
       (if (<= d 1.2e-87)
         (/ (+ a (* b (/ d c))) c)
         (if (<= d 2.9e+155) t_0 (/ (+ b (* c (/ a d))) d)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(b, (d / pow(hypot(d, c), 2.0)), (c * ((a / hypot(d, c)) / hypot(d, c))));
	double t_1 = 1.0 / hypot(d, c);
	double tmp;
	if (d <= -6.9e+149) {
		tmp = fma(b, (1.0 / d), (c * (t_1 * (a * t_1))));
	} else if (d <= -5.5e-82) {
		tmp = t_0;
	} else if (d <= 1.2e-87) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= 2.9e+155) {
		tmp = t_0;
	} else {
		tmp = (b + (c * (a / d))) / d;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = fma(b, Float64(d / (hypot(d, c) ^ 2.0)), Float64(c * Float64(Float64(a / hypot(d, c)) / hypot(d, c))))
	t_1 = Float64(1.0 / hypot(d, c))
	tmp = 0.0
	if (d <= -6.9e+149)
		tmp = fma(b, Float64(1.0 / d), Float64(c * Float64(t_1 * Float64(a * t_1))));
	elseif (d <= -5.5e-82)
		tmp = t_0;
	elseif (d <= 1.2e-87)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	elseif (d <= 2.9e+155)
		tmp = t_0;
	else
		tmp = Float64(Float64(b + Float64(c * Float64(a / d))) / d);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(b * N[(d / N[Power[N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -6.9e+149], N[(b * N[(1.0 / d), $MachinePrecision] + N[(c * N[(t$95$1 * N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -5.5e-82], t$95$0, If[LessEqual[d, 1.2e-87], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 2.9e+155], t$95$0, N[(N[(b + N[(c * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -6.9000000000000004e149

   1. Initial program 35.9%

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

   3. Taylor expanded in a around 0 35.9%

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

      1. +-commutative 35.9%

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

      2. associate-/l* 36.7%

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

      3. fma-define 36.7%

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

   5. Simplified 37.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{a}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right)} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 37.3%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{\color{blue}{1 \cdot a}}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right) \]

      2. unpow2 37.3%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{1 \cdot a}{\color{blue}{\mathsf{hypot}\left(d, c\right) \cdot \mathsf{hypot}\left(d, c\right)}}\right) \]

      3. times-frac 44.9%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]

   7. Applied egg-rr 44.9%

      \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*l/ 44.9%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\frac{1 \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}}\right) \]

      2. *-lft-identity 44.9%

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

   9. Simplified 44.9%

      \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\frac{\frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}}\right) \]
   10. Step-by-step derivation

       1. div-inv 44.9%

          \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{a}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]

       2. div-inv 44.9%

          \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \left(\color{blue}{\left(a \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)} \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)\right) \]

       3. associate-*l* 37.3%

          \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(a \cdot \left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)\right)}\right) \]

   11. Applied egg-rr 37.3%

       \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(a \cdot \left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-*r* 44.9%

          \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\left(a \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right) \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]

   13. Simplified 44.9%

       \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\left(a \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right) \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]

   14. Taylor expanded in d around inf 96.5%

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

   if -6.9000000000000004e149 < d < -5.4999999999999998e-82 or 1.2e-87 < d < 2.8999999999999999e155

   1. Initial program 74.7%

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

   3. Taylor expanded in a around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-/l* 79.1%

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

      3. fma-define 79.1%

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

   5. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{a}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right)} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 82.9%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{\color{blue}{1 \cdot a}}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right) \]

      2. unpow2 82.9%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{1 \cdot a}{\color{blue}{\mathsf{hypot}\left(d, c\right) \cdot \mathsf{hypot}\left(d, c\right)}}\right) \]

      3. times-frac 89.6%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]

   7. Applied egg-rr 89.6%

      \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*l/ 89.7%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\frac{1 \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}}\right) \]

      2. *-lft-identity 89.7%

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

   9. Simplified 89.7%

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

   if -5.4999999999999998e-82 < d < 1.2e-87

   1. Initial program 66.8%

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

   3. Taylor expanded in c around inf 94.3%

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

      1. associate-/l* 94.6%

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

   5. Simplified 94.6%

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

   if 2.8999999999999999e155 < d

   1. Initial program 22.6%

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

   3. Taylor expanded in d around inf 85.4%

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

      1. associate-/l* 94.2%

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

   5. Simplified 94.2%

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

      1. clear-num 94.2%

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

      2. un-div-inv 94.2%

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

   7. Applied egg-rr 94.2%

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

      1. associate-/r/ 94.2%

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

   9. Simplified 94.2%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -6.9 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(b, \frac{1}{d}, c \cdot \left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \left(a \cdot \frac{1}{\mathsf{hypot}\left(d, c\right)}\right)\right)\right)\\ \mathbf{elif}\;d \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{\frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}\right)\\ \mathbf{elif}\;d \leq 1.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq 2.9 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{\frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(b, \frac{1}{d}, c \cdot \frac{\frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}\right)\\ t_1 := {\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}\\ \mathbf{if}\;d \leq -1.02 \cdot 10^{-69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 5.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq 7 \cdot 10^{+105}:\\ \;\;\;\;\mathsf{fma}\left(b, \frac{d}{t\_1}, c \cdot \frac{a}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (fma b (/ 1.0 d) (* c (/ (/ a (hypot d c)) (hypot d c)))))
        (t_1 (pow (hypot d c) 2.0)))
   (if (<= d -1.02e-69)
     t_0
     (if (<= d 5.5e-88)
       (/ (+ a (* b (/ d c))) c)
       (if (<= d 7e+105) (fma b (/ d t_1) (* c (/ a t_1))) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(b, (1.0 / d), (c * ((a / hypot(d, c)) / hypot(d, c))));
	double t_1 = pow(hypot(d, c), 2.0);
	double tmp;
	if (d <= -1.02e-69) {
		tmp = t_0;
	} else if (d <= 5.5e-88) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= 7e+105) {
		tmp = fma(b, (d / t_1), (c * (a / t_1)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = fma(b, Float64(1.0 / d), Float64(c * Float64(Float64(a / hypot(d, c)) / hypot(d, c))))
	t_1 = hypot(d, c) ^ 2.0
	tmp = 0.0
	if (d <= -1.02e-69)
		tmp = t_0;
	elseif (d <= 5.5e-88)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	elseif (d <= 7e+105)
		tmp = fma(b, Float64(d / t_1), Float64(c * Float64(a / t_1)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(b * N[(1.0 / d), $MachinePrecision] + N[(c * N[(N[(a / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Power[N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[d, -1.02e-69], t$95$0, If[LessEqual[d, 5.5e-88], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 7e+105], N[(b * N[(d / t$95$1), $MachinePrecision] + N[(c * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if d < -1.02000000000000005e-69 or 6.99999999999999982e105 < d

   1. Initial program 49.5%

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

   3. Taylor expanded in a around 0 49.5%

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

      1. +-commutative 49.5%

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

      2. associate-/l* 51.8%

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

      3. fma-define 51.8%

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

   5. Simplified 52.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{a}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right)} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 52.3%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{\color{blue}{1 \cdot a}}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right) \]

      2. unpow2 52.3%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{1 \cdot a}{\color{blue}{\mathsf{hypot}\left(d, c\right) \cdot \mathsf{hypot}\left(d, c\right)}}\right) \]

      3. times-frac 57.1%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*l/ 57.1%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\frac{1 \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}}\right) \]

      2. *-lft-identity 57.1%

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

   9. Simplified 57.1%

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

   10. Taylor expanded in d around inf 87.0%

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

   if -1.02000000000000005e-69 < d < 5.49999999999999971e-88

   1. Initial program 66.8%

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

   3. Taylor expanded in c around inf 94.3%

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

      1. associate-/l* 94.6%

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

   5. Simplified 94.6%

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

   if 5.49999999999999971e-88 < d < 6.99999999999999982e105

   1. Initial program 71.2%

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

   3. Taylor expanded in a around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. associate-/l* 76.7%

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

      3. fma-define 76.7%

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

   5. Simplified 85.4%

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

Alternative 3: 79.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -4.8 \cdot 10^{-82} \lor \neg \left(d \leq 1.15 \cdot 10^{-16}\right):\\ \;\;\;\;\mathsf{fma}\left(b, \frac{1}{d}, c \cdot \frac{\frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -4.8e-82) (not (<= d 1.15e-16)))
   (fma b (/ 1.0 d) (* c (/ (/ a (hypot d c)) (hypot d c))))
   (/ (+ a (* b (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -4.8e-82) || !(d <= 1.15e-16)) {
		tmp = fma(b, (1.0 / d), (c * ((a / hypot(d, c)) / hypot(d, c))));
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -4.8e-82) || !(d <= 1.15e-16))
		tmp = fma(b, Float64(1.0 / d), Float64(c * Float64(Float64(a / hypot(d, c)) / hypot(d, c))));
	else
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -4.8e-82], N[Not[LessEqual[d, 1.15e-16]], $MachinePrecision]], N[(b * N[(1.0 / d), $MachinePrecision] + N[(c * N[(N[(a / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[d ^ 2 + c ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -4.80000000000000017e-82 or 1.15e-16 < d

   1. Initial program 52.8%

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

   3. Taylor expanded in a around 0 52.8%

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

      1. +-commutative 52.8%

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

      2. associate-/l* 55.9%

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

      3. fma-define 55.9%

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

   5. Simplified 58.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{a}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right)} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 58.3%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{\color{blue}{1 \cdot a}}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}\right) \]

      2. unpow2 58.3%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \frac{1 \cdot a}{\color{blue}{\mathsf{hypot}\left(d, c\right) \cdot \mathsf{hypot}\left(d, c\right)}}\right) \]

      3. times-frac 63.6%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]

   7. Applied egg-rr 63.6%

      \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\left(\frac{1}{\mathsf{hypot}\left(d, c\right)} \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*l/ 63.6%

         \[\leadsto \mathsf{fma}\left(b, \frac{d}{{\left(\mathsf{hypot}\left(d, c\right)\right)}^{2}}, c \cdot \color{blue}{\frac{1 \cdot \frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}}\right) \]

      2. *-lft-identity 63.6%

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

   9. Simplified 63.6%

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

   10. Taylor expanded in d around inf 84.0%

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

   if -4.80000000000000017e-82 < d < 1.15e-16

   1. Initial program 67.7%

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

   3. Taylor expanded in c around inf 92.1%

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

      1. associate-/l* 92.4%

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

   5. Simplified 92.4%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -4.8 \cdot 10^{-82} \lor \neg \left(d \leq 1.15 \cdot 10^{-16}\right):\\ \;\;\;\;\mathsf{fma}\left(b, \frac{1}{d}, c \cdot \frac{\frac{a}{\mathsf{hypot}\left(d, c\right)}}{\mathsf{hypot}\left(d, c\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot a + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{if}\;d \leq -8.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \mathbf{elif}\;d \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq 3.5 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (+ (* c a) (* d b)) (+ (* c c) (* d d)))))
   (if (<= d -8.8e+67)
     (/ (+ b (* c (/ a d))) d)
     (if (<= d -2.4e-79)
       t_0
       (if (<= d 7.5e-88)
         (/ (+ a (* b (/ d c))) c)
         (if (<= d 3.5e+102) t_0 (/ (+ b (* a (/ c d))) d)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -8.8e+67) {
		tmp = (b + (c * (a / d))) / d;
	} else if (d <= -2.4e-79) {
		tmp = t_0;
	} else if (d <= 7.5e-88) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= 3.5e+102) {
		tmp = t_0;
	} else {
		tmp = (b + (a * (c / d))) / d;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d))
    if (d <= (-8.8d+67)) then
        tmp = (b + (c * (a / d))) / d
    else if (d <= (-2.4d-79)) then
        tmp = t_0
    else if (d <= 7.5d-88) then
        tmp = (a + (b * (d / c))) / c
    else if (d <= 3.5d+102) then
        tmp = t_0
    else
        tmp = (b + (a * (c / d))) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -8.8e+67) {
		tmp = (b + (c * (a / d))) / d;
	} else if (d <= -2.4e-79) {
		tmp = t_0;
	} else if (d <= 7.5e-88) {
		tmp = (a + (b * (d / c))) / c;
	} else if (d <= 3.5e+102) {
		tmp = t_0;
	} else {
		tmp = (b + (a * (c / d))) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d))
	tmp = 0
	if d <= -8.8e+67:
		tmp = (b + (c * (a / d))) / d
	elif d <= -2.4e-79:
		tmp = t_0
	elif d <= 7.5e-88:
		tmp = (a + (b * (d / c))) / c
	elif d <= 3.5e+102:
		tmp = t_0
	else:
		tmp = (b + (a * (c / d))) / d
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * a) + Float64(d * b)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (d <= -8.8e+67)
		tmp = Float64(Float64(b + Float64(c * Float64(a / d))) / d);
	elseif (d <= -2.4e-79)
		tmp = t_0;
	elseif (d <= 7.5e-88)
		tmp = Float64(Float64(a + Float64(b * Float64(d / c))) / c);
	elseif (d <= 3.5e+102)
		tmp = t_0;
	else
		tmp = Float64(Float64(b + Float64(a * Float64(c / d))) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * a) + (d * b)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (d <= -8.8e+67)
		tmp = (b + (c * (a / d))) / d;
	elseif (d <= -2.4e-79)
		tmp = t_0;
	elseif (d <= 7.5e-88)
		tmp = (a + (b * (d / c))) / c;
	elseif (d <= 3.5e+102)
		tmp = t_0;
	else
		tmp = (b + (a * (c / d))) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * a), $MachinePrecision] + N[(d * b), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -8.8e+67], N[(N[(b + N[(c * N[(a / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, -2.4e-79], t$95$0, If[LessEqual[d, 7.5e-88], N[(N[(a + N[(b * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[d, 3.5e+102], t$95$0, N[(N[(b + N[(a * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -8.8e67

   1. Initial program 49.5%

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

   3. Taylor expanded in d around inf 82.5%

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

      1. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

      1. clear-num 89.7%

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

      2. un-div-inv 89.8%

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

   7. Applied egg-rr 89.8%

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

      1. associate-/r/ 91.7%

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

   9. Simplified 91.7%

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

   if -8.8e67 < d < -2.40000000000000006e-79 or 7.50000000000000041e-88 < d < 3.50000000000000011e102

   1. Initial program 76.5%

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

   if -2.40000000000000006e-79 < d < 7.50000000000000041e-88

   1. Initial program 66.8%

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

   3. Taylor expanded in c around inf 94.3%

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

      1. associate-/l* 94.6%

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

   5. Simplified 94.6%

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

   if 3.50000000000000011e102 < d

   1. Initial program 29.9%

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

   3. Taylor expanded in d around inf 77.2%

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

      1. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -8.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \mathbf{elif}\;d \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;\frac{c \cdot a + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;d \leq 3.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{c \cdot a + d \cdot b}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -2200000 \lor \neg \left(d \leq 1.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -2200000.0) (not (<= d 1.8e-15)))
   (/ (+ b (* c (/ a d))) d)
   (/ (+ a (* b (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -2200000.0) || !(d <= 1.8e-15)) {
		tmp = (b + (c * (a / 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 <= (-2200000.0d0)) .or. (.not. (d <= 1.8d-15))) then
        tmp = (b + (c * (a / 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 <= -2200000.0) || !(d <= 1.8e-15)) {
		tmp = (b + (c * (a / d))) / d;
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -2200000.0) or not (d <= 1.8e-15):
		tmp = (b + (c * (a / d))) / d
	else:
		tmp = (a + (b * (d / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -2200000.0) || !(d <= 1.8e-15))
		tmp = Float64(Float64(b + Float64(c * Float64(a / 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 <= -2200000.0) || ~((d <= 1.8e-15)))
		tmp = (b + (c * (a / d))) / d;
	else
		tmp = (a + (b * (d / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -2200000.0], N[Not[LessEqual[d, 1.8e-15]], $MachinePrecision]], N[(N[(b + N[(c * N[(a / 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 < -2.2e6 or 1.8000000000000001e-15 < d

   1. Initial program 49.3%

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

   3. Taylor expanded in d around inf 73.9%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

      1. clear-num 80.6%

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

      2. un-div-inv 80.6%

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

   7. Applied egg-rr 80.6%

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

      1. associate-/r/ 81.4%

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

   9. Simplified 81.4%

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

   if -2.2e6 < d < 1.8000000000000001e-15

   1. Initial program 69.8%

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

   3. Taylor expanded in c around inf 88.4%

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

      1. associate-/l* 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -2200000 \lor \neg \left(d \leq 1.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{b + c \cdot \frac{a}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -490000 \lor \neg \left(d \leq 1.76 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -490000.0) (not (<= d 1.76e-15)))
   (/ (+ 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 <= -490000.0) || !(d <= 1.76e-15)) {
		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 <= (-490000.0d0)) .or. (.not. (d <= 1.76d-15))) 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 <= -490000.0) || !(d <= 1.76e-15)) {
		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 <= -490000.0) or not (d <= 1.76e-15):
		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 <= -490000.0) || !(d <= 1.76e-15))
		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 <= -490000.0) || ~((d <= 1.76e-15)))
		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, -490000.0], N[Not[LessEqual[d, 1.76e-15]], $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 < -4.9e5 or 1.76e-15 < d

   1. Initial program 49.3%

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

   3. Taylor expanded in d around inf 73.9%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -4.9e5 < d < 1.76e-15

   1. Initial program 69.8%

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

   3. Taylor expanded in c around inf 88.4%

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

      1. associate-/l* 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -490000 \lor \neg \left(d \leq 1.76 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.05 \cdot 10^{+48} \lor \neg \left(d \leq 3.1 \cdot 10^{+125}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.05e+48) (not (<= d 3.1e+125)))
   (/ b d)
   (/ (+ a (* b (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.05e+48) || !(d <= 3.1e+125)) {
		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 <= (-1.05d+48)) .or. (.not. (d <= 3.1d+125))) 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 <= -1.05e+48) || !(d <= 3.1e+125)) {
		tmp = b / d;
	} else {
		tmp = (a + (b * (d / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.05e+48) or not (d <= 3.1e+125):
		tmp = b / d
	else:
		tmp = (a + (b * (d / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.05e+48) || !(d <= 3.1e+125))
		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 <= -1.05e+48) || ~((d <= 3.1e+125)))
		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, -1.05e+48], N[Not[LessEqual[d, 3.1e+125]], $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 < -1.0499999999999999e48 or 3.1e125 < d

   1. Initial program 42.1%

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

   3. Taylor expanded in c around 0 82.2%

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

   if -1.0499999999999999e48 < d < 3.1e125

   1. Initial program 69.7%

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

   3. Taylor expanded in c around inf 78.2%

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

      1. associate-/l* 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.05 \cdot 10^{+48} \lor \neg \left(d \leq 3.1 \cdot 10^{+125}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -8000 \lor \neg \left(d \leq 5 \cdot 10^{+127}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -8000.0) (not (<= d 5e+127))) (/ b d) (/ a c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -8000.0) || !(d <= 5e+127)) {
		tmp = b / d;
	} else {
		tmp = 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 ((d <= (-8000.0d0)) .or. (.not. (d <= 5d+127))) then
        tmp = b / d
    else
        tmp = a / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -8000.0) || !(d <= 5e+127)) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -8000.0) or not (d <= 5e+127):
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -8000.0) || !(d <= 5e+127))
		tmp = Float64(b / d);
	else
		tmp = Float64(a / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -8000.0) || ~((d <= 5e+127)))
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -8000.0], N[Not[LessEqual[d, 5e+127]], $MachinePrecision]], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -8e3 or 5.0000000000000004e127 < d

   1. Initial program 45.0%

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

   3. Taylor expanded in c around 0 78.8%

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

   if -8e3 < d < 5.0000000000000004e127

   1. Initial program 69.0%

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

   3. Taylor expanded in c around inf 64.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -8000 \lor \neg \left(d \leq 5 \cdot 10^{+127}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.9% 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 59.2%

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

3. Taylor expanded in c around inf 43.6%

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

Developer Target 1: 99.2% 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 2024131 
(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))))