Complex division, imag part

Percentage Accurate: 61.3% → 80.5%

Time: 8.1s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return ((b * c) - (a * 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 = ((b * c) - (a * d)) / ((c * c) + (d * d))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return ((b * c) - (a * 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 = ((b * c) - (a * d)) / ((c * c) + (d * d))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot \left(\frac{b}{d} + a \cdot \frac{c}{d \cdot d}\right) - a}{d}\\ \mathbf{if}\;d \leq -1.52 \cdot 10^{+85}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq -4.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{d \cdot d + c \cdot c}\\ \mathbf{elif}\;d \leq 7.7 \cdot 10^{+74}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* c (+ (/ b d) (* a (/ c (* d d))))) a) d)))
   (if (<= d -1.52e+85)
     t_0
     (if (<= d -4.6e-106)
       (/ (- (* c b) (* d a)) (+ (* d d) (* c c)))
       (if (<= d 7.7e+74) (/ (- b (* a (/ d c))) c) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * ((b / d) + (a * (c / (d * d))))) - a) / d;
	double tmp;
	if (d <= -1.52e+85) {
		tmp = t_0;
	} else if (d <= -4.6e-106) {
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c));
	} else if (d <= 7.7e+74) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((c * ((b / d) + (a * (c / (d * d))))) - a) / d
    if (d <= (-1.52d+85)) then
        tmp = t_0
    else if (d <= (-4.6d-106)) then
        tmp = ((c * b) - (d * a)) / ((d * d) + (c * c))
    else if (d <= 7.7d+74) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * ((b / d) + (a * (c / (d * d))))) - a) / d;
	double tmp;
	if (d <= -1.52e+85) {
		tmp = t_0;
	} else if (d <= -4.6e-106) {
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c));
	} else if (d <= 7.7e+74) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * ((b / d) + (a * (c / (d * d))))) - a) / d
	tmp = 0
	if d <= -1.52e+85:
		tmp = t_0
	elif d <= -4.6e-106:
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c))
	elif d <= 7.7e+74:
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * Float64(Float64(b / d) + Float64(a * Float64(c / Float64(d * d))))) - a) / d)
	tmp = 0.0
	if (d <= -1.52e+85)
		tmp = t_0;
	elseif (d <= -4.6e-106)
		tmp = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(d * d) + Float64(c * c)));
	elseif (d <= 7.7e+74)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * ((b / d) + (a * (c / (d * d))))) - a) / d;
	tmp = 0.0;
	if (d <= -1.52e+85)
		tmp = t_0;
	elseif (d <= -4.6e-106)
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c));
	elseif (d <= 7.7e+74)
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * N[(N[(b / d), $MachinePrecision] + N[(a * N[(c / N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -1.52e+85], t$95$0, If[LessEqual[d, -4.6e-106], N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(d * d), $MachinePrecision] + N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 7.7e+74], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d < -1.52e85 or 7.70000000000000042e74 < d

   1. Initial program 47.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. flip-+ N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{c \cdot c - d \cdot d}{\left(c \cdot c\right) \cdot \left(c \cdot c\right) - \left(d \cdot d\right) \cdot \left(d \cdot d\right)}\right), \color{blue}{\left(b \cdot c - a \cdot d\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{\left(c \cdot c\right) \cdot \left(c \cdot c\right) - \left(d \cdot d\right) \cdot \left(d \cdot d\right)}{c \cdot c - d \cdot d}}\right), \left(\color{blue}{b \cdot c} - a \cdot d\right)\right) \]

      7. flip-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{c \cdot c + d \cdot d}\right), \left(b \cdot \color{blue}{c} - a \cdot d\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(c \cdot c + d \cdot d\right)\right), \left(\color{blue}{b \cdot c} - a \cdot d\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(c \cdot c\right), \left(d \cdot d\right)\right)\right), \left(b \cdot \color{blue}{c} - a \cdot d\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \left(d \cdot d\right)\right)\right), \left(b \cdot c - a \cdot d\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \mathsf{*.f64}\left(d, d\right)\right)\right), \left(b \cdot c - a \cdot d\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \mathsf{*.f64}\left(d, d\right)\right)\right), \mathsf{\_.f64}\left(\left(b \cdot c\right), \color{blue}{\left(a \cdot d\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \mathsf{*.f64}\left(d, d\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{a} \cdot d\right)\right)\right) \]

      14. *-lowering-*.f64 47.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, c\right), \mathsf{*.f64}\left(d, d\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \color{blue}{d}\right)\right)\right) \]

   4. Applied egg-rr 47.8%

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

   5. Taylor expanded in d around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot a + \left(\frac{a \cdot {c}^{2}}{{d}^{2}} + \frac{b \cdot c}{d}\right)\right), \color{blue}{d}\right) \]

   7. Simplified 84.2%

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

   if -1.52e85 < d < -4.6000000000000002e-106

   1. Initial program 93.5%

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

   if -4.6000000000000002e-106 < d < 7.70000000000000042e74

   1. Initial program 67.6%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto a \cdot \left(\left(0 - \frac{d}{{c}^{2} + {d}^{2}}\right) + \frac{\color{blue}{b \cdot c}}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right) \]

      3. associate-+l- N/A

         \[\leadsto a \cdot \left(0 - \color{blue}{\left(\frac{d}{{c}^{2} + {d}^{2}} - \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)}\right) \]

      4. unsub-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + -1 \cdot \color{blue}{\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto a \cdot \left(0 - \left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \color{blue}{\frac{d}{{c}^{2} + {d}^{2}}}\right)\right) \]

      7. neg-sub0 N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)\right)\right)}\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(0 - \color{blue}{\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)}\right)\right) \]

   5. Simplified 55.0%

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

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{b + -1 \cdot \frac{a \cdot d}{c}}{c}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + -1 \cdot \frac{a \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \left(\mathsf{neg}\left(\frac{a \cdot d}{c}\right)\right)\right), c\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b - \frac{a \cdot d}{c}\right), c\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(\frac{a \cdot d}{c}\right)\right), c\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(a \cdot \frac{d}{c}\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 89.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), c\right) \]

   8. Simplified 89.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.52 \cdot 10^{+85}:\\ \;\;\;\;\frac{c \cdot \left(\frac{b}{d} + a \cdot \frac{c}{d \cdot d}\right) - a}{d}\\ \mathbf{elif}\;d \leq -4.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{d \cdot d + c \cdot c}\\ \mathbf{elif}\;d \leq 7.7 \cdot 10^{+74}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot \left(\frac{b}{d} + a \cdot \frac{c}{d \cdot d}\right) - a}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{c \cdot b}{d} - a}{d}\\ \mathbf{if}\;d \leq -1.25 \cdot 10^{+85}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq -4.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{d \cdot d + c \cdot c}\\ \mathbf{elif}\;d \leq 1.4 \cdot 10^{+82}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (/ (* c b) d) a) d)))
   (if (<= d -1.25e+85)
     t_0
     (if (<= d -4.5e-106)
       (/ (- (* c b) (* d a)) (+ (* d d) (* c c)))
       (if (<= d 1.4e+82) (/ (- b (* a (/ d c))) c) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (((c * b) / d) - a) / d;
	double tmp;
	if (d <= -1.25e+85) {
		tmp = t_0;
	} else if (d <= -4.5e-106) {
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c));
	} else if (d <= 1.4e+82) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (((c * b) / d) - a) / d
    if (d <= (-1.25d+85)) then
        tmp = t_0
    else if (d <= (-4.5d-106)) then
        tmp = ((c * b) - (d * a)) / ((d * d) + (c * c))
    else if (d <= 1.4d+82) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (((c * b) / d) - a) / d;
	double tmp;
	if (d <= -1.25e+85) {
		tmp = t_0;
	} else if (d <= -4.5e-106) {
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c));
	} else if (d <= 1.4e+82) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (((c * b) / d) - a) / d
	tmp = 0
	if d <= -1.25e+85:
		tmp = t_0
	elif d <= -4.5e-106:
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c))
	elif d <= 1.4e+82:
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(Float64(c * b) / d) - a) / d)
	tmp = 0.0
	if (d <= -1.25e+85)
		tmp = t_0;
	elseif (d <= -4.5e-106)
		tmp = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(d * d) + Float64(c * c)));
	elseif (d <= 1.4e+82)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (((c * b) / d) - a) / d;
	tmp = 0.0;
	if (d <= -1.25e+85)
		tmp = t_0;
	elseif (d <= -4.5e-106)
		tmp = ((c * b) - (d * a)) / ((d * d) + (c * c));
	elseif (d <= 1.4e+82)
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(N[(c * b), $MachinePrecision] / d), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -1.25e+85], t$95$0, If[LessEqual[d, -4.5e-106], N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(d * d), $MachinePrecision] + N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 1.4e+82], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d < -1.25e85 or 1.4e82 < d

   1. Initial program 48.3%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. unpow2 N/A

         \[\leadsto \frac{b \cdot c}{d \cdot d} - \frac{a}{d} \]

      5. associate-/r* N/A

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

      6. div-sub N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b \cdot c}{d} - a\right), \color{blue}{d}\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot c}{d}\right), a\right), d\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(b \cdot c\right), d\right), a\right), d\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(c \cdot b\right), d\right), a\right), d\right) \]

      11. *-lowering-*.f64 80.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(c, b\right), d\right), a\right), d\right) \]

   5. Simplified 80.9%

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

   if -1.25e85 < d < -4.49999999999999955e-106

   1. Initial program 93.5%

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

   if -4.49999999999999955e-106 < d < 1.4e82

   1. Initial program 67.0%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto a \cdot \left(\left(0 - \frac{d}{{c}^{2} + {d}^{2}}\right) + \frac{\color{blue}{b \cdot c}}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right) \]

      3. associate-+l- N/A

         \[\leadsto a \cdot \left(0 - \color{blue}{\left(\frac{d}{{c}^{2} + {d}^{2}} - \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)}\right) \]

      4. unsub-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + -1 \cdot \color{blue}{\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto a \cdot \left(0 - \left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \color{blue}{\frac{d}{{c}^{2} + {d}^{2}}}\right)\right) \]

      7. neg-sub0 N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)\right)\right)}\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(0 - \color{blue}{\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)}\right)\right) \]

   5. Simplified 54.5%

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

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{b + -1 \cdot \frac{a \cdot d}{c}}{c}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + -1 \cdot \frac{a \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \left(\mathsf{neg}\left(\frac{a \cdot d}{c}\right)\right)\right), c\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b - \frac{a \cdot d}{c}\right), c\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(\frac{a \cdot d}{c}\right)\right), c\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(a \cdot \frac{d}{c}\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 88.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), c\right) \]

   8. Simplified 88.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.25 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \mathbf{elif}\;d \leq -4.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{d \cdot d + c \cdot c}\\ \mathbf{elif}\;d \leq 1.4 \cdot 10^{+82}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{c \cdot b}{d} - a}{d}\\ \mathbf{if}\;d \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 1.45 \cdot 10^{+81}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (/ (* c b) d) a) d)))
   (if (<= d -1.45e-16)
     t_0
     (if (<= d 1.45e+81) (/ (- b (* a (/ d c))) c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (((c * b) / d) - a) / d;
	double tmp;
	if (d <= -1.45e-16) {
		tmp = t_0;
	} else if (d <= 1.45e+81) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (((c * b) / d) - a) / d
    if (d <= (-1.45d-16)) then
        tmp = t_0
    else if (d <= 1.45d+81) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (((c * b) / d) - a) / d;
	double tmp;
	if (d <= -1.45e-16) {
		tmp = t_0;
	} else if (d <= 1.45e+81) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (((c * b) / d) - a) / d
	tmp = 0
	if d <= -1.45e-16:
		tmp = t_0
	elif d <= 1.45e+81:
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(Float64(c * b) / d) - a) / d)
	tmp = 0.0
	if (d <= -1.45e-16)
		tmp = t_0;
	elseif (d <= 1.45e+81)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (((c * b) / d) - a) / d;
	tmp = 0.0;
	if (d <= -1.45e-16)
		tmp = t_0;
	elseif (d <= 1.45e+81)
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(N[(c * b), $MachinePrecision] / d), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]}, If[LessEqual[d, -1.45e-16], t$95$0, If[LessEqual[d, 1.45e+81], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -1.4499999999999999e-16 or 1.45e81 < d

   1. Initial program 57.3%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. unpow2 N/A

         \[\leadsto \frac{b \cdot c}{d \cdot d} - \frac{a}{d} \]

      5. associate-/r* N/A

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

      6. div-sub N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b \cdot c}{d} - a\right), \color{blue}{d}\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot c}{d}\right), a\right), d\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(b \cdot c\right), d\right), a\right), d\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(c \cdot b\right), d\right), a\right), d\right) \]

      11. *-lowering-*.f64 77.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(c, b\right), d\right), a\right), d\right) \]

   5. Simplified 77.5%

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

   if -1.4499999999999999e-16 < d < 1.45e81

   1. Initial program 72.0%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto a \cdot \left(\left(0 - \frac{d}{{c}^{2} + {d}^{2}}\right) + \frac{\color{blue}{b \cdot c}}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right) \]

      3. associate-+l- N/A

         \[\leadsto a \cdot \left(0 - \color{blue}{\left(\frac{d}{{c}^{2} + {d}^{2}} - \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)}\right) \]

      4. unsub-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + -1 \cdot \color{blue}{\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto a \cdot \left(0 - \left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \color{blue}{\frac{d}{{c}^{2} + {d}^{2}}}\right)\right) \]

      7. neg-sub0 N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)\right)\right)}\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(0 - \color{blue}{\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)}\right)\right) \]

   5. Simplified 59.2%

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

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{b + -1 \cdot \frac{a \cdot d}{c}}{c}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + -1 \cdot \frac{a \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \left(\mathsf{neg}\left(\frac{a \cdot d}{c}\right)\right)\right), c\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b - \frac{a \cdot d}{c}\right), c\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(\frac{a \cdot d}{c}\right)\right), c\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(a \cdot \frac{d}{c}\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 84.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), c\right) \]

   8. Simplified 84.5%

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

Alternative 4: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a}{0 - d}\\ \mathbf{if}\;d \leq -27500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 7.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ a (- 0.0 d))))
   (if (<= d -27500000.0)
     t_0
     (if (<= d 7.5e+128) (/ (- b (* a (/ d c))) c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = a / (0.0 - d);
	double tmp;
	if (d <= -27500000.0) {
		tmp = t_0;
	} else if (d <= 7.5e+128) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (0.0d0 - d)
    if (d <= (-27500000.0d0)) then
        tmp = t_0
    else if (d <= 7.5d+128) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = a / (0.0 - d);
	double tmp;
	if (d <= -27500000.0) {
		tmp = t_0;
	} else if (d <= 7.5e+128) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = a / (0.0 - d)
	tmp = 0
	if d <= -27500000.0:
		tmp = t_0
	elif d <= 7.5e+128:
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(a / Float64(0.0 - d))
	tmp = 0.0
	if (d <= -27500000.0)
		tmp = t_0;
	elseif (d <= 7.5e+128)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = a / (0.0 - d);
	tmp = 0.0;
	if (d <= -27500000.0)
		tmp = t_0;
	elseif (d <= 7.5e+128)
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(a / N[(0.0 - d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -27500000.0], t$95$0, If[LessEqual[d, 7.5e+128], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -2.75e7 or 7.50000000000000076e128 < d

   1. Initial program 54.0%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{a}{d}\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{a}{d}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a}{d}\right)}\right) \]

      4. /-lowering-/.f64 72.0%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(a, \color{blue}{d}\right)\right) \]

   5. Simplified 72.0%

      \[\leadsto \color{blue}{0 - \frac{a}{d}} \]

   if -2.75e7 < d < 7.50000000000000076e128

   1. Initial program 72.7%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto a \cdot \left(\left(0 - \frac{d}{{c}^{2} + {d}^{2}}\right) + \frac{\color{blue}{b \cdot c}}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right) \]

      3. associate-+l- N/A

         \[\leadsto a \cdot \left(0 - \color{blue}{\left(\frac{d}{{c}^{2} + {d}^{2}} - \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)}\right) \]

      4. unsub-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + -1 \cdot \color{blue}{\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto a \cdot \left(0 - \left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \color{blue}{\frac{d}{{c}^{2} + {d}^{2}}}\right)\right) \]

      7. neg-sub0 N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)\right)\right)}\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(0 - \color{blue}{\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)}\right)\right) \]

   5. Simplified 61.5%

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

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{\frac{b + -1 \cdot \frac{a \cdot d}{c}}{c}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + -1 \cdot \frac{a \cdot d}{c}\right), \color{blue}{c}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b + \left(\mathsf{neg}\left(\frac{a \cdot d}{c}\right)\right)\right), c\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b - \frac{a \cdot d}{c}\right), c\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(\frac{a \cdot d}{c}\right)\right), c\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \left(a \cdot \frac{d}{c}\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \left(\frac{d}{c}\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(d, c\right)\right)\right), c\right) \]

   8. Simplified 80.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -27500000:\\ \;\;\;\;\frac{a}{0 - d}\\ \mathbf{elif}\;d \leq 7.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{0 - d}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a}{0 - d}\\ \mathbf{if}\;d \leq -1.12 \cdot 10^{-36}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ a (- 0.0 d))))
   (if (<= d -1.12e-36) t_0 (if (<= d 8.2e-8) (/ b c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = a / (0.0 - d);
	double tmp;
	if (d <= -1.12e-36) {
		tmp = t_0;
	} else if (d <= 8.2e-8) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (0.0d0 - d)
    if (d <= (-1.12d-36)) then
        tmp = t_0
    else if (d <= 8.2d-8) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = a / (0.0 - d);
	double tmp;
	if (d <= -1.12e-36) {
		tmp = t_0;
	} else if (d <= 8.2e-8) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = a / (0.0 - d)
	tmp = 0
	if d <= -1.12e-36:
		tmp = t_0
	elif d <= 8.2e-8:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(a / Float64(0.0 - d))
	tmp = 0.0
	if (d <= -1.12e-36)
		tmp = t_0;
	elseif (d <= 8.2e-8)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = a / (0.0 - d);
	tmp = 0.0;
	if (d <= -1.12e-36)
		tmp = t_0;
	elseif (d <= 8.2e-8)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(a / N[(0.0 - d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.12e-36], t$95$0, If[LessEqual[d, 8.2e-8], N[(b / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -1.12e-36 or 8.20000000000000063e-8 < d

   1. Initial program 57.9%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{d}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{a}{d}\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{a}{d}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a}{d}\right)}\right) \]

      4. /-lowering-/.f64 63.8%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(a, \color{blue}{d}\right)\right) \]

   5. Simplified 63.8%

      \[\leadsto \color{blue}{0 - \frac{a}{d}} \]

   if -1.12e-36 < d < 8.20000000000000063e-8

   1. Initial program 73.6%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 68.6%

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{c}\right) \]

   5. Simplified 68.6%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.12 \cdot 10^{-36}:\\ \;\;\;\;\frac{a}{0 - d}\\ \mathbf{elif}\;d \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{0 - d}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := a \cdot \frac{-1}{d}\\ \mathbf{if}\;d \leq -5.2 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d \leq 8 \cdot 10^{-8}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (* a (/ -1.0 d))))
   (if (<= d -5.2e-38) t_0 (if (<= d 8e-8) (/ b c) t_0))))

C

double code(double a, double b, double c, double d) {
	double t_0 = a * (-1.0 / d);
	double tmp;
	if (d <= -5.2e-38) {
		tmp = t_0;
	} else if (d <= 8e-8) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a * ((-1.0d0) / d)
    if (d <= (-5.2d-38)) then
        tmp = t_0
    else if (d <= 8d-8) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = a * (-1.0 / d);
	double tmp;
	if (d <= -5.2e-38) {
		tmp = t_0;
	} else if (d <= 8e-8) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = a * (-1.0 / d)
	tmp = 0
	if d <= -5.2e-38:
		tmp = t_0
	elif d <= 8e-8:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(a * Float64(-1.0 / d))
	tmp = 0.0
	if (d <= -5.2e-38)
		tmp = t_0;
	elseif (d <= 8e-8)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = a * (-1.0 / d);
	tmp = 0.0;
	if (d <= -5.2e-38)
		tmp = t_0;
	elseif (d <= 8e-8)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(a * N[(-1.0 / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -5.2e-38], t$95$0, If[LessEqual[d, 8e-8], N[(b / c), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if d < -5.20000000000000022e-38 or 8.0000000000000002e-8 < d

   1. Initial program 57.9%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto a \cdot \left(\left(0 - \frac{d}{{c}^{2} + {d}^{2}}\right) + \frac{\color{blue}{b \cdot c}}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right) \]

      3. associate-+l- N/A

         \[\leadsto a \cdot \left(0 - \color{blue}{\left(\frac{d}{{c}^{2} + {d}^{2}} - \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)}\right) \]

      4. unsub-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(0 - \left(\frac{d}{{c}^{2} + {d}^{2}} + -1 \cdot \color{blue}{\frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)}}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto a \cdot \left(0 - \left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \color{blue}{\frac{d}{{c}^{2} + {d}^{2}}}\right)\right) \]

      7. neg-sub0 N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)\right)\right)}\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(0 - \color{blue}{\left(-1 \cdot \frac{b \cdot c}{a \cdot \left({c}^{2} + {d}^{2}\right)} + \frac{d}{{c}^{2} + {d}^{2}}\right)}\right)\right) \]

   5. Simplified 53.8%

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

   6. Taylor expanded in c around 0

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{d}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 63.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(-1, \color{blue}{d}\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto a \cdot \color{blue}{\frac{-1}{d}} \]

   if -5.20000000000000022e-38 < d < 8.0000000000000002e-8

   1. Initial program 73.6%

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

   3. Taylor expanded in c around inf

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

      1. /-lowering-/.f64 68.6%

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{c}\right) \]

   5. Simplified 68.6%

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

Alternative 7: 42.6% accurate, 5.0× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c, double d) {
	return b / 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 = b / c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.7%

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

3. Taylor expanded in c around inf

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

   1. /-lowering-/.f64 39.4%

      \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{c}\right) \]

5. Simplified 39.4%

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

Developer Target 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left|d\right| < \left|c\right|:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-a\right) + b \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (< (fabs d) (fabs c))
   (/ (- b (* a (/ d c))) (+ c (* d (/ d c))))
   (/ (+ (- a) (* b (/ 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 = (b - (a * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (-a + (b * (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 = (b - (a * (d / c))) / (c + (d * (d / c)))
    else
        tmp = (-a + (b * (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 = (b - (a * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (-a + (b * (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 = (b - (a * (d / c))) / (c + (d * (d / c)))
	else:
		tmp = (-a + (b * (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(b - Float64(a * Float64(d / c))) / Float64(c + Float64(d * Float64(d / c))));
	else
		tmp = Float64(Float64(Float64(-a) + Float64(b * 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 = (b - (a * (d / c))) / (c + (d * (d / c)));
	else
		tmp = (-a + (b * (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[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c + N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-a) + N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(d + N[(c * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024158 
(FPCore (a b c d)
  :name "Complex division, imag part"
  :precision binary64

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

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