Complex division, real part

Percentage Accurate: 62.4% → 86.0%

Time: 8.9s

Alternatives: 8

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 62.4% 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: 86.0% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) 5e+299)
   (* (/ 1.0 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
   (* (/ -1.0 c) (- (- a) (/ b (/ c d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((a * c) + (b * d)) / ((c * c) + (d * d))) <= 5e+299) {
		tmp = (1.0 / hypot(c, d)) * (fma(a, c, (b * d)) / hypot(c, d));
	} else {
		tmp = (-1.0 / c) * (-a - (b / (c / 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))) <= 5e+299)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(fma(a, c, Float64(b * d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(-1.0 / c) * Float64(Float64(-a) - Float64(b / Float64(c / 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], 5e+299], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(a * c + N[(b * d), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / c), $MachinePrecision] * N[((-a) - N[(b / N[(c / d), $MachinePrecision]), $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))) < 5.0000000000000003e299

   1. Initial program 76.4%

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

      1. *-un-lft-identity 76.4%

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

      2. add-sqr-sqrt 76.4%

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

      3. times-frac 76.4%

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

      4. hypot-def 76.5%

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

      5. fma-def 76.5%

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

      6. hypot-def 96.9%

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

   3. Applied egg-rr 96.9%

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

   if 5.0000000000000003e299 < (/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 12.6%

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

      1. *-un-lft-identity 12.6%

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

      2. add-sqr-sqrt 12.6%

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

      3. times-frac 12.6%

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

      4. hypot-def 12.6%

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

      5. fma-def 12.6%

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

      6. hypot-def 18.1%

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

   3. Applied egg-rr 18.1%

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

   4. Taylor expanded in c around -inf 30.2%

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

      1. neg-mul-1 30.2%

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

      2. +-commutative 30.2%

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

      3. unsub-neg 30.2%

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

      4. mul-1-neg 30.2%

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

      5. associate-/l* 35.2%

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

      6. distribute-neg-frac 35.2%

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

   6. Simplified 35.2%

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

   7. Taylor expanded in c around -inf 67.6%

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

4. Final simplification 90.2%

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

Alternative 2: 78.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \mathbf{if}\;d \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;\left(b + \frac{a}{\frac{d}{c}}\right) \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 8 \cdot 10^{+39}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (* (/ 1.0 c) (+ a (/ (* b d) c)))))
   (if (<= d -2.6e+34)
     (* (+ b (/ a (/ d c))) (/ -1.0 (hypot c d)))
     (if (<= d 6e-175)
       t_0
       (if (<= d 8e+39)
         (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
         (if (<= d 7.2e+68) t_0 (+ (/ b d) (/ (/ (* a c) d) d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (1.0 / c) * (a + ((b * d) / c));
	double tmp;
	if (d <= -2.6e+34) {
		tmp = (b + (a / (d / c))) * (-1.0 / hypot(c, d));
	} else if (d <= 6e-175) {
		tmp = t_0;
	} else if (d <= 8e+39) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 7.2e+68) {
		tmp = t_0;
	} else {
		tmp = (b / d) + (((a * c) / d) / d);
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (1.0 / c) * (a + ((b * d) / c));
	double tmp;
	if (d <= -2.6e+34) {
		tmp = (b + (a / (d / c))) * (-1.0 / Math.hypot(c, d));
	} else if (d <= 6e-175) {
		tmp = t_0;
	} else if (d <= 8e+39) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 7.2e+68) {
		tmp = t_0;
	} else {
		tmp = (b / d) + (((a * c) / d) / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (1.0 / c) * (a + ((b * d) / c))
	tmp = 0
	if d <= -2.6e+34:
		tmp = (b + (a / (d / c))) * (-1.0 / math.hypot(c, d))
	elif d <= 6e-175:
		tmp = t_0
	elif d <= 8e+39:
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
	elif d <= 7.2e+68:
		tmp = t_0
	else:
		tmp = (b / d) + (((a * c) / d) / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(1.0 / c) * Float64(a + Float64(Float64(b * d) / c)))
	tmp = 0.0
	if (d <= -2.6e+34)
		tmp = Float64(Float64(b + Float64(a / Float64(d / c))) * Float64(-1.0 / hypot(c, d)));
	elseif (d <= 6e-175)
		tmp = t_0;
	elseif (d <= 8e+39)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 7.2e+68)
		tmp = t_0;
	else
		tmp = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (1.0 / c) * (a + ((b * d) / c));
	tmp = 0.0;
	if (d <= -2.6e+34)
		tmp = (b + (a / (d / c))) * (-1.0 / hypot(c, d));
	elseif (d <= 6e-175)
		tmp = t_0;
	elseif (d <= 8e+39)
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	elseif (d <= 7.2e+68)
		tmp = t_0;
	else
		tmp = (b / d) + (((a * c) / d) / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(N[(b * d), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -2.6e+34], N[(N[(b + N[(a / N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 6e-175], t$95$0, If[LessEqual[d, 8e+39], 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, 7.2e+68], t$95$0, N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if d < -2.59999999999999997e34

   1. Initial program 44.3%

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

      1. *-un-lft-identity 44.3%

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

      2. add-sqr-sqrt 44.3%

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

      3. times-frac 44.4%

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

      4. hypot-def 44.4%

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

      5. fma-def 44.4%

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

      6. hypot-def 77.0%

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

   3. Applied egg-rr 77.0%

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

   4. Taylor expanded in d around -inf 85.6%

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

      1. neg-mul-1 85.6%

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

      2. +-commutative 85.6%

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

      3. unsub-neg 85.6%

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

      4. mul-1-neg 85.6%

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

      5. associate-/l* 89.8%

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

      6. distribute-neg-frac 89.8%

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

   6. Simplified 89.8%

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

   if -2.59999999999999997e34 < d < 6e-175 or 7.99999999999999952e39 < d < 7.1999999999999998e68

   1. Initial program 64.4%

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

      1. *-un-lft-identity 64.4%

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

      2. add-sqr-sqrt 64.4%

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

      3. times-frac 64.5%

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

      4. hypot-def 64.5%

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

      5. fma-def 64.5%

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

      6. hypot-def 77.7%

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

   3. Applied egg-rr 77.7%

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

   4. Taylor expanded in c around inf 46.3%

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

   5. Taylor expanded in c around inf 86.8%

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

   if 6e-175 < d < 7.99999999999999952e39

   1. Initial program 83.2%

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

   if 7.1999999999999998e68 < d

   1. Initial program 48.1%

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

   2. Taylor expanded in c around 0 77.1%

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

      1. associate-/l* 77.3%

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

      2. associate-/r/ 77.2%

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

   4. Simplified 77.2%

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

      1. pow2 77.2%

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

      2. associate-*l/ 77.1%

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

      3. associate-/r* 87.3%

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

   6. Applied egg-rr 87.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;\left(b + \frac{a}{\frac{d}{c}}\right) \cdot \frac{-1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-175}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \mathbf{elif}\;d \leq 8 \cdot 10^{+39}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \end{array} \]

Alternative 3: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ t_1 := \frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{if}\;d \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 8 \cdot 10^{+39}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (* (/ 1.0 c) (+ a (/ (* b d) c))))
        (t_1 (+ (/ b d) (/ (/ (* a c) d) d))))
   (if (<= d -1.2e+34)
     t_1
     (if (<= d 6e-175)
       t_0
       (if (<= d 8e+39)
         (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))
         (if (<= d 1.4e+69) t_0 t_1))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (1.0 / c) * (a + ((b * d) / c));
	double t_1 = (b / d) + (((a * c) / d) / d);
	double tmp;
	if (d <= -1.2e+34) {
		tmp = t_1;
	} else if (d <= 6e-175) {
		tmp = t_0;
	} else if (d <= 8e+39) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 1.4e+69) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (1.0d0 / c) * (a + ((b * d) / c))
    t_1 = (b / d) + (((a * c) / d) / d)
    if (d <= (-1.2d+34)) then
        tmp = t_1
    else if (d <= 6d-175) then
        tmp = t_0
    else if (d <= 8d+39) then
        tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
    else if (d <= 1.4d+69) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (1.0 / c) * (a + ((b * d) / c));
	double t_1 = (b / d) + (((a * c) / d) / d);
	double tmp;
	if (d <= -1.2e+34) {
		tmp = t_1;
	} else if (d <= 6e-175) {
		tmp = t_0;
	} else if (d <= 8e+39) {
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	} else if (d <= 1.4e+69) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (1.0 / c) * (a + ((b * d) / c))
	t_1 = (b / d) + (((a * c) / d) / d)
	tmp = 0
	if d <= -1.2e+34:
		tmp = t_1
	elif d <= 6e-175:
		tmp = t_0
	elif d <= 8e+39:
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d))
	elif d <= 1.4e+69:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(1.0 / c) * Float64(a + Float64(Float64(b * d) / c)))
	t_1 = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d))
	tmp = 0.0
	if (d <= -1.2e+34)
		tmp = t_1;
	elseif (d <= 6e-175)
		tmp = t_0;
	elseif (d <= 8e+39)
		tmp = Float64(Float64(Float64(a * c) + Float64(b * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 1.4e+69)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (1.0 / c) * (a + ((b * d) / c));
	t_1 = (b / d) + (((a * c) / d) / d);
	tmp = 0.0;
	if (d <= -1.2e+34)
		tmp = t_1;
	elseif (d <= 6e-175)
		tmp = t_0;
	elseif (d <= 8e+39)
		tmp = ((a * c) + (b * d)) / ((c * c) + (d * d));
	elseif (d <= 1.4e+69)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(N[(b * d), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.2e+34], t$95$1, If[LessEqual[d, 6e-175], t$95$0, If[LessEqual[d, 8e+39], 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, 1.4e+69], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if d < -1.19999999999999993e34 or 1.39999999999999991e69 < d

   1. Initial program 46.2%

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

   2. Taylor expanded in c around 0 75.7%

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

      1. associate-/l* 75.9%

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

      2. associate-/r/ 77.5%

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

   4. Simplified 77.5%

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

      1. pow2 77.5%

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

      2. associate-*l/ 75.7%

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

      3. associate-/r* 85.9%

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

   6. Applied egg-rr 85.9%

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

   if -1.19999999999999993e34 < d < 6e-175 or 7.99999999999999952e39 < d < 1.39999999999999991e69

   1. Initial program 64.4%

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

      1. *-un-lft-identity 64.4%

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

      2. add-sqr-sqrt 64.4%

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

      3. times-frac 64.5%

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

      4. hypot-def 64.5%

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

      5. fma-def 64.5%

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

      6. hypot-def 77.7%

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

   3. Applied egg-rr 77.7%

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

   4. Taylor expanded in c around inf 46.3%

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

   5. Taylor expanded in c around inf 86.8%

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

   if 6e-175 < d < 7.99999999999999952e39

   1. Initial program 83.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{elif}\;d \leq 6 \cdot 10^{-175}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \mathbf{elif}\;d \leq 8 \cdot 10^{+39}:\\ \;\;\;\;\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \end{array} \]

Alternative 4: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -8 \cdot 10^{+33} \lor \neg \left(d \leq 5400000000000 \lor \neg \left(d \leq 7.5 \cdot 10^{+38}\right) \land d \leq 10^{+69}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -8e+33)
         (not
          (or (<= d 5400000000000.0) (and (not (<= d 7.5e+38)) (<= d 1e+69)))))
   (/ b d)
   (* (/ 1.0 c) (+ a (/ (* b d) c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -8e+33) || !((d <= 5400000000000.0) || (!(d <= 7.5e+38) && (d <= 1e+69)))) {
		tmp = b / d;
	} else {
		tmp = (1.0 / c) * (a + ((b * d) / 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 <= (-8d+33)) .or. (.not. (d <= 5400000000000.0d0) .or. (.not. (d <= 7.5d+38)) .and. (d <= 1d+69))) then
        tmp = b / d
    else
        tmp = (1.0d0 / c) * (a + ((b * d) / c))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -8e+33) || !((d <= 5400000000000.0) || (!(d <= 7.5e+38) && (d <= 1e+69)))) {
		tmp = b / d;
	} else {
		tmp = (1.0 / c) * (a + ((b * d) / c));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -8e+33) or not ((d <= 5400000000000.0) or (not (d <= 7.5e+38) and (d <= 1e+69))):
		tmp = b / d
	else:
		tmp = (1.0 / c) * (a + ((b * d) / c))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -8e+33) || !((d <= 5400000000000.0) || (!(d <= 7.5e+38) && (d <= 1e+69))))
		tmp = Float64(b / d);
	else
		tmp = Float64(Float64(1.0 / c) * Float64(a + Float64(Float64(b * d) / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -8e+33) || ~(((d <= 5400000000000.0) || (~((d <= 7.5e+38)) && (d <= 1e+69)))))
		tmp = b / d;
	else
		tmp = (1.0 / c) * (a + ((b * d) / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -8e+33], N[Not[Or[LessEqual[d, 5400000000000.0], And[N[Not[LessEqual[d, 7.5e+38]], $MachinePrecision], LessEqual[d, 1e+69]]]], $MachinePrecision]], N[(b / d), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(N[(b * d), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -7.9999999999999996e33 or 5.4e12 < d < 7.4999999999999999e38 or 1.0000000000000001e69 < d

   1. Initial program 51.8%

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

   2. Taylor expanded in c around 0 72.0%

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

   if -7.9999999999999996e33 < d < 5.4e12 or 7.4999999999999999e38 < d < 1.0000000000000001e69

   1. Initial program 69.0%

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

      1. *-un-lft-identity 69.0%

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

      2. add-sqr-sqrt 69.0%

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

      3. times-frac 69.0%

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

      4. hypot-def 69.1%

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

      5. fma-def 69.1%

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

      6. hypot-def 80.1%

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

   3. Applied egg-rr 80.1%

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

   4. Taylor expanded in c around inf 41.8%

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

   5. Taylor expanded in c around inf 81.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -8 \cdot 10^{+33} \lor \neg \left(d \leq 5400000000000 \lor \neg \left(d \leq 7.5 \cdot 10^{+38}\right) \land d \leq 10^{+69}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \end{array} \]

Alternative 5: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -6.2 \cdot 10^{+33} \lor \neg \left(d \leq 8 \cdot 10^{-5}\right) \land \left(d \leq 8 \cdot 10^{+39} \lor \neg \left(d \leq 7.2 \cdot 10^{+68}\right)\right):\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -6.2e+33)
         (and (not (<= d 8e-5)) (or (<= d 8e+39) (not (<= d 7.2e+68)))))
   (+ (/ b d) (/ (/ (* a c) d) d))
   (* (/ 1.0 c) (+ a (/ (* b d) c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -6.2e+33) || (!(d <= 8e-5) && ((d <= 8e+39) || !(d <= 7.2e+68)))) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else {
		tmp = (1.0 / c) * (a + ((b * d) / 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 <= (-6.2d+33)) .or. (.not. (d <= 8d-5)) .and. (d <= 8d+39) .or. (.not. (d <= 7.2d+68))) then
        tmp = (b / d) + (((a * c) / d) / d)
    else
        tmp = (1.0d0 / c) * (a + ((b * d) / c))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -6.2e+33) || (!(d <= 8e-5) && ((d <= 8e+39) || !(d <= 7.2e+68)))) {
		tmp = (b / d) + (((a * c) / d) / d);
	} else {
		tmp = (1.0 / c) * (a + ((b * d) / c));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -6.2e+33) or (not (d <= 8e-5) and ((d <= 8e+39) or not (d <= 7.2e+68))):
		tmp = (b / d) + (((a * c) / d) / d)
	else:
		tmp = (1.0 / c) * (a + ((b * d) / c))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -6.2e+33) || (!(d <= 8e-5) && ((d <= 8e+39) || !(d <= 7.2e+68))))
		tmp = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d));
	else
		tmp = Float64(Float64(1.0 / c) * Float64(a + Float64(Float64(b * d) / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -6.2e+33) || (~((d <= 8e-5)) && ((d <= 8e+39) || ~((d <= 7.2e+68)))))
		tmp = (b / d) + (((a * c) / d) / d);
	else
		tmp = (1.0 / c) * (a + ((b * d) / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -6.2e+33], And[N[Not[LessEqual[d, 8e-5]], $MachinePrecision], Or[LessEqual[d, 8e+39], N[Not[LessEqual[d, 7.2e+68]], $MachinePrecision]]]], N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(a + N[(N[(b * d), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -6.2e33 or 8.00000000000000065e-5 < d < 7.99999999999999952e39 or 7.1999999999999998e68 < d

   1. Initial program 52.7%

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

   2. Taylor expanded in c around 0 75.9%

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

      1. associate-/l* 75.2%

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

      2. associate-/r/ 77.4%

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

   4. Simplified 77.4%

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

      1. pow2 77.4%

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

      2. associate-*l/ 75.9%

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

      3. associate-/r* 84.6%

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

   6. Applied egg-rr 84.6%

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

   if -6.2e33 < d < 8.00000000000000065e-5 or 7.99999999999999952e39 < d < 7.1999999999999998e68

   1. Initial program 68.8%

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

      1. *-un-lft-identity 68.8%

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

      2. add-sqr-sqrt 68.8%

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

      3. times-frac 68.9%

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

      4. hypot-def 68.9%

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

      5. fma-def 68.9%

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

      6. hypot-def 79.6%

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

   3. Applied egg-rr 79.6%

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

   4. Taylor expanded in c around inf 42.9%

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

   5. Taylor expanded in c around inf 82.6%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -6.2 \cdot 10^{+33} \lor \neg \left(d \leq 8 \cdot 10^{-5}\right) \land \left(d \leq 8 \cdot 10^{+39} \lor \neg \left(d \leq 7.2 \cdot 10^{+68}\right)\right):\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(a + \frac{b \cdot d}{c}\right)\\ \end{array} \]

Alternative 6: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{-89} \lor \neg \left(c \leq 6.3 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{-1}{c} \cdot \left(\left(-a\right) - \frac{b}{\frac{c}{d}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.2e-89) (not (<= c 6.3e-18)))
   (* (/ -1.0 c) (- (- a) (/ b (/ c d))))
   (+ (/ b d) (/ (/ (* a c) d) d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.2e-89) || !(c <= 6.3e-18)) {
		tmp = (-1.0 / c) * (-a - (b / (c / d)));
	} else {
		tmp = (b / d) + (((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) :: tmp
    if ((c <= (-2.2d-89)) .or. (.not. (c <= 6.3d-18))) then
        tmp = ((-1.0d0) / c) * (-a - (b / (c / d)))
    else
        tmp = (b / d) + (((a * c) / d) / d)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.2e-89) || !(c <= 6.3e-18)) {
		tmp = (-1.0 / c) * (-a - (b / (c / d)));
	} else {
		tmp = (b / d) + (((a * c) / d) / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.2e-89) or not (c <= 6.3e-18):
		tmp = (-1.0 / c) * (-a - (b / (c / d)))
	else:
		tmp = (b / d) + (((a * c) / d) / d)
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.2e-89) || !(c <= 6.3e-18))
		tmp = Float64(Float64(-1.0 / c) * Float64(Float64(-a) - Float64(b / Float64(c / d))));
	else
		tmp = Float64(Float64(b / d) + Float64(Float64(Float64(a * c) / d) / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.2e-89) || ~((c <= 6.3e-18)))
		tmp = (-1.0 / c) * (-a - (b / (c / d)));
	else
		tmp = (b / d) + (((a * c) / d) / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.2e-89], N[Not[LessEqual[c, 6.3e-18]], $MachinePrecision]], N[(N[(-1.0 / c), $MachinePrecision] * N[((-a) - N[(b / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / d), $MachinePrecision] + N[(N[(N[(a * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.20000000000000012e-89 or 6.3000000000000004e-18 < c

   1. Initial program 53.5%

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

      1. *-un-lft-identity 53.5%

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

      2. add-sqr-sqrt 53.5%

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

      3. times-frac 53.5%

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

      4. hypot-def 53.5%

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

      5. fma-def 53.5%

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

      6. hypot-def 71.9%

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

   3. Applied egg-rr 71.9%

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

   4. Taylor expanded in c around -inf 49.7%

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

      1. neg-mul-1 49.7%

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

      2. +-commutative 49.7%

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

      3. unsub-neg 49.7%

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

      4. mul-1-neg 49.7%

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

      5. associate-/l* 51.6%

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

      6. distribute-neg-frac 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in c around -inf 75.8%

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

   if -2.20000000000000012e-89 < c < 6.3000000000000004e-18

   1. Initial program 74.4%

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

   2. Taylor expanded in c around 0 80.4%

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

      1. associate-/l* 80.7%

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

      2. associate-/r/ 78.9%

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

   4. Simplified 78.9%

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

      1. pow2 78.9%

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

      2. associate-*l/ 80.4%

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

      3. associate-/r* 88.1%

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

   6. Applied egg-rr 88.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{-89} \lor \neg \left(c \leq 6.3 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{-1}{c} \cdot \left(\left(-a\right) - \frac{b}{\frac{c}{d}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{d} + \frac{\frac{a \cdot c}{d}}{d}\\ \end{array} \]

Alternative 7: 63.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -3.1 \cdot 10^{+34} \lor \neg \left(d \leq 1850000000000 \lor \neg \left(d \leq 8 \cdot 10^{+39}\right) \land d \leq 1.05 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -3.1e+34)
         (not
          (or (<= d 1850000000000.0)
              (and (not (<= d 8e+39)) (<= d 1.05e+70)))))
   (/ b d)
   (/ a c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.1e+34) || !((d <= 1850000000000.0) || (!(d <= 8e+39) && (d <= 1.05e+70)))) {
		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 <= (-3.1d+34)) .or. (.not. (d <= 1850000000000.0d0) .or. (.not. (d <= 8d+39)) .and. (d <= 1.05d+70))) 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 <= -3.1e+34) || !((d <= 1850000000000.0) || (!(d <= 8e+39) && (d <= 1.05e+70)))) {
		tmp = b / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -3.1e+34) or not ((d <= 1850000000000.0) or (not (d <= 8e+39) and (d <= 1.05e+70))):
		tmp = b / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -3.1e+34) || !((d <= 1850000000000.0) || (!(d <= 8e+39) && (d <= 1.05e+70))))
		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 <= -3.1e+34) || ~(((d <= 1850000000000.0) || (~((d <= 8e+39)) && (d <= 1.05e+70)))))
		tmp = b / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -3.1e+34], N[Not[Or[LessEqual[d, 1850000000000.0], And[N[Not[LessEqual[d, 8e+39]], $MachinePrecision], LessEqual[d, 1.05e+70]]]], $MachinePrecision]], N[(b / d), $MachinePrecision], N[(a / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -3.09999999999999977e34 or 1.85e12 < d < 7.99999999999999952e39 or 1.05000000000000004e70 < d

   1. Initial program 51.8%

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

   2. Taylor expanded in c around 0 72.0%

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

   if -3.09999999999999977e34 < d < 1.85e12 or 7.99999999999999952e39 < d < 1.05000000000000004e70

   1. Initial program 69.0%

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

   2. Taylor expanded in c around inf 70.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -3.1 \cdot 10^{+34} \lor \neg \left(d \leq 1850000000000 \lor \neg \left(d \leq 8 \cdot 10^{+39}\right) \land d \leq 1.05 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{b}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \]

Alternative 8: 43.0% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.0%

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

2. Taylor expanded in c around inf 47.4%

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

3. Final simplification 47.4%

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

Developer target: 99.4% 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 2023332 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :herbie-target
  (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))))